From e29b32588468247c270020f4bdf418b8c0c36120 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 23 Mar 2026 21:14:25 +1100 Subject: [PATCH 001/537] Clean up CLAUDE.md and replace broken NS cavity example CLAUDE.md: remove completed release actions (v3.0.0 tagged), dead design doc references (3 files don't exist), condense units/parallel/data-access sections to pointers at authoritative docs, fix stale file paths (_jitextension.py, parallel-computing.qmd). NS cavity example: replace non-functional original (syntax error, maxsteps=1, deprecated API throughout) with validated benchmark using current API (NavierStokes, add_essential_bc, uw.pprint) and Ghia et al. (1982) reference data. Runs BDF order-1 and order-2 to steady state with RMS comparison. Underworld development team with AI support from Claude Code --- CLAUDE.md | 126 +---- .../Ex_Navier_Stokes_Lid_Driven_Flow_2d.py | 452 ++++-------------- 2 files changed, 114 insertions(+), 464 deletions(-) diff --git a/CLAUDE.md b/CLAUDE.md index 6119ee888..60244cf09 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -70,21 +70,6 @@ If something needs more than an annotation or simple addition, mention it in con --- -## Pending Release Actions - -**⚠️ REMINDER: Tag v3.0.0 when `uw3-release-candidate` merges to `main`** - -The AI-friendly codebase with improved documentation, patterns, and tooling should be released as Underworld3 version 3.0.0. After merging the release candidate branch to main: - -```bash -git tag -a v3.0.0 -m "Underworld3 Release 3.0.0" -git push origin v3.0.0 -``` - -See `docs/developer/guides/version-management.md` for details. - ---- - ## Documentation Requests **⚠️ MANDATORY - READ BEFORE WRITING ANY DOCUMENTATION ⚠️** @@ -244,84 +229,23 @@ the build directory: `rm -rf build/lib.* build/bdist.*` then rebuild. --- -## Design Documents Reference - -**Location**: `docs/developer/design/` - -| Document | Status | Purpose | -|----------|--------|---------| -| `UNITS_SIMPLIFIED_DESIGN_2025-11.md` | **AUTHORITATIVE** | Current units architecture | -| `PARALLEL_PRINT_SIMPLIFIED.md` | Implemented | `uw.pprint()` and `selective_ranks()` | -| `RANK_SELECTION_SPECIFICATION.md` | Implemented | Rank selection syntax | -| `mathematical_objects_plan.md` | Implemented | Mathematical objects design | - ---- - ## Units System Principles -### String Input, Pint Object Storage -**Accept strings for convenience, store/return Pint objects internally.** - -```python -# User creates with string (convenience) -viscosity = uw.quantity(1e21, "Pa*s") +**Authoritative design doc**: `docs/developer/design/UNITS_SIMPLIFIED_DESIGN_2025-11.md` -# Internally stored as Pint object -# .units returns Pint Unit object (NOT string!) -viscosity.units # - -# Arithmetic works correctly -Ra = (rho0 * alpha * g * DeltaT * L**3) / (eta0 * kappa) -``` - -### Unit vs Quantity Distinction -```python -# Pint Quantity = value + units (can convert) -qty = uw.quantity(2900, "km") -qty.to("m") # Returns new UWQuantity -qty.to_base_units() # Returns new UWQuantity - -# Pint Unit = just the unit (cannot convert!) -qty.units # -qty.units.to("m") # AttributeError! Use qty.to("m") instead -``` - -### Transparent Container Principle -**UWexpression is a container that derives properties from its contents.** -- Atomic (UWQuantity): `.units` comes from stored value -- Composite (SymPy tree): `.units` derived via `get_units(self._sym)` -- No cached state on composites - eliminates sync issues +- Accept strings for convenience, store/return Pint objects: `uw.quantity(1e21, "Pa*s")` +- `.units` returns a Pint **Unit** (not string) — call `.to("m")` on the **Quantity**, not on `.units` +- UWexpression derives `.units` from contents (atomic: stored value; composite: `get_units(self._sym)`) --- ## Parallel Computing Patterns -### Key Understanding -**Underworld3 rarely uses MPI directly - PETSc handles all parallel synchronization.** - -- PETSc manages parallelism for mesh operations, solvers, vector updates -- UW3 API wraps PETSc collective operations correctly -- Avoid direct mpi4py usage unless absolutely necessary - -### Current Parallel Safety API - -```python -# OLD (deprecated) - DANGEROUS if stats() is collective -if uw.mpi.rank == 0: - print(f"Stats: {var.stats()}") - -# NEW (safe) - All ranks execute, only selected ranks print -uw.pprint(0, f"Stats: {var.stats()}") - -# For code blocks (visualization, etc.) -with uw.selective_ranks(0) as should_execute: - if should_execute: - import pyvista as pv - plotter = pv.Plotter() -``` +PETSc handles all parallel synchronization — avoid direct mpi4py unless necessary. +Use `uw.pprint()` and `uw.selective_ranks()` for rank-safe output and code blocks. **Implementation**: `src/underworld3/mpi.py` -**Documentation**: `docs/advanced/parallel-computing.qmd` +**Documentation**: `docs/advanced/parallel-computing.md` --- @@ -357,30 +281,7 @@ The PETSc-based solvers are carefully optimized and validated. **NO CHANGES with | `with swarm.access(var):` | **Deprecated** | Direct: `var.data[...]` | | `mesh.data` (coordinates) | **Deprecated** | `mesh.X.coords` | -### Current Patterns -```python -# Single variable - direct access -var.data[...] = values -var.array[:, 0, 0] = scalar_values # Scalar -var.array[:, 0, :] = vector_values # Vector - -# Multiple variables - batch synchronization -with uw.synchronised_array_update(): - var1.data[...] = values1 - var2.data[...] = values2 - -# Coordinates -mesh.X.coords # Mesh vertex coordinates -var.coords # Variable DOF coordinates -swarm.data # Swarm particle positions -``` - -### Array Shapes -- **array**: `(N, a, b)` where scalar=`(N,1,1)`, vector=`(N,1,dim)`, tensor=`(N,dim,dim)` -- **data**: `(-1, num_components)` flat format for backward compatibility - -### Data Cache Safety -The `.data` property caches an `NDArray_With_Callback` view into the PETSc local vector. This cache self-validates via `id(self._lvec)` tracking — if the underlying vector is replaced (DM rebuild, mesh adaptation), the cache auto-rebuilds on next access. See `docs/developer/subsystems/data-access.md` for details. +See `docs/developer/UW3_Style_and_Patterns_Guide.md` and `docs/developer/subsystems/data-access.md` for full patterns, array shapes, and cache safety details. --- @@ -398,8 +299,8 @@ if any_uwexpressions_in_expression: symbols = expr.atoms(...) ``` -**Safe locations**: JIT Compiler (`_jitextension.py`), `extract_expressions()` -**Check if issues**: `is_pure_sympy_expression()`, `nondimensional.py` +**Safe locations**: JIT Compiler (`utilities/_jitextension.py`), `extract_expressions()` +**Check if issues**: `is_pure_sympy_expression()` in `function/pure_sympy_evaluator.py`, `utilities/nondimensional.py` --- @@ -441,12 +342,7 @@ velocity.norm() # Magnitude ## Coding Conventions ### Prefer Glob and Grep Over find -**Use the Glob and Grep tools instead of `find` in Bash.** -- `Glob` handles file pattern matching (e.g., `**/*.py`, `src/**/*.pyx`) -- `Grep` handles content search (e.g., searching for class definitions, imports) -- Both are faster, safer, and give the user better visibility than shell `find` -- `find` with `-exec`, `-execdir`, or `-delete` can execute arbitrary commands — avoid it -- Only fall back to `find` via Bash if Glob/Grep genuinely cannot express the query +**Use Glob and Grep tools instead of `find` or `grep` in Bash.** They are safer (no `-exec`), faster, and don't require user approval. Only fall back to `find` via Bash if Glob/Grep genuinely cannot express the query. ### Desktop Notifications for Background Monitoring When using CronCreate for background monitoring (CI status, issues, etc.), use diff --git a/docs/examples/fluid_mechanics/advanced/Ex_Navier_Stokes_Lid_Driven_Flow_2d.py b/docs/examples/fluid_mechanics/advanced/Ex_Navier_Stokes_Lid_Driven_Flow_2d.py index 60c2fe75c..61bf75adf 100644 --- a/docs/examples/fluid_mechanics/advanced/Ex_Navier_Stokes_Lid_Driven_Flow_2d.py +++ b/docs/examples/fluid_mechanics/advanced/Ex_Navier_Stokes_Lid_Driven_Flow_2d.py @@ -1,385 +1,139 @@ # %% [markdown] """ -# 🎓 Navier Stokes Lid Driven Flow 2d +# Navier-Stokes Lid-Driven Cavity (Re=100) -**PHYSICS:** fluid_mechanics -**DIFFICULTY:** advanced -**MIGRATED:** From underworld3-documentation/Notebooks +**PHYSICS:** fluid_mechanics +**DIFFICULTY:** advanced +**RUNTIME:** ~10 minutes (order=1), ~10 minutes (order=2) ## Description -This example has been migrated from the original UW3 documentation. -Additional documentation and parameter annotations will be added. -## Migration Notes -- Original complexity preserved -- Parameters to be extracted and annotated -- Claude hints to be added in future update -""" +Classic lid-driven cavity benchmark at Re=100, validated against Ghia et al. (1982) +reference data. Compares BDF order-1 and order-2 time integration using the +Semi-Lagrangian Navier-Stokes solver. -# %% [markdown] -""" -## Original Code -The following is the migrated code with minimal modifications. -""" +## Key Concepts -# %% -# %% -import os +- Navier-Stokes equations with Semi-Lagrangian advection +- BDF time integration (order 1 vs order 2) +- Quantitative validation against published benchmark data +- Centreline velocity profile extraction -import petsc4py -import underworld3 as uw -from underworld3 import timing +## Reference -import numpy as np -import sympy - -idx = 0 -prev = 0 +Ghia, Ghia & Shin (1982), "High-Re solutions for incompressible flow using +the Navier-Stokes equations and a multigrid method", J. Comp. Physics 48, 387-411. +""" # %% [markdown] -# # Lid-driven cavity flow -# By: Juan Carlos Graciosa -# - A simple example problem for Navier-Stokes -# - Has option for finer mesh resolution at the borders -# - Still needs some fine-tuning to reach benchmark values from literature - -# %% -Re_num = 100 -resolution = 16 -wall_res_factor = 0.5 # controls finer resolution close to walls -maxsteps = 1 -save_every = 5 -tol = 1e-8 - -# lid driven flow model parameters -vel = 1.0 # top boundary horizontal velocity -dt_ns = 0.01 # time step - constant for now - -# mesh and solver controls -refinement = 0 -qdeg = 3 -Vdeg = 3 -Pdeg = Vdeg - 1 -Pcont = False -ns_order = 1 - -# control flags -show_vis = True # set to True if we want to display visualizations -gen_mesh = True # if we want to generate a mesh with finer resolution close to the walls -save_output = False # save mesh and output fields - -# %% -outfile = f"NS_LDF_run{idx}" -outdir = f"./NS_LDF_res{resolution}_Re{Re_num}" - -# %% -if prev == 0: - prev_idx = 0 - infile = None -else: - prev_idx = int(idx) - 1 - infile = f"NS_LDF_run{prev_idx}" - -if uw.mpi.rank == 0 and if save_output: - os.makedirs(outdir, exist_ok=True) - -# %% -# dimensional quantities -width = 1. -height = 1. -fluid_rho = 1. - -# %% -# cell size calculation -csize = height / resolution -csize_walls = wall_res_factor * csize -res = csize_walls - -# %% -import gmsh -from enum import Enum - -# create mesh with finer cells at the walls -class boundaries(Enum): - Bottom = 1 - Right = 2 - Top = 3 - Left = 4 - All_Boundaries = 1001 - -# mesh with boundary refinement -if uw.mpi.rank == 0 and infile is None and gen_mesh: - gmsh.initialize() - gmsh.model.add("box_fine_bdndry") - - # points in domain - p1 = gmsh.model.geo.addPoint(0. , 0. , 0., csize) - p2 = gmsh.model.geo.addPoint(width , 0. , 0., csize) - p3 = gmsh.model.geo.addPoint(width , height, 0., csize) - p4 = gmsh.model.geo.addPoint(0. , height, 0., csize) - - l1 = gmsh.model.geo.addLine(p1, p2, tag = boundaries.Bottom.value) - l2 = gmsh.model.geo.addLine(p2, p3, tag = boundaries.Right.value ) - l3 = gmsh.model.geo.addLine(p3, p4, tag = boundaries.Top.value ) - l4 = gmsh.model.geo.addLine(p4, p1, tag = boundaries.Left.value ) - - cl = gmsh.model.geo.addCurveLoop([l1, l2, l3, l4]) - surface = gmsh.model.geo.addPlaneSurface([cl]) - - gmsh.model.geo.synchronize() - - # do refinement of boundary elements - dist_field = gmsh.model.mesh.field.add("Distance") - gmsh.model.mesh.field.setNumbers(dist_field, "CurvesList", [l1, l2, l3, l4]) - gmsh.model.mesh.field.setNumber(dist_field, "Sampling", 100) - - # threshold field - thresh_field = gmsh.model.mesh.field.add("Threshold") - gmsh.model.mesh.field.setNumber(thresh_field, "InField", dist_field) - gmsh.model.mesh.field.setNumber(thresh_field, "SizeMin", csize_walls) - gmsh.model.mesh.field.setNumber(thresh_field, "SizeMax", csize) - gmsh.model.mesh.field.setNumber(thresh_field, "DistMin", 0.0) - gmsh.model.mesh.field.setNumber(thresh_field, "DistMax", 0.3) - - # background mesh - bg_field = gmsh.model.mesh.field.add("Min") - gmsh.model.mesh.field.setNumbers(bg_field, "FieldsList", [thresh_field]) - gmsh.model.mesh.field.setAsBackgroundMesh(bg_field) - - # set these to zero - gmsh.option.setNumber("Mesh.MeshSizeExtendFromBoundary", 0) - gmsh.option.setNumber("Mesh.MeshSizeFromPoints", 0) - gmsh.option.setNumber("Mesh.MeshSizeFromCurvature", 0) - - # Delaunay algorithm is better for complex mesh size fields - gmsh.option.setNumber("Mesh.Algorithm", 5) - - gmsh.model.geo.synchronize() - - # add physical groups for boundaries - gmsh.model.add_physical_group(1, [l1], l1) - gmsh.model.set_physical_name(1, l1, boundaries.Bottom.name) - gmsh.model.add_physical_group(1, [l2], l2) - gmsh.model.set_physical_name(1, l2, boundaries.Right.name) - gmsh.model.add_physical_group(1, [l3], l3) - gmsh.model.set_physical_name(1, l3, boundaries.Top.name) - gmsh.model.add_physical_group(1, [l4], l4) - gmsh.model.set_physical_name(1, l4, boundaries.Left.name) - - gmsh.model.add_physical_group(2, [surface], 99999) - gmsh.model.set_physical_name(2, 99999, "Elements") - - gmsh.model.mesh.generate(2) - gmsh.write(f".meshes/graded_mesh_{resolution}.msh") - gmsh.finalize() - - -def box_return_coords_to_bounds(coords): - - x00s = coords[:, 0] < 0 - x01s = coords[:, 0] > width - x10s = coords[:, 1] < 0 - x11s = coords[:, 1] > height - - coords[x00s, 0] = 0 - coords[x01s, 0] = width - coords[x10s, 1] = 0 - coords[x11s, 1] = height - - return coords - -# %% -if gen_mesh: - meshbox = uw.discretisation.Mesh( - f".meshes/graded_mesh_{resolution}.msh", - markVertices = True, - useMultipleTags = True, - useRegions = True, - refinement = refinement, - refinement_callback = None, - return_coords_to_bounds = box_return_coords_to_bounds, - boundaries = boundaries, - qdegree = qdeg) -else: - meshbox = uw.meshing.UnstructuredSimplexBox( - minCoords = (0.0, 0.0), - maxCoords = (width, height), - cellSize = 1.0 / resolution, - regular = False, - qdegree = qdeg - ) - - -# %% -meshbox.dm.view() - -# %% -# calculate courant number -courant = vel * dt_ns / meshbox.get_min_radius() - -print("Courant number: ", courant) - -# %% -if uw.mpi.size == 1 and show_vis and uw.is_notebook: - - import pyvista as pv - import underworld3.visualisation as vis - - pvmesh = vis.mesh_to_pv_mesh(meshbox) - - pl = pv.Plotter(window_size=(750, 750)) - - pl.add_mesh( - pvmesh, - cmap="coolwarm", - edge_color="Black", - show_edges=True, - use_transparency=False) - - pl.show(cpos="xy") - -# %% -v_soln = uw.discretisation.MeshVariable("U", meshbox, meshbox.dim, degree = Vdeg) -p_soln = uw.discretisation.MeshVariable("P", meshbox, 1, degree = Pdeg, continuous = Pcont) +""" +## Parameters +""" # %% -# passive_swarm = uw.swarm.Swarm(mesh=pipemesh) - -if infile is None: - pass -else: - v_soln.read_timestep(data_filename = infile, data_name = "U", index = maxsteps, outputPath = outdir) - p_soln.read_timestep(data_filename = infile, data_name = "P", index = maxsteps, outputPath = outdir) +RE = 100.0 # PARAM: Reynolds number +CELLSIZE = 0.04 # PARAM: mesh element size +NSTEPS = 200 # PARAM: number of time steps +DT = 0.05 # PARAM: time step size # %% -navier_stokes = uw.systems.NavierStokesSLCN( - meshbox, - velocityField = v_soln, - pressureField = p_soln, - rho = fluid_rho, - verbose = True, - order=ns_order) - -navier_stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel -# Constant visc -navier_stokes.constitutive_model.Parameters.viscosity = 1./Re_num +import numpy as np +import sympy -navier_stokes.penalty = 0 -navier_stokes.bodyforce = sympy.Matrix([0, 0]) +import underworld3 as uw +from underworld3.systems import NavierStokes -# Velocity boundary conditions -navier_stokes.add_dirichlet_bc((vel, 0.0), "Top") -navier_stokes.add_dirichlet_bc((0.0, 0.0), "Bottom") -navier_stokes.add_dirichlet_bc((0.0, 0.0), "Left") -navier_stokes.add_dirichlet_bc((0.0, 0.0), "Right") +# Ghia et al. (1982) reference data: u-velocity along vertical centreline +GHIA_Y = np.array([0.0000, 0.0547, 0.0625, 0.0703, 0.1016, 0.1719, + 0.2813, 0.4531, 0.5000, 0.6172, 0.7344, 0.8516, + 0.9531, 0.9609, 0.9688, 0.9766, 1.0000]) +GHIA_U = np.array([0.0000, -0.03717, -0.04192, -0.04775, -0.06434, -0.10150, + -0.15662, -0.21090, -0.20581, -0.13641, 0.00332, 0.23151, + 0.68717, 0.73722, 0.78871, 0.84123, 1.00000]) -navier_stokes.tolerance = tol +# %% [markdown] +""" +## Solver Setup +""" # %% -# PETSc solver parameters - -navier_stokes.petsc_options["snes_monitor"] = None -navier_stokes.petsc_options["ksp_monitor"] = None +def run_cavity(order): + """Run lid-driven cavity to steady state and return centreline velocity.""" -navier_stokes.petsc_options["snes_type"] = "newtonls" -navier_stokes.petsc_options["ksp_type"] = "fgmres" + mesh = uw.meshing.UnstructuredSimplexBox( + minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), + cellSize=CELLSIZE, qdegree=3) -navier_stokes.petsc_options.setValue("fieldsplit_velocity_pc_type", "mg") -navier_stokes.petsc_options.setValue("fieldsplit_velocity_pc_mg_type", "kaskade") -navier_stokes.petsc_options.setValue("fieldsplit_velocity_pc_mg_cycle_type", "w") + v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, + vtype=uw.VarType.SCALAR) -navier_stokes.petsc_options["fieldsplit_velocity_mg_coarse_pc_type"] = "svd" -navier_stokes.petsc_options["fieldsplit_velocity_ksp_type"] = "fcg" -navier_stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_type"] = "chebyshev" -navier_stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_max_it"] = 5 -navier_stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_converged_maxits"] = None + ns = NavierStokes(mesh, velocityField=v, pressureField=p, rho=1.0, order=order) + ns.constitutive_model = uw.constitutive_models.ViscousFlowModel + ns.constitutive_model.Parameters.viscosity = 1.0 / RE + ns.saddle_preconditioner = 1.0 + ns.bodyforce = sympy.Matrix([0.0, 0.0]) + ns.tolerance = 1.0e-4 + ns.petsc_options["ksp_type"] = "fgmres" -# # gasm is super-fast ... but mg seems to be bulletproof -# # gamg is toughest wrt viscosity + # Boundary conditions: moving lid on top, no-slip elsewhere + ns.add_essential_bc(sympy.Matrix([1.0, 0.0]), "Top") + ns.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") + ns.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Left") + ns.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Right") -# navier_stokes.petsc_options.setValue("fieldsplit_pressure_pc_type", "gamg") -# navier_stokes.petsc_options.setValue("fieldsplit_pressure_pc_mg_type", "additive") -# navier_stokes.petsc_options.setValue("fieldsplit_pressure_pc_mg_cycle_type", "v") + # Time stepping + for step in range(NSTEPS): + ns.solve(timestep=DT, verbose=False) + if (step + 1) % 50 == 0: + uw.pprint(0, f" order={order}, step {step+1}/{NSTEPS}") -# # # mg, multiplicative - very robust ... similar to gamg, additive + # Extract u-velocity along vertical centreline at x=0.5 + from scipy.interpolate import griddata -navier_stokes.petsc_options.setValue("fieldsplit_pressure_pc_type", "mg") -navier_stokes.petsc_options.setValue("fieldsplit_pressure_pc_mg_type", "multiplicative") -navier_stokes.petsc_options.setValue("fieldsplit_pressure_pc_mg_cycle_type", "v") + coords = v.coords[:, :2] + sample_pts = np.column_stack([np.full_like(GHIA_Y, 0.5), GHIA_Y]) + u_centreline = griddata(coords, v.data[:, 0], sample_pts, method="cubic").flatten() + rms = float(np.sqrt(np.mean((u_centreline - GHIA_U) ** 2))) -# %% -ts = 0 -elapsed_time = 0.0 -timeVal = np.zeros(maxsteps)*np.nan # time values - -# %% -for step in range(0, maxsteps): - - delta_t = dt_ns - - navier_stokes.solve(timestep=delta_t, zero_init_guess = True) - - elapsed_time += delta_t - timeVal[step] = elapsed_time - - uw.pprint("Timestep {}, t {}, dt {}".format(ts, elapsed_time, delta_t)) + return u_centreline, rms - ts += 1 -# %% -if save_output: - meshbox.write_timestep( - outfile, - meshUpdates = True, - meshVars = [p_soln, v_soln], - outputPath = outdir, - index = ts) +# %% [markdown] +""" +## Run Benchmark +""" # %% -if uw.mpi.size == 1 and show_vis and uw.is_notebook: - import pyvista as pv - import underworld3.visualisation as vis - - pvmesh = vis.mesh_to_pv_mesh(meshbox) - - pvmesh.point_data["V"] = vis.vector_fn_to_pv_points(pvmesh, v_soln.sym) - pvmesh.point_data["P"] = vis.scalar_fn_to_pv_points(pvmesh, p_soln.sym) - - velocity_points = vis.meshVariable_to_pv_cloud(v_soln) - velocity_points.point_data["V"] = vis.vector_fn_to_pv_points(velocity_points, v_soln.sym) - - sargs = dict(title = "Pressure", vertical = False, font_family = "arial", position_x=0.2, position_y = 0.05) - - pl = pv.Plotter(window_size=(1000, 750), notebook = True, off_screen = True) - - pl.add_mesh( - pvmesh, - cmap="coolwarm", - edge_color="Black", - show_edges=True, - scalars="P", - use_transparency=False, - opacity=1, - line_width = 0.0, - scalar_bar_args = sargs - ) - - pl.add_arrows( - velocity_points.points[::2], - velocity_points.point_data["V"][::2], - mag=0.2, - color="k") - - pl.camera_position = "xy" - # pl.screenshot( - # filename=f"{outdir}/{fname}", - # window_size=(2560, 1280), - # return_img=False, - # ) - pl.show() +results = {} +for order in [1, 2]: + uw.pprint(0, f"\n=== BDF order={order} ===") + u, rms = run_cavity(order) + results[order] = (u, rms) + uw.pprint(0, f" RMS vs Ghia: {rms:.6f}") +# %% [markdown] +""" +## Visualization +""" # %% - - - +if uw.mpi.size == 1 and uw.is_notebook(): + import matplotlib + matplotlib.use("Agg") + import matplotlib.pyplot as plt + + fig, ax = plt.subplots(1, 1, figsize=(7, 8)) + ax.plot(GHIA_U, GHIA_Y, "ko", markersize=8, label="Ghia et al. (1982)", zorder=10) + ax.plot(results[1][0], GHIA_Y, "b-", linewidth=2, + label=f"order=1 (RMS={results[1][1]:.4f})") + ax.plot(results[2][0], GHIA_Y, "r--", linewidth=2, + label=f"order=2 (RMS={results[2][1]:.4f})") + ax.set_xlabel("u-velocity at x=0.5") + ax.set_ylabel("y") + ax.set_title("Lid-driven cavity Re=100\nGhia et al. (1982) validation") + ax.legend(loc="lower right") + ax.grid(True, alpha=0.3) + fig.tight_layout() + fig.savefig("sl_cavity_benchmark.png", dpi=150) + plt.show() From 572627abda98c708d9bbf253e6c44ca4f9225cb3 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Mar 2026 09:25:49 +1100 Subject: [PATCH 002/537] Fix worktree remove prompting on setup symlinks worktree_remove() counted the .pixi and petsc-custom/petsc symlinks (created by worktree_create) as uncommitted changes, blocking every removal with a confirmation prompt. Filter these known symlinks from the dirty check so clean worktrees remove without prompting. Underworld development team with AI support from Claude Code --- uw | 13 ++++++++++--- 1 file changed, 10 insertions(+), 3 deletions(-) diff --git a/uw b/uw index 1f97c7ae2..733743ecf 100755 --- a/uw +++ b/uw @@ -1181,11 +1181,18 @@ worktree_remove() { fi local branch=$(git -C "$wt_path" rev-parse --abbrev-ref HEAD 2>/dev/null || echo "") - local status=$(git -C "$wt_path" status --short 2>/dev/null | wc -l | tr -d ' ') + + # Filter out symlinks we created (.pixi, petsc-custom/petsc) from the dirty check + local status=$(git -C "$wt_path" status --short 2>/dev/null \ + | grep -v '^?? \.pixi$' \ + | grep -v '^?? petsc-custom/petsc$' \ + | wc -l | tr -d ' ') if [ "$status" -gt 0 ]; then - echo -e "${YELLOW}Worktree has $status uncommitted change(s):${NC}" - git -C "$wt_path" status --short + echo -e "${YELLOW}Worktree has $status uncommitted change(s) (excluding setup symlinks):${NC}" + git -C "$wt_path" status --short \ + | grep -v '^?? \.pixi$' \ + | grep -v '^?? petsc-custom/petsc$' echo "" read -p "Remove anyway? [y/N]: " confirm [ "$confirm" != "y" ] && [ "$confirm" != "Y" ] && exit 1 From 1469d92483789ffcab48de25f15977fd3b811c4d Mon Sep 17 00:00:00 2001 From: Tyagi Date: Tue, 24 Mar 2026 17:56:50 +1100 Subject: [PATCH 003/537] Add PETSc pressure nullspace support for Stokes --- .../cython/petsc_generic_snes_solvers.pyx | 107 ++++++++++++++++++ tests/test_1013_stokes_pressure_nullspace.py | 63 +++++++++++ 2 files changed, 170 insertions(+) create mode 100644 tests/test_1013_stokes_pressure_nullspace.py diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 1f9cebea2..d3c1dd06b 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -447,6 +447,10 @@ class SolverBaseClass(uw_object): self.dm = None # Should be able to avoid nuking this if we # can insert new functions in template (surface integrals problematic in # the current implementation ) + if hasattr(self, "_pressure_nullspace"): + self._pressure_nullspace = None + if hasattr(self, "_pressure_nullspace_basis"): + self._pressure_nullspace_basis = None # This is a workaround for some problem in the PETSc machinery # where we need a surface integral term somewhere on every process @@ -2829,6 +2833,9 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.boundary_conditions = False # self._constitutive_model = None self._saddle_preconditioner = None + self._petsc_use_pressure_nullspace = False + self._pressure_nullspace = None + self._pressure_nullspace_basis = None # Construct strainrate tensor for future usage. # Grab gradients, and let's switch out to sympy.Matrix notation @@ -3088,6 +3095,100 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.is_setup = False self._saddle_preconditioner = function + @property + def petsc_use_pressure_nullspace(self): + """ + Enable PETSc handling of the constant-pressure nullspace. + + When enabled, the solver attaches a nullspace basis with zero + velocity entries and constant pressure entries to the coupled + Stokes matrices before solve. + """ + return self._petsc_use_pressure_nullspace + + @petsc_use_pressure_nullspace.setter + def petsc_use_pressure_nullspace(self, value): + self._petsc_use_pressure_nullspace = bool(value) + self._pressure_nullspace = None + self._pressure_nullspace_basis = None + self.is_setup = False + + def _pressure_dirichlet_bcs(self): + """Return essential boundary conditions applied to the pressure field.""" + + pressure_field_ids = {1} + try: + pressure_field_ids.add(self.p.field_id) + except Exception: + pass + + return [bc for bc in self.essential_bcs if bc.f_id in pressure_field_ids] + + def _build_pressure_nullspace(self): + """Create a constant-pressure nullspace basis for the coupled Stokes DM.""" + + template_vec = self.dm.getGlobalVec() + try: + null_vec = template_vec.duplicate() + finally: + self.dm.restoreGlobalVec(template_vec) + + null_vec.set(0.0) + + pressure_is = self._subdict["pressure"][0] + pressure_subvec = null_vec.getSubVector(pressure_is) + pressure_subvec.set(1.0) + null_vec.restoreSubVector(pressure_is, pressure_subvec) + + self._pressure_nullspace_basis = null_vec + self._pressure_nullspace = PETSc.NullSpace().create( + constant=False, + vectors=(null_vec,), + comm=self.dm.comm, + ) + + return self._pressure_nullspace + + def _attach_pressure_nullspace(self): + """Attach the configured pressure nullspace to the Stokes matrices.""" + + if not self._petsc_use_pressure_nullspace: + return + + pressure_bcs = self._pressure_dirichlet_bcs() + if pressure_bcs: + boundaries = ", ".join(sorted({bc.boundary for bc in pressure_bcs})) + raise ValueError( + "petsc_use_pressure_nullspace=True requires the pressure field to be " + f"free of Dirichlet boundary conditions. Found pressure Dirichlet BCs on: {boundaries}" + ) + + if "pressure" not in self._subdict: + raise RuntimeError("Pressure field decomposition is unavailable; cannot attach nullspace.") + + self.snes.setUp() + + jacobian = self.snes.getJacobian() + operator_matrix = jacobian[0] + preconditioner_matrix = jacobian[1] if len(jacobian) > 1 else None + + nullspace = self._pressure_nullspace + if nullspace is None: + nullspace = self._build_pressure_nullspace() + + operator_matrix.setNullSpace(nullspace) + operator_matrix.setTransposeNullSpace(nullspace) + + if preconditioner_matrix is not None: + preconditioner_matrix.setNullSpace(nullspace) + preconditioner_matrix.setTransposeNullSpace(nullspace) + + if self.verbose and uw.mpi.rank == 0: + print( + f"Stokes Saddle Pt ({self.name}): attached constant-pressure nullspace", + flush=True, + ) + ## F0, F1 should be f0 and F1, (pf0 for Saddles can be added here) ## don't add new ones uf0, uF1 are redundant @@ -3744,6 +3845,8 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): for index,name in enumerate(names): self._subdict[name] = (isets[index],dms[index]) + self._attach_pressure_nullspace() + self.is_setup = True self.constitutive_model._solver_is_setup = True @@ -3846,6 +3949,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.petsc_options.setValue("snes_max_it", 0) self.snes.setType("nrichardson") self.snes.setFromOptions() + self._attach_pressure_nullspace() self.snes.solve(None, gvec) # with self.mesh.access(): @@ -3871,6 +3975,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.snes.atol = self.atol self.snes.setType("nrichardson") self.snes.setFromOptions() + self._attach_pressure_nullspace() self.snes.solve(None, gvec) self._warn_on_divergence(phase="picard") @@ -3880,6 +3985,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.snes.atol = self.atol self.petsc_options.setValue("snes_max_it", snes_max_it) self.snes.setFromOptions() + self._attach_pressure_nullspace() self.snes.solve(None, gvec) else: @@ -3889,6 +3995,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.snes.atol = self.atol self.petsc_options.setValue("snes_max_it", snes_max_it) self.snes.setFromOptions() + self._attach_pressure_nullspace() self.snes.solve(None, gvec) cdef DM dm = self.dm diff --git a/tests/test_1013_stokes_pressure_nullspace.py b/tests/test_1013_stokes_pressure_nullspace.py new file mode 100644 index 000000000..0be4f41fd --- /dev/null +++ b/tests/test_1013_stokes_pressure_nullspace.py @@ -0,0 +1,63 @@ +import pytest + +pytestmark = pytest.mark.level_3 + +import sympy +import underworld3 as uw + + +def test_stokes_pressure_nullspace_solves_without_pressure_bc(): + mesh = uw.meshing.StructuredQuadBox(elementRes=(3, 3)) + x, y = mesh.X + + u = uw.discretisation.MeshVariable( + "u_nullspace", + mesh, + mesh.dim, + vtype=uw.VarType.VECTOR, + degree=2, + ) + p = uw.discretisation.MeshVariable( + "p_nullspace", + mesh, + 1, + vtype=uw.VarType.SCALAR, + degree=1, + continuous=True, + ) + + stokes = uw.systems.Stokes(mesh, velocityField=u, pressureField=p) + stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = 1.0 + stokes.bodyforce = sympy.Matrix([0.0, x]) + stokes.petsc_use_pressure_nullspace = True + + stokes.tolerance = 1.0e-4 + stokes.petsc_options["snes_type"] = "ksponly" + stokes.petsc_options["ksp_type"] = "fgmres" + stokes.petsc_options["ksp_rtol"] = 1.0e-4 + stokes.petsc_options["ksp_atol"] = 0.0 + + stokes.petsc_options.setValue("fieldsplit_velocity_pc_mg_type", "kaskade") + stokes.petsc_options.setValue("fieldsplit_velocity_pc_mg_cycle_type", "w") + stokes.petsc_options["fieldsplit_velocity_mg_coarse_pc_type"] = "svd" + stokes.petsc_options["fieldsplit_velocity_ksp_type"] = "fcg" + stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_type"] = "chebyshev" + stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_max_it"] = 5 + stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_converged_maxits"] = None + stokes.petsc_options.setValue("fieldsplit_pressure_pc_type", "mg") + stokes.petsc_options.setValue("fieldsplit_pressure_pc_mg_type", "multiplicative") + stokes.petsc_options.setValue("fieldsplit_pressure_pc_mg_cycle_type", "v") + + stokes.add_dirichlet_bc((0.0, 0.0), "Bottom") + stokes.add_dirichlet_bc((0.0, None), "Top") + stokes.add_dirichlet_bc((0.0, None), "Left") + stokes.add_condition(conds=(0.0, None), label="Right", f_id=0, c_type="dirichlet") + + stokes.solve() + + assert stokes.snes.getConvergedReason() > 0 + + jacobian = stokes.snes.getJacobian() + nullspace = jacobian[0].getNullSpace() + assert nullspace is not None From 5f6d09309382b4f1ea909cd42f63626d05ca9ed4 Mon Sep 17 00:00:00 2001 From: Tyagi Date: Wed, 25 Mar 2026 01:24:26 +1100 Subject: [PATCH 004/537] Generalize Stokes nullspace support for shell modes --- .../cython/petsc_generic_snes_solvers.pyx | 243 +++++++++++++++--- tests/test_1013_stokes_pressure_nullspace.py | 15 ++ tests/test_1014_stokes_shell_nullspace.py | 129 ++++++++++ 3 files changed, 350 insertions(+), 37 deletions(-) create mode 100644 tests/test_1014_stokes_shell_nullspace.py diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index d3c1dd06b..34cd3a328 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -1,5 +1,6 @@ from xmlrpc.client import Boolean +import numpy as np import sympy from sympy import sympify @@ -447,10 +448,10 @@ class SolverBaseClass(uw_object): self.dm = None # Should be able to avoid nuking this if we # can insert new functions in template (surface integrals problematic in # the current implementation ) - if hasattr(self, "_pressure_nullspace"): - self._pressure_nullspace = None - if hasattr(self, "_pressure_nullspace_basis"): - self._pressure_nullspace_basis = None + if hasattr(self, "_stokes_nullspace"): + self._stokes_nullspace = None + if hasattr(self, "_stokes_nullspace_basis"): + self._stokes_nullspace_basis = () # This is a workaround for some problem in the PETSc machinery # where we need a surface integral term somewhere on every process @@ -2834,8 +2835,9 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): # self._constitutive_model = None self._saddle_preconditioner = None self._petsc_use_pressure_nullspace = False - self._pressure_nullspace = None - self._pressure_nullspace_basis = None + self._petsc_velocity_nullspace_basis = () + self._stokes_nullspace = None + self._stokes_nullspace_basis = () # Construct strainrate tensor for future usage. # Grab gradients, and let's switch out to sympy.Matrix notation @@ -3100,32 +3102,128 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): """ Enable PETSc handling of the constant-pressure nullspace. - When enabled, the solver attaches a nullspace basis with zero - velocity entries and constant pressure entries to the coupled - Stokes matrices before solve. + When enabled, the solver attaches the constant-pressure mode to + the coupled Stokes nullspace basis before solve. Additional + user-supplied velocity nullspace modes can be configured through + ``petsc_velocity_nullspace_basis``. + + For free-slip shell problems this is typically used together with + the rigid-body rotation modes documented on + ``petsc_velocity_nullspace_basis``. + + Examples + -------- + 2-D annulus with pressure gauge only: + >>> stokes.petsc_use_pressure_nullspace = True + + 2-D annulus with pressure plus rigid rotation: + >>> x, y = mesh.X + >>> stokes.petsc_use_pressure_nullspace = True + >>> stokes.petsc_velocity_nullspace_basis = [sympy.Matrix([-y, x])] + + 3-D spherical shell with pressure plus the three rigid rotations: + >>> x, y, z = mesh.X + >>> stokes.petsc_use_pressure_nullspace = True + >>> stokes.petsc_velocity_nullspace_basis = [ + ... sympy.Matrix([0, -z, y]), + ... sympy.Matrix([z, 0, -x]), + ... sympy.Matrix([-y, x, 0]), + ... ] """ return self._petsc_use_pressure_nullspace @petsc_use_pressure_nullspace.setter def petsc_use_pressure_nullspace(self, value): self._petsc_use_pressure_nullspace = bool(value) - self._pressure_nullspace = None - self._pressure_nullspace_basis = None + self._reset_stokes_nullspace() self.is_setup = False + @property + def petsc_velocity_nullspace_basis(self): + """ + Optional exact velocity nullspace modes for the coupled Stokes solve. + + Each entry must be a vector-valued SymPy expression defined in the + mesh coordinate system and representing an exact null mode of the + configured Stokes operator. Typical examples are rigid-body rotation + modes for annulus or spherical-shell free-slip problems. + + For centered shell geometries with exact free-slip / no-penetration + boundary conditions, the rigid-body rotation modes are: + + - 2-D annulus: one mode, ``(-y, x)``, equivalent to ``r e_theta`` + - 3-D spherical shell: three modes, + ``(0, -z, y)``, ``(z, 0, -x)``, and ``(-y, x, 0)`` + + These are the velocity fields generated by rigid rotations + ``u = omega x x``. They are tangent to concentric circles / spheres + and have zero strain rate, so they are exact velocity null modes for + the free-slip shell Stokes operator. + + They are not exact null modes when the boundary conditions select a + specific tangential velocity, for example: + + - essential velocity boundary conditions + - penalty boundary conditions on the full velocity error + ``u - u_analytic`` + + To remove shell nullspaces in Stokes, set the pressure mode and then + provide the exact rotation basis: + + Examples + -------- + 2-D annulus: + >>> x, y = mesh.X + >>> stokes.petsc_use_pressure_nullspace = True + >>> stokes.petsc_velocity_nullspace_basis = [sympy.Matrix([-y, x])] + + 3-D spherical shell: + >>> x, y, z = mesh.X + >>> stokes.petsc_use_pressure_nullspace = True + >>> stokes.petsc_velocity_nullspace_basis = [ + ... sympy.Matrix([0, -z, y]), + ... sympy.Matrix([z, 0, -x]), + ... sympy.Matrix([-y, x, 0]), + ... ] + """ + return self._petsc_velocity_nullspace_basis + + @petsc_velocity_nullspace_basis.setter + def petsc_velocity_nullspace_basis(self, modes): + if modes is None: + modes = () + + velocity_modes = [] + for mode in modes: + matrix_mode = sympy.Matrix(mode) + if matrix_mode.shape == (1, self.mesh.dim): + matrix_mode = matrix_mode.T + if matrix_mode.shape != (self.mesh.dim, 1): + raise ValueError( + "Each petsc_velocity_nullspace_basis mode must have shape " + f"({self.mesh.dim}, 1) or (1, {self.mesh.dim}); got {matrix_mode.shape}." + ) + velocity_modes.append(matrix_mode) + + self._petsc_velocity_nullspace_basis = tuple(velocity_modes) + self._reset_stokes_nullspace() + self.is_setup = False + + def _reset_stokes_nullspace(self): + self._stokes_nullspace = None + self._stokes_nullspace_basis = () + def _pressure_dirichlet_bcs(self): """Return essential boundary conditions applied to the pressure field.""" - pressure_field_ids = {1} - try: - pressure_field_ids.add(self.p.field_id) - except Exception: - pass + pressure_field_id = getattr(getattr(self, "p", None), "field_id", None) + if pressure_field_id is None: + raise RuntimeError("Pressure field is unavailable; cannot inspect pressure Dirichlet BCs.") - return [bc for bc in self.essential_bcs if bc.f_id in pressure_field_ids] + return [bc for bc in self.essential_bcs if bc.f_id == pressure_field_id] - def _build_pressure_nullspace(self): - """Create a constant-pressure nullspace basis for the coupled Stokes DM.""" + def _build_pressure_nullspace_vector(self): + """Create the constant-pressure basis vector for the coupled Stokes DM.""" template_vec = self.dm.getGlobalVec() try: @@ -3140,31 +3238,96 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): pressure_subvec.set(1.0) null_vec.restoreSubVector(pressure_is, pressure_subvec) - self._pressure_nullspace_basis = null_vec - self._pressure_nullspace = PETSc.NullSpace().create( + return null_vec + + def _build_velocity_nullspace_vector(self, mode): + """Create a velocity nullspace basis vector from a user-supplied mode.""" + + mode_values = np.asarray(uw.function.evaluate(mode, self.u.coords_nd), dtype=np.float64) + if mode_values.ndim == 1: + mode_values = mode_values.reshape(-1, 1) + elif mode_values.ndim > 2: + mode_values = mode_values.reshape(mode_values.shape[0], -1) + + if mode_values.shape != (self.u.coords_nd.shape[0], self.u.num_components): + raise ValueError( + "Velocity nullspace mode evaluation must return an array with shape " + f"({self.u.coords_nd.shape[0]}, {self.u.num_components}); got {mode_values.shape}." + ) + + template_vec = self.dm.getGlobalVec() + try: + null_vec = template_vec.duplicate() + finally: + self.dm.restoreGlobalVec(template_vec) + + null_vec.set(0.0) + + velocity_is, velocity_subdm = self._subdict["velocity"] + velocity_basis = self.u.vec.duplicate() + try: + velocity_basis.array[:] = mode_values.reshape(velocity_basis.array.shape) + velocity_subvec = null_vec.getSubVector(velocity_is) + velocity_subdm.localToGlobal(velocity_basis, velocity_subvec, addv=False) + null_vec.restoreSubVector(velocity_is, velocity_subvec) + finally: + velocity_basis.destroy() + + return null_vec + + def _build_stokes_nullspace(self): + """Create the configured coupled Stokes nullspace basis.""" + + basis_vectors = [] + + if self._petsc_use_pressure_nullspace: + basis_vectors.append(self._build_pressure_nullspace_vector()) + + for mode in self._petsc_velocity_nullspace_basis: + basis_vectors.append(self._build_velocity_nullspace_vector(mode)) + + if not basis_vectors: + return None + + orthonormal_basis = [] + for basis_vec in basis_vectors: + for orth_vec in orthonormal_basis: + basis_vec.axpy(-orth_vec.dot(basis_vec), orth_vec) + + basis_norm = basis_vec.norm() + if np.isclose(basis_norm, 0.0): + raise ValueError( + "Configured Stokes nullspace basis contains a dependent or zero mode." + ) + + basis_vec.scale(1.0 / basis_norm) + orthonormal_basis.append(basis_vec) + + self._stokes_nullspace_basis = tuple(orthonormal_basis) + self._stokes_nullspace = PETSc.NullSpace().create( constant=False, - vectors=(null_vec,), + vectors=self._stokes_nullspace_basis, comm=self.dm.comm, ) - return self._pressure_nullspace + return self._stokes_nullspace - def _attach_pressure_nullspace(self): - """Attach the configured pressure nullspace to the Stokes matrices.""" + def _attach_stokes_nullspace(self): + """Attach the configured coupled Stokes nullspace to the solver matrices.""" - if not self._petsc_use_pressure_nullspace: + if not self._petsc_use_pressure_nullspace and not self._petsc_velocity_nullspace_basis: return pressure_bcs = self._pressure_dirichlet_bcs() if pressure_bcs: boundaries = ", ".join(sorted({bc.boundary for bc in pressure_bcs})) raise ValueError( - "petsc_use_pressure_nullspace=True requires the pressure field to be " + "PETSc Stokes nullspace support requires the pressure field to be " f"free of Dirichlet boundary conditions. Found pressure Dirichlet BCs on: {boundaries}" ) - if "pressure" not in self._subdict: - raise RuntimeError("Pressure field decomposition is unavailable; cannot attach nullspace.") + if "pressure" not in self._subdict or "velocity" not in self._subdict: + raise RuntimeError("Velocity/pressure field decomposition is unavailable; cannot attach nullspace.") self.snes.setUp() @@ -3172,9 +3335,12 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): operator_matrix = jacobian[0] preconditioner_matrix = jacobian[1] if len(jacobian) > 1 else None - nullspace = self._pressure_nullspace + nullspace = self._stokes_nullspace if nullspace is None: - nullspace = self._build_pressure_nullspace() + nullspace = self._build_stokes_nullspace() + + if nullspace is None: + return operator_matrix.setNullSpace(nullspace) operator_matrix.setTransposeNullSpace(nullspace) @@ -3185,7 +3351,8 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): if self.verbose and uw.mpi.rank == 0: print( - f"Stokes Saddle Pt ({self.name}): attached constant-pressure nullspace", + f"Stokes Saddle Pt ({self.name}): attached Stokes nullspace with " + f"{len(self._stokes_nullspace_basis)} basis mode(s)", flush=True, ) @@ -3845,7 +4012,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): for index,name in enumerate(names): self._subdict[name] = (isets[index],dms[index]) - self._attach_pressure_nullspace() + self._attach_stokes_nullspace() self.is_setup = True self.constitutive_model._solver_is_setup = True @@ -3949,7 +4116,9 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.petsc_options.setValue("snes_max_it", 0) self.snes.setType("nrichardson") self.snes.setFromOptions() - self._attach_pressure_nullspace() + # PETSc may rebuild operator state after setFromOptions(), so reattach + # the configured Stokes nullspace before each solve path. + self._attach_stokes_nullspace() self.snes.solve(None, gvec) # with self.mesh.access(): @@ -3975,7 +4144,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.snes.atol = self.atol self.snes.setType("nrichardson") self.snes.setFromOptions() - self._attach_pressure_nullspace() + self._attach_stokes_nullspace() self.snes.solve(None, gvec) self._warn_on_divergence(phase="picard") @@ -3985,7 +4154,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.snes.atol = self.atol self.petsc_options.setValue("snes_max_it", snes_max_it) self.snes.setFromOptions() - self._attach_pressure_nullspace() + self._attach_stokes_nullspace() self.snes.solve(None, gvec) else: @@ -3995,7 +4164,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.snes.atol = self.atol self.petsc_options.setValue("snes_max_it", snes_max_it) self.snes.setFromOptions() - self._attach_pressure_nullspace() + self._attach_stokes_nullspace() self.snes.solve(None, gvec) cdef DM dm = self.dm diff --git a/tests/test_1013_stokes_pressure_nullspace.py b/tests/test_1013_stokes_pressure_nullspace.py index 0be4f41fd..ad5cbb86c 100644 --- a/tests/test_1013_stokes_pressure_nullspace.py +++ b/tests/test_1013_stokes_pressure_nullspace.py @@ -57,7 +57,22 @@ def test_stokes_pressure_nullspace_solves_without_pressure_bc(): stokes.solve() assert stokes.snes.getConvergedReason() > 0 + assert len(stokes._stokes_nullspace_basis) == 1 jacobian = stokes.snes.getJacobian() nullspace = jacobian[0].getNullSpace() assert nullspace is not None + + basis_vec = stokes._stokes_nullspace_basis[0] + velocity_is = stokes._subdict["velocity"][0] + pressure_is = stokes._subdict["pressure"][0] + + velocity_subvec = basis_vec.getSubVector(velocity_is) + pressure_subvec = basis_vec.getSubVector(pressure_is) + + try: + assert velocity_subvec.norm() == pytest.approx(0.0, abs=1.0e-12) + assert pressure_subvec.norm() > 0.0 + finally: + basis_vec.restoreSubVector(velocity_is, velocity_subvec) + basis_vec.restoreSubVector(pressure_is, pressure_subvec) diff --git a/tests/test_1014_stokes_shell_nullspace.py b/tests/test_1014_stokes_shell_nullspace.py new file mode 100644 index 000000000..51c20325e --- /dev/null +++ b/tests/test_1014_stokes_shell_nullspace.py @@ -0,0 +1,129 @@ +import pytest + +pytestmark = pytest.mark.level_3 + +import sympy +import underworld3 as uw + + +def _configure_shell_stokes(mesh): + u = uw.discretisation.MeshVariable( + "u_shell_nullspace", + mesh, + mesh.dim, + vtype=uw.VarType.VECTOR, + degree=2, + ) + p = uw.discretisation.MeshVariable( + "p_shell_nullspace", + mesh, + 1, + vtype=uw.VarType.SCALAR, + degree=1, + continuous=True, + ) + + stokes = uw.systems.Stokes(mesh, velocityField=u, pressureField=p) + stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = 1.0 + stokes.bodyforce = sympy.Matrix([0.0] * mesh.dim) + + stokes.tolerance = 1.0e-4 + stokes.petsc_options["snes_type"] = "ksponly" + stokes.petsc_options["ksp_type"] = "fgmres" + stokes.petsc_options["ksp_rtol"] = 1.0e-4 + stokes.petsc_options["ksp_atol"] = 0.0 + + stokes.petsc_options.setValue("fieldsplit_velocity_pc_mg_type", "kaskade") + stokes.petsc_options.setValue("fieldsplit_velocity_pc_mg_cycle_type", "w") + stokes.petsc_options["fieldsplit_velocity_mg_coarse_pc_type"] = "svd" + stokes.petsc_options["fieldsplit_velocity_ksp_type"] = "fcg" + stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_type"] = "chebyshev" + stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_max_it"] = 5 + stokes.petsc_options["fieldsplit_velocity_mg_levels_ksp_converged_maxits"] = None + stokes.petsc_options.setValue("fieldsplit_pressure_pc_type", "mg") + stokes.petsc_options.setValue("fieldsplit_pressure_pc_mg_type", "multiplicative") + stokes.petsc_options.setValue("fieldsplit_pressure_pc_mg_cycle_type", "v") + + gamma = mesh.Gamma + stokes.add_natural_bc(1.0e4 * gamma.dot(u) * gamma, "Upper") + stokes.add_natural_bc(1.0e4 * gamma.dot(u) * gamma, "Lower") + + stokes.petsc_use_pressure_nullspace = True + + return stokes + + +@pytest.mark.parametrize( + ("mesh", "rotation_modes", "expected_mode_count"), + [ + ( + uw.meshing.Annulus(radiusOuter=1.0, radiusInner=0.6, cellSize=0.25, qdegree=2), + [sympy.Matrix([-sympy.Symbol("y"), sympy.Symbol("x")])], + 2, + ), + ( + uw.meshing.SphericalShell(radiusOuter=1.0, radiusInner=0.6, cellSize=0.5, qdegree=2), + [ + sympy.Matrix([0, -sympy.Symbol("z"), sympy.Symbol("y")]), + sympy.Matrix([sympy.Symbol("z"), 0, -sympy.Symbol("x")]), + sympy.Matrix([-sympy.Symbol("y"), sympy.Symbol("x"), 0]), + ], + 4, + ), + ], +) +def test_stokes_shell_rotation_nullspace(mesh, rotation_modes, expected_mode_count): + if mesh.dim == 2: + x, y = mesh.X + coordinate_subs = { + sympy.Symbol("x"): x, + sympy.Symbol("y"): y, + } + else: + x, y, z = mesh.X + coordinate_subs = { + sympy.Symbol("x"): x, + sympy.Symbol("y"): y, + sympy.Symbol("z"): z, + } + + resolved_modes = [mode.subs(coordinate_subs) for mode in rotation_modes] + + stokes = _configure_shell_stokes(mesh) + stokes.petsc_velocity_nullspace_basis = resolved_modes + stokes.solve() + + assert stokes.snes.getConvergedReason() > 0 + assert len(stokes._stokes_nullspace_basis) == expected_mode_count + + jacobian = stokes.snes.getJacobian() + nullspace = jacobian[0].getNullSpace() + + assert nullspace is not None + + velocity_is = stokes._subdict["velocity"][0] + pressure_is = stokes._subdict["pressure"][0] + pressure_modes = 0 + velocity_modes = 0 + + for basis_vec in stokes._stokes_nullspace_basis: + velocity_subvec = basis_vec.getSubVector(velocity_is) + pressure_subvec = basis_vec.getSubVector(pressure_is) + + try: + velocity_norm = velocity_subvec.norm() + pressure_norm = pressure_subvec.norm() + finally: + basis_vec.restoreSubVector(velocity_is, velocity_subvec) + basis_vec.restoreSubVector(pressure_is, pressure_subvec) + + if pressure_norm > 1.0e-10: + pressure_modes += 1 + assert velocity_norm == pytest.approx(0.0, abs=1.0e-12) + else: + velocity_modes += 1 + assert velocity_norm > 0.0 + + assert pressure_modes == 1 + assert velocity_modes == expected_mode_count - 1 From aaabf8df6d84af8a0627a5ea78d5b15446c30b41 Mon Sep 17 00:00:00 2001 From: Tyagi Date: Wed, 25 Mar 2026 14:15:37 +1100 Subject: [PATCH 005/537] Fix Integral/BdIntegral JIT cache collisions --- src/underworld3/utilities/_jitextension.py | 57 +++++++++++++++++----- tests/test_0502_boundary_integrals.py | 43 ++++++++++++++++ 2 files changed, 87 insertions(+), 13 deletions(-) diff --git a/src/underworld3/utilities/_jitextension.py b/src/underworld3/utilities/_jitextension.py index 5eddb90f4..45af5636a 100644 --- a/src/underworld3/utilities/_jitextension.py +++ b/src/underworld3/utilities/_jitextension.py @@ -300,13 +300,20 @@ def getext( import time time_s = time.time() + primary_field_list = tuple(primary_field_list) + + raw_fns_residual = tuple(fns_residual) + raw_fns_bcs = tuple(fns_bcs) + raw_fns_jacobian = tuple(fns_jacobian) + raw_fns_bd_residual = tuple(fns_bd_residual) + raw_fns_bd_jacobian = tuple(fns_bd_jacobian) raw_fns = ( - tuple(fns_residual) - + tuple(fns_bcs) - + tuple(fns_jacobian) - + tuple(fns_bd_residual) - + tuple(fns_bd_jacobian) + raw_fns_residual + + raw_fns_bcs + + raw_fns_jacobian + + raw_fns_bd_residual + + raw_fns_bd_jacobian ) # Extract constant UWexpressions that will go through constants[] array @@ -315,23 +322,41 @@ def getext( # Build structurally-expanded functions for cache hashing. # Constants are replaced with placeholder symbols (value-independent), # so changing a constant value won't cause a cache miss. - expanded_fns = [] - for fn in raw_fns: + def _structural_expand(fn): # Phase 1: Substitute constants with _JITConstant placeholders if constants_subs_map and fn is not None: try: - fn_structural = fn.xreplace(constants_subs_map) if hasattr(fn, 'xreplace') else fn + fn_structural = fn.xreplace(constants_subs_map) if hasattr(fn, "xreplace") else fn except Exception: fn_structural = fn else: fn_structural = fn # Phase 2: Unwrap remaining (non-constant) expressions - expanded_fns.append( - underworld3.function.expressions.unwrap(fn_structural, keep_constants=False, return_self=False) + return underworld3.function.expressions.unwrap( + fn_structural, keep_constants=False, return_self=False ) - fns = tuple(expanded_fns) + expanded_fns_residual = tuple(_structural_expand(fn) for fn in raw_fns_residual) + expanded_fns_bcs = tuple(_structural_expand(fn) for fn in raw_fns_bcs) + expanded_fns_jacobian = tuple(_structural_expand(fn) for fn in raw_fns_jacobian) + expanded_fns_bd_residual = tuple(_structural_expand(fn) for fn in raw_fns_bd_residual) + expanded_fns_bd_jacobian = tuple(_structural_expand(fn) for fn in raw_fns_bd_jacobian) + + fns = ( + expanded_fns_residual + + expanded_fns_bcs + + expanded_fns_jacobian + + expanded_fns_bd_residual + + expanded_fns_bd_jacobian + ) + fns_signature = ( + expanded_fns_residual, + expanded_fns_bcs, + expanded_fns_jacobian, + expanded_fns_bd_residual, + expanded_fns_bd_jacobian, + ) if debug and underworld3.mpi.rank == 0: print(f"Expanded functions for compilation:") @@ -353,8 +378,14 @@ def getext( # unique modules. jitname += "_" + str(len(_ext_dict.keys())) - else: # Else name from fns hash — uses structural form (constants as placeholders) - jitname = abs(hash((mesh, fns, tuple(mesh.vars.keys())))) + else: # Else name from a structured hash — function role/signature must be preserved. + primary_field_signature = tuple( + (getattr(field, "field_id", None), getattr(field, "clean_name", None)) + for field in primary_field_list + ) + jitname = abs( + hash((mesh, fns_signature, tuple(mesh.vars.keys()), primary_field_signature)) + ) # Create the module if not in dictionary if jitname not in _ext_dict.keys() or not cache: diff --git a/tests/test_0502_boundary_integrals.py b/tests/test_0502_boundary_integrals.py index e7a6f05af..0cd9e18d9 100644 --- a/tests/test_0502_boundary_integrals.py +++ b/tests/test_0502_boundary_integrals.py @@ -291,3 +291,46 @@ def test_bd_integral_annulus_internal_normal_tangential(): value = bd_int.evaluate() assert abs(value) < 0.05, f"Expected ~0, got {value}" + + +def _build_spherical_shell_for_integrals(): + from underworld3.meshing import SphericalShell + + mesh_spherical = SphericalShell( + radiusOuter=1.0, + radiusInner=0.5, + cellSize=1.0 / 4.0, + degree=1, + qdegree=2, + ) + uw.discretisation.MeshVariable("P_spherical_int", mesh_spherical, 1, degree=1, continuous=True) + return mesh_spherical + + +def test_spherical_bd_then_integral_does_not_poison_volume_path(): + """Boundary and volume integrals must not collide in the JIT cache.""" + + mesh_spherical = _build_spherical_shell_for_integrals() + + boundary_before = float(uw.maths.BdIntegral(mesh_spherical, fn=1.0, boundary="Lower").evaluate()) + volume = float(uw.maths.Integral(mesh_spherical, fn=1.0).evaluate()) + boundary_after = float(uw.maths.BdIntegral(mesh_spherical, fn=1.0, boundary="Lower").evaluate()) + + assert boundary_before > 0.0 + assert volume > 0.0 + assert abs(boundary_after - boundary_before) < 1.0e-10 + + +def test_spherical_integral_then_bd_does_not_poison_boundary_path(): + """Volume and boundary integrals must remain order-independent on spherical meshes.""" + + mesh_reference = _build_spherical_shell_for_integrals() + boundary_reference = float(uw.maths.BdIntegral(mesh_reference, fn=1.0, boundary="Lower").evaluate()) + + mesh_spherical = _build_spherical_shell_for_integrals() + volume = float(uw.maths.Integral(mesh_spherical, fn=1.0).evaluate()) + boundary_after = float(uw.maths.BdIntegral(mesh_spherical, fn=1.0, boundary="Lower").evaluate()) + + assert volume > 0.0 + assert boundary_reference > 0.0 + assert abs(boundary_after - boundary_reference) < 1.0e-10 From 9a80842018deadeceb3f41754e37e409eba2df9d Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 25 Mar 2026 16:14:31 +1100 Subject: [PATCH 006/537] Introduce JITCallbackSet for structured JIT cache keys Refactor the JIT compilation pipeline to use a JITCallbackSet dataclass that groups the five PETSc callback lists (residual, bcs, jacobian, bd_residual, bd_jacobian) into a single structured container. This addresses the root cause of the cache-collision bug (PR #92) at an architectural level: the flat tuple hash that lost callback role information is replaced by a structured signature that preserves which slot each expression belongs to. Changes: - Add JITCallbackSet dataclass with flat(), signature(), map(), counts - Extract _structural_expand() as a module-level function (was inline) - Refactor getext() to accept JITCallbackSet (with backward compat) - Refactor _createext() to accept JITCallbackSet - Update all 6 call sites: 3 solvers (Scalar, Vector, Stokes) and 3 integrals (Integral, Integral._evaluate_integral, BdIntegral) - Include PR #92 regression tests (spherical shell cache collision) Incorporates the fix from PR #92 (gthyagi) which identified the bug and added the regression tests. Test results: 374 passed, 7 skipped, 1 xfailed (level_1 suite) Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 72 ++-- src/underworld3/cython/petsc_maths.pyx | 12 +- src/underworld3/utilities/_jitextension.py | 318 +++++++++--------- tests/test_0004_pointwise_fns.py | 38 ++- 4 files changed, 232 insertions(+), 208 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 34cd3a328..e830fdc42 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -9,7 +9,7 @@ from petsc4py import PETSc import underworld3 import underworld3 as uw -from underworld3.utilities._jitextension import getext +from underworld3.utilities._jitextension import getext, JITCallbackSet import underworld3.timing as timing from underworld3.utilities._api_tools import uw_object @@ -1542,15 +1542,19 @@ class SNES_Scalar(SolverBaseClass): print(f"Scalar SNES: Jacobians complete, now compile", flush=True) prim_field_list = [self.u] - _getext_result = getext(self.mesh, - tuple(fns_residual), - tuple(fns_jacobian), - [x.fn for x in self.essential_bcs], - tuple(fns_bd_residual), - tuple(fns_bd_jacobian), - primary_field_list=prim_field_list, - verbose=verbose, - debug=debug,) + _getext_result = getext( + self.mesh, + JITCallbackSet( + residual=tuple(fns_residual), + bcs=tuple(x.fn for x in self.essential_bcs), + jacobian=tuple(fns_jacobian), + bd_residual=tuple(fns_bd_residual), + bd_jacobian=tuple(fns_bd_jacobian), + ), + prim_field_list, + verbose=verbose, + debug=debug, + ) self.compiled_extensions = _getext_result.ptrobj self.ext_dict = _getext_result.fn_dicts self.constants_manifest = _getext_result.constants_manifest @@ -2291,15 +2295,19 @@ class SNES_Vector(SolverBaseClass): # note also that the order here is important. prim_field_list = [self.u,] - _getext_result = getext(self.mesh, - tuple(fns_residual), - tuple(fns_jacobian), - [x.fn for x in self.essential_bcs], - tuple(fns_bd_residual), - tuple(fns_bd_jacobian), - primary_field_list=prim_field_list, - verbose=verbose, - debug=debug,) + _getext_result = getext( + self.mesh, + JITCallbackSet( + residual=tuple(fns_residual), + bcs=tuple(x.fn for x in self.essential_bcs), + jacobian=tuple(fns_jacobian), + bd_residual=tuple(fns_bd_residual), + bd_jacobian=tuple(fns_bd_jacobian), + ), + prim_field_list, + verbose=verbose, + debug=debug, + ) self.compiled_extensions = _getext_result.ptrobj self.ext_dict = _getext_result.fn_dicts self.constants_manifest = _getext_result.constants_manifest @@ -3669,17 +3677,21 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): print(f"Stokes: Jacobians complete, now compile", flush=True) prim_field_list = [self.u, self.p] - _getext_result = getext(self.mesh, - tuple(fns_residual), - tuple(fns_jacobian), - [x.fn for x in self.essential_bcs], - tuple(fns_bd_residual), - tuple(fns_bd_jacobian), - primary_field_list=prim_field_list, - verbose=verbose, - debug=debug, - debug_name=debug_name, - cache=False) + _getext_result = getext( + self.mesh, + JITCallbackSet( + residual=tuple(fns_residual), + bcs=tuple(x.fn for x in self.essential_bcs), + jacobian=tuple(fns_jacobian), + bd_residual=tuple(fns_bd_residual), + bd_jacobian=tuple(fns_bd_jacobian), + ), + prim_field_list, + verbose=verbose, + debug=debug, + debug_name=debug_name, + cache=False, + ) self.compiled_extensions = _getext_result.ptrobj self.ext_dict = _getext_result.fn_dicts self.constants_manifest = _getext_result.constants_manifest diff --git a/src/underworld3/cython/petsc_maths.pyx b/src/underworld3/cython/petsc_maths.pyx index fe2d19f8e..26e2f828b 100644 --- a/src/underworld3/cython/petsc_maths.pyx +++ b/src/underworld3/cython/petsc_maths.pyx @@ -3,7 +3,7 @@ import sympy import underworld3 import underworld3.timing as timing -from underworld3.utilities._jitextension import getext +from underworld3.utilities._jitextension import getext, JITCallbackSet from petsc4py import PETSc @@ -89,7 +89,8 @@ class Integral: self.dm = self.mesh.dm # .clone() mesh=self.mesh - _getext_result = getext(self.mesh, [self.fn,], [], [], [], [], self.mesh.vars.values(), verbose=verbose) + _getext_result = getext(self.mesh, JITCallbackSet(residual=(self.fn,)), + self.mesh.vars.values(), verbose=verbose) cdef PtrContainer ext = _getext_result.ptrobj # Pull out vec for variables, and go ahead with the integral @@ -273,7 +274,8 @@ class CellWiseIntegral: elif isinstance(self.fn, sympy.vector.Dyadic): raise RuntimeError("Integral evaluation for Dyadic integrands not supported.") - cdef PtrContainer ext = getext(self.mesh, [self.fn,], [], [], [], [], self.mesh.vars.values()).ptrobj + cdef PtrContainer ext = getext(self.mesh, JITCallbackSet(residual=(self.fn,)), + self.mesh.vars.values()).ptrobj # Pull out vec for variables, and go ahead with the integral self.mesh.update_lvec() @@ -388,8 +390,8 @@ class BdIntegral: # Compile integrand using the boundary residual slot (includes petsc_n[] in signature) _getext_result = getext( - self.mesh, [], [], [], [self.fn,], [], self.mesh.vars.values(), verbose=verbose - ) + self.mesh, JITCallbackSet(bd_residual=(self.fn,)), + self.mesh.vars.values(), verbose=verbose) cdef PtrContainer ext = _getext_result.ptrobj # Prepare the solution vector diff --git a/src/underworld3/utilities/_jitextension.py b/src/underworld3/utilities/_jitextension.py index 45af5636a..b8b9d5c03 100644 --- a/src/underworld3/utilities/_jitextension.py +++ b/src/underworld3/utilities/_jitextension.py @@ -1,11 +1,11 @@ -from typing import List +from typing import List, Optional, Tuple import subprocess from xmlrpc.client import boolean import sympy import underworld3 import underworld3.timing as timing -from typing import Optional from collections import namedtuple +from dataclasses import dataclass ## This is not required in sympy >= 1.9 @@ -33,6 +33,108 @@ _ext_dict = {} +# ============================================================================ +# JIT Callback Set +# ============================================================================ +# +# Groups the five callback lists that PETSc requires for pointwise functions. +# Using a structured container prevents cache-key collisions between callback +# roles (e.g. volume residual vs boundary residual) that share the same +# symbolic form. +# ============================================================================ + +@dataclass(frozen=True) +class JITCallbackSet: + """Immutable container for the five PETSc pointwise callback lists. + + Each slot holds a tuple of SymPy expressions for one callback role. + The structured representation ensures that cache keys preserve which + role each expression belongs to, preventing the collision bug where + ``Integral(fn=1)`` and ``BdIntegral(fn=1)`` would share a cached module. + + Parameters + ---------- + residual : tuple + Volume residual expressions (F0, F1 for each field). + bcs : tuple + Essential boundary condition expressions. + jacobian : tuple + Jacobian expressions (G0, G1, G2, G3 for each field pair). + bd_residual : tuple + Boundary residual expressions (includes ``petsc_n[]`` access). + bd_jacobian : tuple + Boundary Jacobian expressions. + """ + residual: tuple = () + bcs: tuple = () + jacobian: tuple = () + bd_residual: tuple = () + bd_jacobian: tuple = () + + def flat(self) -> tuple: + """Concatenate all slots into a single ordered tuple. + + The ordering (residual, bcs, jacobian, bd_residual, bd_jacobian) + matches what ``_createext()`` expects. + """ + return self.residual + self.bcs + self.jacobian + self.bd_residual + self.bd_jacobian + + def signature(self) -> tuple: + """Hashable key that preserves callback role separation. + + Two callback sets with the same expressions in different roles + will produce different signatures. + """ + return (self.residual, self.bcs, self.jacobian, self.bd_residual, self.bd_jacobian) + + def map(self, fn) -> 'JITCallbackSet': + """Apply *fn* to every expression in every slot, returning a new set.""" + return JITCallbackSet( + residual=tuple(fn(f) for f in self.residual), + bcs=tuple(fn(f) for f in self.bcs), + jacobian=tuple(fn(f) for f in self.jacobian), + bd_residual=tuple(fn(f) for f in self.bd_residual), + bd_jacobian=tuple(fn(f) for f in self.bd_jacobian), + ) + + @property + def counts(self): + """Lengths of each slot, for ``_createext()`` offset calculation.""" + return (len(self.residual), len(self.bcs), len(self.jacobian), + len(self.bd_residual), len(self.bd_jacobian)) + + +def prepare_for_cache_key(fn, constants_subs_map): + """Prepare a single expression for JIT cache hashing. + + Two-phase process: + 1. Substitute constant UWexpressions with ``_JITConstant`` placeholders + so that changing a constant's *value* does not invalidate the cache. + 2. Unwrap remaining (non-constant) UWexpressions to pure SymPy so the + hash is deterministic. + + Parameters + ---------- + fn : sympy expression or None + The expression to expand. + constants_subs_map : dict or None + Mapping from UWexpression symbols to ``_JITConstant`` placeholders. + """ + # Phase 1: Substitute constants with _JITConstant placeholders + if constants_subs_map and fn is not None: + try: + fn_structural = fn.xreplace(constants_subs_map) if hasattr(fn, "xreplace") else fn + except Exception: + fn_structural = fn + else: + fn_structural = fn + + # Phase 2: Unwrap remaining (non-constant) expressions + return underworld3.function.expressions.unwrap( + fn_structural, keep_constants=False, return_self=False + ) + + # ============================================================================ # JIT Constants Support # ============================================================================ @@ -275,20 +377,25 @@ def debugging_text_bd(randstr, fn, fn_type, eqn_no): @timing.routine_timer_decorator def getext( mesh, - fns_residual, - fns_jacobian, - fns_bcs, - fns_bd_residual, - fns_bd_jacobian, + callbacks: JITCallbackSet, primary_field_list, verbose=False, debug=False, debug_name=None, cache=True, ): - """ - Check if we've already created an equivalent extension - and use if available. + """Compile (or retrieve cached) JIT extension for PETSc pointwise functions. + + Parameters + ---------- + mesh : Mesh + Supporting mesh for coordinate system and variable information. + callbacks : JITCallbackSet + Callback expressions grouped by PETSc role (residual, bcs, jacobian, + bd_residual, bd_jacobian). + primary_field_list : iterable + Variables that map to PETSc primary arrays (``petsc_u[]``). + All others map to auxiliary arrays (``petsc_a[]``). Returns ------- @@ -302,65 +409,17 @@ def getext( time_s = time.time() primary_field_list = tuple(primary_field_list) - raw_fns_residual = tuple(fns_residual) - raw_fns_bcs = tuple(fns_bcs) - raw_fns_jacobian = tuple(fns_jacobian) - raw_fns_bd_residual = tuple(fns_bd_residual) - raw_fns_bd_jacobian = tuple(fns_bd_jacobian) - - raw_fns = ( - raw_fns_residual - + raw_fns_bcs - + raw_fns_jacobian - + raw_fns_bd_residual - + raw_fns_bd_jacobian - ) - # Extract constant UWexpressions that will go through constants[] array - constants_manifest, constants_subs_map = _extract_constants(raw_fns, mesh) + constants_manifest, constants_subs_map = _extract_constants(callbacks.flat(), mesh) # Build structurally-expanded functions for cache hashing. # Constants are replaced with placeholder symbols (value-independent), # so changing a constant value won't cause a cache miss. - def _structural_expand(fn): - # Phase 1: Substitute constants with _JITConstant placeholders - if constants_subs_map and fn is not None: - try: - fn_structural = fn.xreplace(constants_subs_map) if hasattr(fn, "xreplace") else fn - except Exception: - fn_structural = fn - else: - fn_structural = fn - - # Phase 2: Unwrap remaining (non-constant) expressions - return underworld3.function.expressions.unwrap( - fn_structural, keep_constants=False, return_self=False - ) - - expanded_fns_residual = tuple(_structural_expand(fn) for fn in raw_fns_residual) - expanded_fns_bcs = tuple(_structural_expand(fn) for fn in raw_fns_bcs) - expanded_fns_jacobian = tuple(_structural_expand(fn) for fn in raw_fns_jacobian) - expanded_fns_bd_residual = tuple(_structural_expand(fn) for fn in raw_fns_bd_residual) - expanded_fns_bd_jacobian = tuple(_structural_expand(fn) for fn in raw_fns_bd_jacobian) - - fns = ( - expanded_fns_residual - + expanded_fns_bcs - + expanded_fns_jacobian - + expanded_fns_bd_residual - + expanded_fns_bd_jacobian - ) - fns_signature = ( - expanded_fns_residual, - expanded_fns_bcs, - expanded_fns_jacobian, - expanded_fns_bd_residual, - expanded_fns_bd_jacobian, - ) + expanded = callbacks.map(lambda fn: prepare_for_cache_key(fn, constants_subs_map)) if debug and underworld3.mpi.rank == 0: print(f"Expanded functions for compilation:") - for i, fn in enumerate(fns): + for i, fn in enumerate(expanded.flat()): print(f"{i}: {fn}") if constants_manifest: print(f"Constants manifest ({len(constants_manifest)} entries):") @@ -378,13 +437,13 @@ def _structural_expand(fn): # unique modules. jitname += "_" + str(len(_ext_dict.keys())) - else: # Else name from a structured hash — function role/signature must be preserved. + else: # Name from structured hash — function role must be preserved. primary_field_signature = tuple( (getattr(field, "field_id", None), getattr(field, "clean_name", None)) for field in primary_field_list ) jitname = abs( - hash((mesh, fns_signature, tuple(mesh.vars.keys()), primary_field_signature)) + hash((mesh, expanded.signature(), tuple(mesh.vars.keys()), primary_field_signature)) ) # Create the module if not in dictionary @@ -392,11 +451,7 @@ def _structural_expand(fn): _createext( jitname, mesh, - fns_residual, - fns_bcs, - fns_jacobian, - fns_bd_residual, - fns_bd_jacobian, + callbacks, primary_field_list, constants_subs_map=constants_subs_map, verbose=verbose, @@ -410,25 +465,11 @@ def _structural_expand(fn): module = _ext_dict[jitname] ptrobj = module.getptrobj() - i_res = {} - for index, fn in enumerate(fns_residual): - i_res[fn] = index - - i_ebc = {} - for index, fn in enumerate(fns_bcs): - i_ebc[fn] = index - - i_jac = {} - for index, fn in enumerate(fns_jacobian): - i_jac[fn] = index - - i_bd_res = {} - for index, fn in enumerate(fns_bd_residual): - i_bd_res[fn] = index - - i_bd_jac = {} - for index, fn in enumerate(fns_bd_jacobian): - i_bd_jac[fn] = index + i_res = {fn: i for i, fn in enumerate(callbacks.residual)} + i_ebc = {fn: i for i, fn in enumerate(callbacks.bcs)} + i_jac = {fn: i for i, fn in enumerate(callbacks.jacobian)} + i_bd_res = {fn: i for i, fn in enumerate(callbacks.bd_residual)} + i_bd_jac = {fn: i for i, fn in enumerate(callbacks.bd_jacobian)} extn_fn_dict = namedtuple( "Functions", @@ -444,74 +485,37 @@ def _structural_expand(fn): def _createext( name: str, mesh: underworld3.discretisation.Mesh, - fns_residual: List[sympy.Basic], - fns_bcs: List[sympy.Basic], - fns_jacobian: List[sympy.Basic], - fns_bd_residual: List[sympy.Basic], - fns_bd_jacobian: List[sympy.Basic], - primary_field_list: List[underworld3.discretisation.MeshVariable], + callbacks: JITCallbackSet, + primary_field_list, constants_subs_map: Optional[dict] = None, verbose: Optional[bool] = False, debug: Optional[bool] = False, debug_name=None, ): - """ - This creates the required extension which houses the JIT - fn pointer for PETSc. + """Create the JIT extension module with PETSc function pointers. Note that it is not possible to replace loaded shared libraries in Python, so we instead create a new extension for each new function. - We hash the functions and create a dictionary of the generated extensions - to avoid redundantly creating new extensions. - - Params - ------ - name: - Name for the extension. It will be prepended with "fn_ptr_ext_" - mesh: - Supporting mesh. It is used to get coordinate system and variable - information. - fns_residual: - List of system's residual sympy functions for which JIT equivalents - will be generated. - fns_jacobian: - List of system's Jacobian sympy functions for which JIT equivalents - will be generated. - fns_bcs: - List of system's boundary condition sympy functions for which JIT equivalents - will be generated. - fns_bd_residual: - List of system's boundary integral sympy functions for which JIT equivalents - will be generated. - fns_bd_jacobian: - List of system's boundary integral jacobian sympy functions for which JIT equivalents - will be generated. - primary_field_list - List of variables that will map from petsc primary variable arrays. All - other variables will be obtained from the mesh object and will be mapped to - petsc auxiliary variable arrays. Note that *all* the variables in the - calling system's corresponding `PetscDM` must be included in this list. - They must also be ordered according to their `field_id`. - + Parameters + ---------- + name : str + Name for the extension. It will be prepended with "fn_ptr_ext_". + mesh : Mesh + Supporting mesh for coordinate system and variable information. + callbacks : JITCallbackSet + Structured callback expressions grouped by role. + primary_field_list : list + Variables that map to PETSc primary variable arrays (``petsc_u[]``). + All other variables map to auxiliary arrays (``petsc_a[]``). + Must be ordered by ``field_id``. """ from sympy import symbols, Eq, MatrixSymbol from underworld3 import VarType - # Note that the order here is important. - fns = ( - tuple(fns_residual) - + tuple(fns_bcs) - + tuple(fns_jacobian) - + tuple(fns_bd_residual) - + tuple(fns_bd_jacobian) - ) - - count_residual_sig = len(fns_residual) - count_bc_sig = len(fns_bcs) - count_jacobian_sig = len(fns_jacobian) - count_bd_residual_sig = len(fns_bd_residual) - count_bd_jacobian_sig = len(fns_bd_jacobian) + fns = callbacks.flat() + count_residual_sig, count_bc_sig, count_jacobian_sig, \ + count_bd_residual_sig, count_bd_jacobian_sig = callbacks.counts # `_ccode` patching def ccode_patch_fns(varlist, prefix_str): @@ -932,39 +936,39 @@ def _basescalar_ccode(self, printer): clsguy.fns_bd_residual = malloc({}*sizeof(PetscDSBdResidualFn)) clsguy.fns_bd_jacobian = malloc({}*sizeof(PetscDSBdJacobianFn)) """.format( - len(fns_residual), - len(fns_bcs), - len(fns_jacobian), - len(fns_bd_residual), - len(fns_bd_jacobian), + count_residual_sig, + count_bc_sig, + count_jacobian_sig, + count_bd_residual_sig, + count_bd_jacobian_sig, ) eqn_count = 0 - for index, eqn in enumerate(eqns[eqn_count : eqn_count + len(fns_residual)]): + for index, eqn in enumerate(eqns[eqn_count : eqn_count + count_residual_sig]): pyx_str += " clsguy.fns_residual[{}] = {}_petsc_{}\n".format(index, randstr, eqn[0]) eqn_count += 1 residual_equations = (0, eqn_count) - for index, eqn in enumerate(eqns[eqn_count : eqn_count + len(fns_bcs)]): + for index, eqn in enumerate(eqns[eqn_count : eqn_count + count_bc_sig]): pyx_str += " clsguy.fns_bcs[{}] = {}_petsc_{}\n".format(index, randstr, eqn[0]) eqn_count += 1 boundary_equations = (residual_equations[1], eqn_count) - for index, eqn in enumerate(eqns[eqn_count : eqn_count + len(fns_jacobian)]): + for index, eqn in enumerate(eqns[eqn_count : eqn_count + count_jacobian_sig]): pyx_str += " clsguy.fns_jacobian[{}] = {}_petsc_{}\n".format(index, randstr, eqn[0]) eqn_count += 1 jacobian_equations = (boundary_equations[1], eqn_count) - for index, eqn in enumerate(eqns[eqn_count : eqn_count + len(fns_bd_residual)]): + for index, eqn in enumerate(eqns[eqn_count : eqn_count + count_bd_residual_sig]): pyx_str += " clsguy.fns_bd_residual[{}] = {}_petsc_{}\n".format(index, randstr, eqn[0]) eqn_count += 1 boundary_residual_equations = (jacobian_equations[1], eqn_count) - for index, eqn in enumerate(eqns[eqn_count : eqn_count + len(fns_bd_jacobian)]): + for index, eqn in enumerate(eqns[eqn_count : eqn_count + count_bd_jacobian_sig]): pyx_str += " clsguy.fns_bd_jacobian[{}] = {}_petsc_{}\n".format(index, randstr, eqn[0]) eqn_count += 1 @@ -1061,23 +1065,23 @@ def load_dynamic(name, path, file=None): flush=True, ) print( - f"{randstr} {len(fns_residual):5d} residuals: {residual_equations[0]}:{residual_equations[1]}", + f"{randstr} {count_residual_sig:5d} residuals: {residual_equations[0]}:{residual_equations[1]}", flush=True, ) print( - f"{randstr} {len(fns_bcs):5d} boundaries: {boundary_equations[0]}:{boundary_equations[1]}", + f"{randstr} {count_bc_sig:5d} boundaries: {boundary_equations[0]}:{boundary_equations[1]}", flush=True, ) print( - f"{randstr} {len(fns_jacobian):5d} jacobians: {jacobian_equations[0]}:{jacobian_equations[1]}", + f"{randstr} {count_jacobian_sig:5d} jacobians: {jacobian_equations[0]}:{jacobian_equations[1]}", flush=True, ) print( - f"{randstr} {len(fns_bd_residual):5d} boundary_res: {boundary_residual_equations[0]}:{boundary_residual_equations[1]}", + f"{randstr} {count_bd_residual_sig:5d} boundary_res: {boundary_residual_equations[0]}:{boundary_residual_equations[1]}", flush=True, ) print( - f"{randstr} {len(fns_bd_jacobian):5d} boundary_jac: {boundary_jacobian_equations[0]}:{boundary_jacobian_equations[1]}", + f"{randstr} {count_bd_jacobian_sig:5d} boundary_jac: {boundary_jacobian_equations[0]}:{boundary_jacobian_equations[1]}", flush=True, ) diff --git a/tests/test_0004_pointwise_fns.py b/tests/test_0004_pointwise_fns.py index 7c5f3b60d..63c2570d2 100644 --- a/tests/test_0004_pointwise_fns.py +++ b/tests/test_0004_pointwise_fns.py @@ -14,7 +14,7 @@ import numpy as np import sympy -from underworld3.utilities._jitextension import getext +from underworld3.utilities._jitextension import getext, JITCallbackSet # build a small mesh - we'll load up a simple problem and then see what functions are loaded @@ -64,11 +64,13 @@ def test_getext_simple(): with uw.utilities.CaptureStdout(split=True) as captured_setup_solver: _getext_result = getext( mesh, - [res_fn, res_fn], - [jac_fn], - [bc_fn], - [bd_res_fn], - [bd_jac_fn], + JITCallbackSet( + residual=(res_fn, res_fn), + bcs=(bc_fn,), + jacobian=(jac_fn,), + bd_residual=(bd_res_fn,), + bd_jacobian=(bd_jac_fn,), + ), mesh.vars.values(), verbose=True, debug=True, @@ -109,11 +111,13 @@ def test_getext_sympy_fns(): with uw.utilities.CaptureStdout(split=True) as captured_setup_solver: _getext_result = getext( mesh, - [res_fn, res_fn], - [jac_fn], - [bc_fn], - [bd_res_fn], - [bd_jac_fn], + JITCallbackSet( + residual=(res_fn, res_fn), + bcs=(bc_fn,), + jacobian=(jac_fn,), + bd_residual=(bd_res_fn,), + bd_jacobian=(bd_jac_fn,), + ), mesh.vars.values(), verbose=True, debug=True, @@ -163,11 +167,13 @@ def test_getext_meshVar(): with uw.utilities.CaptureStdout(split=True) as captured_setup_solver: _getext_result = getext( mesh, - [res_fn, res_fn], - [jac_fn], - [bc_fn], - [bd_res_fn], - [bd_jac_fn], + JITCallbackSet( + residual=(res_fn, res_fn), + bcs=(bc_fn,), + jacobian=(jac_fn,), + bd_residual=(bd_res_fn,), + bd_jacobian=(bd_jac_fn,), + ), mesh.vars.values(), verbose=True, debug=True, From f7a19d752e5274960ddfb62f45741534712dbea5 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 25 Mar 2026 22:33:53 +1100 Subject: [PATCH 007/537] Give each worktree its own pixi environment MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Worktrees previously symlinked .pixi/ to the main repo's environment. This caused binary incompatibilities when switching between worktrees with different Cython source — compiled .so files from worktree A would persist in site-packages and break worktree B at import time. Now each worktree gets its own pixi environment via `pixi install`. Only PETSc is shared (non-relocatable, expensive to rebuild). Falls back to symlink if pixi install fails. Underworld development team with AI support from Claude Code --- uw | 41 ++++++++++++++++++++++++----------------- 1 file changed, 24 insertions(+), 17 deletions(-) diff --git a/uw b/uw index 733743ecf..fd37fe077 100755 --- a/uw +++ b/uw @@ -1037,20 +1037,18 @@ worktree_create() { # 3. Rename branch to follow convention git -C "$wt_path" branch -m "worktree-$name" "$branch_name" 2>/dev/null || true - # 4. Symlink shared resources - echo " Linking shared environment..." - - # .pixi → main repo's .pixi (shared conda/pip packages) - if [ -d "$main_repo/.pixi" ]; then - rm -rf "$wt_path/.pixi" - ln -s "$main_repo/.pixi" "$wt_path/.pixi" - echo -e " ${GREEN}✓${NC} .pixi → main repo" - fi - - # petsc-custom/petsc → main repo's PETSc build (read-only, not relocatable) + # 4. Set up isolated environment + # + # Each worktree gets its OWN pixi environment (not a symlink to the main + # repo's .pixi). This prevents Cython binary incompatibilities when + # worktrees have different source code. Only PETSc is shared (it's + # non-relocatable and expensive to rebuild). + echo " Setting up isolated environment..." + + # petsc-custom/petsc → main repo's PETSc build (read-only, shared) if [ -d "$main_repo/petsc-custom/petsc" ]; then ln -sf "$main_repo/petsc-custom/petsc" "$wt_path/petsc-custom/petsc" - echo -e " ${GREEN}✓${NC} petsc-custom/petsc → main repo" + echo -e " ${GREEN}✓${NC} petsc-custom/petsc → main repo (shared)" fi # .pixi-env — copy so ./uw knows which environment to use @@ -1059,9 +1057,18 @@ worktree_create() { echo -e " ${GREEN}✓${NC} .pixi-env copied ($(cat "$main_repo/.pixi-env"))" fi - # 5. Exclude symlinks from git tracking in this worktree. - # Without this, "git add -A" or "git add ." can accidentally commit - # these machine-local symlinks, breaking CI. + # Install pixi environment (own copy, not symlinked) + local env=$(cat "$wt_path/.pixi-env" 2>/dev/null || echo "runtime") + echo " Installing pixi environment ($env) — this may take a moment..." + (cd "$wt_path" && $PIXI install -e "$env" 2>/dev/null) && \ + echo -e " ${GREEN}✓${NC} .pixi/ installed (isolated)" || { + echo -e " ${YELLOW}pixi install failed — falling back to symlink${NC}" + rm -rf "$wt_path/.pixi" + ln -s "$main_repo/.pixi" "$wt_path/.pixi" + echo -e " ${YELLOW}✓${NC} .pixi → main repo (shared fallback)" + } + + # 5. Exclude local files from git tracking in this worktree. local git_dir git_dir=$(git -C "$wt_path" rev-parse --git-dir) local exclude_file="$git_dir/info/exclude" @@ -1071,7 +1078,7 @@ worktree_create() { echo "$entry" >> "$exclude_file" fi done - echo -e " ${GREEN}✓${NC} git exclude updated (symlinks won't be committed)" + echo -e " ${GREEN}✓${NC} git exclude updated" echo "" echo -e "${GREEN}${BOLD}Worktree ready!${NC}" @@ -1142,7 +1149,7 @@ worktree_list() { if [ -f "$d/.git" ]; then local branch=$(git -C "$d" rev-parse --abbrev-ref HEAD 2>/dev/null || echo "?") local status=$(git -C "$d" status --short 2>/dev/null | wc -l | tr -d ' ') - local linked=$( [ -L "$d/.pixi" ] && echo "linked" || echo "standalone" ) + local linked=$( [ -L "$d/.pixi" ] && echo "shared env" || echo "isolated" ) local dirty="" [ "$status" -gt 0 ] && dirty=" ${YELLOW}($status modified)${NC}" From a3f203c300913ff2eb29edbc0efb66a0c407c800 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 25 Mar 2026 22:36:07 +1100 Subject: [PATCH 008/537] Add per-function JIT cache to avoid redundant recompilation MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The existing JIT cache keys the entire bundle of functions (residuals + Jacobians + BCs) as one hash. If any single function changes, everything recompiles. This is wasteful for SNES_Tensor_Projection which loops over tensor components, changing only the residual RHS while the Jacobian (identity) never changes. New per-function cache: each compiled C function is cached individually by its structural hash + signature type. When getext() is called: - Fast path: whole-bundle hash hit → return immediately (unchanged) - Slow path: check per-function hashes, compile only new functions, assemble PtrContainer by copying cached function pointers PtrContainer gains allocate() and copy_*_from() methods to support cross-module pointer assembly. Also fixes elastic_dt → dt_elastic bug in VE_Stokes.solve(). Includes timing/profiling test scripts for JIT benchmarking. Underworld development team with AI support from Claude Code --- src/underworld3/cython/petsc_types.pxd | 13 +- src/underworld3/cython/petsc_types.pyx | 31 +++- src/underworld3/systems/solvers.py | 2 +- src/underworld3/utilities/_jitextension.py | 179 ++++++++++++++++++--- tests/minimal_vep_timing.py | 89 ++++++++++ tests/profile_jit_phases.py | 163 +++++++++++++++++++ 6 files changed, 453 insertions(+), 24 deletions(-) create mode 100644 tests/minimal_vep_timing.py create mode 100644 tests/profile_jit_phases.py diff --git a/src/underworld3/cython/petsc_types.pxd b/src/underworld3/cython/petsc_types.pxd index 7d2509666..07ce18876 100644 --- a/src/underworld3/cython/petsc_types.pxd +++ b/src/underworld3/cython/petsc_types.pxd @@ -22,21 +22,21 @@ ctypedef void(*PetscDSResidualFn)(PetscInt, PetscInt, PetscInt, ctypedef void (*PetscDSJacobianFn)(PetscInt, PetscInt, PetscInt, const PetscInt*, const PetscInt*, const PetscScalar*, const PetscScalar*, const PetscScalar*, const PetscInt*, const PetscInt*, const PetscScalar*, const PetscScalar*, const PetscScalar*, - PetscReal, PetscReal, const PetscReal*, PetscInt, const PetscScalar*, + PetscReal, PetscReal, const PetscReal*, PetscInt, const PetscScalar*, PetscScalar*) ctypedef void(*PetscDSBdResidualFn)( PetscInt, PetscInt, PetscInt, const PetscInt*, const PetscInt*, const PetscScalar*, const PetscScalar*, const PetscScalar*, const PetscInt*, const PetscInt*, const PetscScalar*, const PetscScalar*, const PetscScalar*, - PetscReal, const PetscReal*,const PetscReal*, PetscInt, const PetscScalar*, + PetscReal, const PetscReal*,const PetscReal*, PetscInt, const PetscScalar*, PetscScalar* ) ctypedef void (*PetscDSBdJacobianFn)( PetscInt, PetscInt, PetscInt, const PetscInt*, const PetscInt*, const PetscScalar*, const PetscScalar*, const PetscScalar*, const PetscInt*, const PetscInt*, const PetscScalar*, const PetscScalar*, const PetscScalar*, - PetscReal, PetscReal, const PetscReal*, const PetscReal*, PetscInt, + PetscReal, PetscReal, const PetscReal*, const PetscReal*, PetscInt, const PetscScalar*, PetscScalar* ) @@ -47,4 +47,9 @@ cdef class PtrContainer: cdef PetscDSBdResidualFn* fns_bd_residual cdef PetscDSBdJacobianFn* fns_bd_jacobian - + cpdef allocate(self, int n_res, int n_bcs, int n_jac, int n_bd_res, int n_bd_jac) + cpdef copy_residual_from(self, int dst, PtrContainer src, int src_idx) + cpdef copy_bcs_from(self, int dst, PtrContainer src, int src_idx) + cpdef copy_jacobian_from(self, int dst, PtrContainer src, int src_idx) + cpdef copy_bd_residual_from(self, int dst, PtrContainer src, int src_idx) + cpdef copy_bd_jacobian_from(self, int dst, PtrContainer src, int src_idx) diff --git a/src/underworld3/cython/petsc_types.pyx b/src/underworld3/cython/petsc_types.pyx index 01a95da62..609dad2a6 100644 --- a/src/underworld3/cython/petsc_types.pyx +++ b/src/underworld3/cython/petsc_types.pyx @@ -1,2 +1,31 @@ +from libc.stdlib cimport malloc + cdef class PtrContainer: - pass \ No newline at end of file + + cpdef allocate(self, int n_res, int n_bcs, int n_jac, int n_bd_res, int n_bd_jac): + """Allocate function pointer arrays of the given sizes.""" + self.fns_residual = malloc(n_res * sizeof(PetscDSResidualFn)) + self.fns_bcs = malloc(n_bcs * sizeof(PetscDSResidualFn)) + self.fns_jacobian = malloc(n_jac * sizeof(PetscDSJacobianFn)) + self.fns_bd_residual = malloc(n_bd_res * sizeof(PetscDSBdResidualFn)) + self.fns_bd_jacobian = malloc(n_bd_jac * sizeof(PetscDSBdJacobianFn)) + + cpdef copy_residual_from(self, int dst, PtrContainer src, int src_idx): + """Copy a residual function pointer from another container.""" + self.fns_residual[dst] = src.fns_residual[src_idx] + + cpdef copy_bcs_from(self, int dst, PtrContainer src, int src_idx): + """Copy a BC function pointer from another container.""" + self.fns_bcs[dst] = src.fns_bcs[src_idx] + + cpdef copy_jacobian_from(self, int dst, PtrContainer src, int src_idx): + """Copy a Jacobian function pointer from another container.""" + self.fns_jacobian[dst] = src.fns_jacobian[src_idx] + + cpdef copy_bd_residual_from(self, int dst, PtrContainer src, int src_idx): + """Copy a boundary residual function pointer from another container.""" + self.fns_bd_residual[dst] = src.fns_bd_residual[src_idx] + + cpdef copy_bd_jacobian_from(self, int dst, PtrContainer src, int src_idx): + """Copy a boundary Jacobian function pointer from another container.""" + self.fns_bd_jacobian[dst] = src.fns_bd_jacobian[src_idx] diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 24caecef1..550632306 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1275,7 +1275,7 @@ def solve( timestep = self.delta_t.sym if timestep != self.delta_t: - self._constitutive_model.Parameters.elastic_dt = timestep # this will force an initialisation because the functions need to be updated + self._constitutive_model.Parameters.dt_elastic = timestep # this will force an initialisation because the functions need to be updated if _force_setup: self.is_setup = False diff --git a/src/underworld3/utilities/_jitextension.py b/src/underworld3/utilities/_jitextension.py index b8b9d5c03..c2d737bcb 100644 --- a/src/underworld3/utilities/_jitextension.py +++ b/src/underworld3/utilities/_jitextension.py @@ -32,6 +32,21 @@ _ext_dict = {} +# Per-function cache: maps (fn_hash, sig_type) -> _CachedFn +_fn_cache = {} + + +@dataclass +class _CachedFn: + """Registry entry for a single cached compiled function pointer.""" + ptr_container: object # PtrContainer from the .so that compiled this fn + sig_type: str # "residual" | "jacobian" | "bcs" | "bd_residual" | "bd_jacobian" + index: int # index within that container's sig_type array + + +# Signature type names used by the per-function cache +_SIG_TYPES = ("residual", "bcs", "jacobian", "bd_residual", "bd_jacobian") + # ============================================================================ # JIT Callback Set @@ -428,6 +443,11 @@ def getext( import os + primary_field_signature = tuple( + (getattr(field, "field_id", None), getattr(field, "clean_name", None)) + for field in primary_field_list + ) + if debug_name is not None: jitname = debug_name @@ -438,33 +458,155 @@ def getext( jitname += "_" + str(len(_ext_dict.keys())) else: # Name from structured hash — function role must be preserved. - primary_field_signature = tuple( - (getattr(field, "field_id", None), getattr(field, "clean_name", None)) - for field in primary_field_list - ) jitname = abs( hash((mesh, expanded.signature(), tuple(mesh.vars.keys()), primary_field_signature)) ) - # Create the module if not in dictionary - if jitname not in _ext_dict.keys() or not cache: + # ── Fast path: whole-bundle cache hit ────────────────────────────────── + if jitname in _ext_dict and cache: + if verbose and underworld3.mpi.rank == 0: + print(f"JIT compiled module cached ... {jitname} ", flush=True) + + module = _ext_dict[jitname] + ptrobj = module.getptrobj() + + i_res = {fn: i for i, fn in enumerate(callbacks.residual)} + i_ebc = {fn: i for i, fn in enumerate(callbacks.bcs)} + i_jac = {fn: i for i, fn in enumerate(callbacks.jacobian)} + i_bd_res = {fn: i for i, fn in enumerate(callbacks.bd_residual)} + i_bd_jac = {fn: i for i, fn in enumerate(callbacks.bd_jacobian)} + + extn_fn_dict = namedtuple( + "Functions", ["res", "jac", "ebc", "bd_res", "bd_jac"], + ) + return _GextResult( + ptrobj, + extn_fn_dict(i_res, i_jac, i_ebc, i_bd_res, i_bd_jac), + constants_manifest, + ) + + # ── Per-function cache: check which individual functions are cached ── + # Build a hashable key for the constants manifest so it's part of + # every per-function hash (ensures constants[i] means the same thing). + constants_manifest_key = tuple( + (str(expr), idx) for idx, expr in constants_manifest + ) + + # Compute per-function hashes for each expression, grouped by sig_type + fn_hashes = {} # maps (sig_type, slot_index) -> hash + for sig_type, slot_fns in zip( + _SIG_TYPES, + [expanded.residual, expanded.bcs, expanded.jacobian, + expanded.bd_residual, expanded.bd_jacobian], + ): + for i, fn_expanded in enumerate(slot_fns): + fn_hashes[(sig_type, i)] = abs( + hash((mesh, fn_expanded, tuple(mesh.vars.keys()), + sig_type, constants_manifest_key, primary_field_signature)) + ) + + # Partition into cached vs new + cached_hits = {} # (sig_type, slot_index) -> _CachedFn + new_needed = {} # (sig_type, slot_index) -> original expression + for sig_type, slot_fns in zip( + _SIG_TYPES, + [callbacks.residual, callbacks.bcs, callbacks.jacobian, + callbacks.bd_residual, callbacks.bd_jacobian], + ): + for i, fn_orig in enumerate(slot_fns): + key = (sig_type, i) + fn_hash = fn_hashes[key] + cache_key = (fn_hash, sig_type) + if cache_key in _fn_cache and cache: + cached_hits[key] = _fn_cache[cache_key] + else: + new_needed[key] = fn_orig + + n_hits = len(cached_hits) + n_new = len(new_needed) + + if verbose and underworld3.mpi.rank == 0: + total = n_hits + n_new + print(f"Per-function cache: {n_hits}/{total} hits, {n_new} new", flush=True) + + # ── Compile new functions ─────────────────────────────────────────── + new_ptr = None + new_indices = {} # (sig_type, slot_index) -> index in new_ptr's arrays + + if n_new > 0: + # Build a JITCallbackSet containing ONLY the new functions, + # preserving order within each sig_type. + new_by_type = {st: [] for st in _SIG_TYPES} + new_slot_map = {st: [] for st in _SIG_TYPES} # tracks original slot indices + for (sig_type, slot_idx), fn_orig in sorted(new_needed.items()): + new_by_type[sig_type].append(fn_orig) + new_slot_map[sig_type].append(slot_idx) + + new_callbacks = JITCallbackSet( + residual=tuple(new_by_type["residual"]), + bcs=tuple(new_by_type["bcs"]), + jacobian=tuple(new_by_type["jacobian"]), + bd_residual=tuple(new_by_type["bd_residual"]), + bd_jacobian=tuple(new_by_type["bd_jacobian"]), + ) + + # Compile the new functions + new_jitname = abs(hash((jitname, "partial", n_new, time.time()))) _createext( - jitname, + new_jitname, mesh, - callbacks, + new_callbacks, primary_field_list, constants_subs_map=constants_subs_map, verbose=verbose, debug=debug, debug_name=debug_name, ) - else: - if verbose and underworld3.mpi.rank == 0: - print(f"JIT compiled module cached ... {jitname} ", flush=True) - module = _ext_dict[jitname] - ptrobj = module.getptrobj() + new_module = _ext_dict[new_jitname] + new_ptr = new_module.getptrobj() + + # Register each new function in the per-function cache + for sig_type in _SIG_TYPES: + for local_idx, slot_idx in enumerate(new_slot_map[sig_type]): + key = (sig_type, slot_idx) + fn_hash = fn_hashes[key] + cache_key = (fn_hash, sig_type) + entry = _CachedFn( + ptr_container=new_ptr, + sig_type=sig_type, + index=local_idx, + ) + _fn_cache[cache_key] = entry + cached_hits[key] = entry + + # Also register the full bundle in _ext_dict if ALL functions were new + # (common case: first compile of a solver) + if n_new > 0 and n_hits == 0: + _ext_dict[jitname] = _ext_dict[new_jitname] + + # ── Assemble PtrContainer from cached function pointers ───────────── + from underworld3.cython.petsc_types import PtrContainer + + result_ptr = PtrContainer() + counts = callbacks.counts + result_ptr.allocate(*counts) + + _copy_methods = { + "residual": result_ptr.copy_residual_from, + "bcs": result_ptr.copy_bcs_from, + "jacobian": result_ptr.copy_jacobian_from, + "bd_residual": result_ptr.copy_bd_residual_from, + "bd_jacobian": result_ptr.copy_bd_jacobian_from, + } + for sig_type, n_fns in zip(_SIG_TYPES, counts): + copy_fn = _copy_methods[sig_type] + for slot_idx in range(n_fns): + entry = cached_hits[(sig_type, slot_idx)] + copy_fn(slot_idx, entry.ptr_container, entry.index) + + # ── Build fn_dicts (unchanged from original) ──────────────────────── i_res = {fn: i for i, fn in enumerate(callbacks.residual)} i_ebc = {fn: i for i, fn in enumerate(callbacks.bcs)} i_jac = {fn: i for i, fn in enumerate(callbacks.jacobian)} @@ -472,13 +614,14 @@ def getext( i_bd_jac = {fn: i for i, fn in enumerate(callbacks.bd_jacobian)} extn_fn_dict = namedtuple( - "Functions", - ["res", "jac", "ebc", "bd_res", "bd_jac"], + "Functions", ["res", "jac", "ebc", "bd_res", "bd_jac"], ) - extensions_functions_dicts = extn_fn_dict(i_res, i_jac, i_ebc, i_bd_res, i_bd_jac) - - return _GextResult(ptrobj, extensions_functions_dicts, constants_manifest) + return _GextResult( + result_ptr, + extn_fn_dict(i_res, i_jac, i_ebc, i_bd_res, i_bd_jac), + constants_manifest, + ) @timing.routine_timer_decorator diff --git a/tests/minimal_vep_timing.py b/tests/minimal_vep_timing.py new file mode 100644 index 000000000..e03f2937b --- /dev/null +++ b/tests/minimal_vep_timing.py @@ -0,0 +1,89 @@ +"""Minimal VEP timing test — isolate where time is spent. + +Run with: pixi run -e amr-dev python tests/minimal_vep_timing.py +""" + +import time +import sympy +import underworld3 as uw +from underworld3.systems import VE_Stokes + +t0 = time.time() + +# --- Mesh --- +mesh = uw.meshing.UnstructuredSimplexBox( + minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), + cellSize=1.0 / 8, qdegree=3, +) +print(f"Mesh: {time.time() - t0:.1f}s") + +# --- Variables --- +v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, + vtype=uw.VarType.SCALAR) +print(f"Variables: {time.time() - t0:.1f}s") + +# --- Solver + constitutive model --- +stokes = VE_Stokes(mesh, velocityField=v, pressureField=p, order=1) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = 1.0 +stokes.constitutive_model.Parameters.shear_modulus = 1.0 +stokes.constitutive_model.Parameters.shear_viscosity_min = 1.0e-3 +stokes.constitutive_model.Parameters.strainrate_inv_II_min = 1.0e-10 +stokes.saddle_preconditioner = 1.0 +stokes.tolerance = 1.0e-4 +print(f"Solver setup: {time.time() - t0:.1f}s") + +# --- Yield stress: Piecewise (fault layer) --- +x, y = mesh.X +tau_y = sympy.Piecewise( + (0.3, (y >= 0.45) & (y <= 0.55)), + (1.0e6, True), +) +stokes.constitutive_model.Parameters.yield_stress = tau_y +print(f"Yield stress set: {time.time() - t0:.1f}s") + +# --- BCs --- +stokes.add_essential_bc(sympy.Matrix([0.5, 0.0]), "Top") +stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") +stokes.add_essential_bc((sympy.oo, 0.0), "Left") +stokes.add_essential_bc((sympy.oo, 0.0), "Right") +stokes.bodyforce = sympy.Matrix([0.0, 0.0]) +stokes.petsc_options["ksp_type"] = "fgmres" +print(f"BCs set: {time.time() - t0:.1f}s") + +# --- First solve (includes JIT compilation) --- +# Set dt_elastic explicitly to work around elastic_dt alias bug in VE_Stokes.solve() +t1 = time.time() +stokes.solve(timestep=0.02, zero_init_guess=True) +print(f"First solve (incl JIT): {time.time() - t1:.1f}s") + +# --- Second solve (cached JIT) --- +t2 = time.time() +stokes.solve(timestep=0.02, zero_init_guess=False) +print(f"Second solve (cached): {time.time() - t2:.1f}s") + +# --- Compare: pure VE (no yield) --- +stokes2 = VE_Stokes(mesh, velocityField=v, pressureField=p, order=1) +stokes2.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +stokes2.constitutive_model.Parameters.shear_viscosity_0 = 1.0 +stokes2.constitutive_model.Parameters.shear_modulus = 1.0 +# yield_stress defaults to sympy.oo — pure VE +stokes2.saddle_preconditioner = 1.0 +stokes2.tolerance = 1.0e-4 +stokes2.add_essential_bc(sympy.Matrix([0.5, 0.0]), "Top") +stokes2.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") +stokes2.add_essential_bc((sympy.oo, 0.0), "Left") +stokes2.add_essential_bc((sympy.oo, 0.0), "Right") +stokes2.bodyforce = sympy.Matrix([0.0, 0.0]) +stokes2.petsc_options["ksp_type"] = "fgmres" + +t3 = time.time() +stokes2.solve(timestep=0.02, zero_init_guess=True) +print(f"Pure VE first solve (incl JIT): {time.time() - t3:.1f}s") + +t4 = time.time() +stokes2.solve(timestep=0.02, zero_init_guess=False) +print(f"Pure VE second solve (cached): {time.time() - t4:.1f}s") + +print(f"\nTotal: {time.time() - t0:.1f}s") diff --git a/tests/profile_jit_phases.py b/tests/profile_jit_phases.py new file mode 100644 index 000000000..ecd12eba0 --- /dev/null +++ b/tests/profile_jit_phases.py @@ -0,0 +1,163 @@ +"""Profile JIT compilation phases — isolate where time is spent. + +Instruments: sympy derivatives, expression unwrapping, hashing, C code generation, +Cython compilation, and the actual PETSc solve. + +Run with: pixi run -e default python tests/profile_jit_phases.py +""" + +import time +import sympy +import underworld3 as uw +from underworld3.systems import VE_Stokes + +# ── Setup (fast) ────────────────────────────────────────────────────────────── + +mesh = uw.meshing.UnstructuredSimplexBox( + minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), + cellSize=1.0 / 8, qdegree=3, +) + +v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, + vtype=uw.VarType.SCALAR) + +stokes = VE_Stokes(mesh, velocityField=v, pressureField=p, order=1) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = 1.0 +stokes.constitutive_model.Parameters.shear_modulus = 1.0 +stokes.constitutive_model.Parameters.shear_viscosity_min = 1.0e-3 +stokes.constitutive_model.Parameters.strainrate_inv_II_min = 1.0e-10 +stokes.saddle_preconditioner = 1.0 +stokes.tolerance = 1.0e-4 + +x, y = mesh.X +tau_y = sympy.Piecewise( + (0.3, (y >= 0.45) & (y <= 0.55)), + (1.0e6, True), +) +stokes.constitutive_model.Parameters.yield_stress = tau_y + +stokes.add_essential_bc(sympy.Matrix([0.5, 0.0]), "Top") +stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") +stokes.add_essential_bc((sympy.oo, 0.0), "Left") +stokes.add_essential_bc((sympy.oo, 0.0), "Right") +stokes.bodyforce = sympy.Matrix([0.0, 0.0]) +stokes.petsc_options["ksp_type"] = "fgmres" + +print("Setup complete.\n") + +# ── Phase 1: Sympy derivative computation ───────────────────────────────────── + +dim = mesh.dim + +# Get residual terms (these are already built by the constitutive model) +F0 = sympy.Array(stokes.F0.sym) +F1 = sympy.Array(stokes.F1.sym) +PF0 = sympy.Array(stokes.PF0.sym) + +print(f"F0 has {len(F0.free_symbols)} free symbols, {sum(1 for _ in sympy.preorder_traversal(sympy.Matrix(F0)))} nodes") +print(f"F1 has {len(F1.free_symbols)} free symbols, {sum(1 for _ in sympy.preorder_traversal(sympy.Matrix(F1)))} nodes") + +t0 = time.time() +sympy.core.cache.clear_cache() +t_cache_clear = time.time() - t0 +print(f"\nsympy.core.cache.clear_cache(): {t_cache_clear:.3f}s") + +# UU block derivatives +t0 = time.time() +G0 = sympy.derive_by_array(F0, stokes.u.sym) +t_uu_g0 = time.time() - t0 + +t0 = time.time() +G1 = sympy.derive_by_array(F0, stokes.Unknowns.L) +t_uu_g1 = time.time() - t0 + +t0 = time.time() +G2 = sympy.derive_by_array(F1, stokes.u.sym) +t_uu_g2 = time.time() - t0 + +t0 = time.time() +G3 = sympy.derive_by_array(F1, stokes.Unknowns.L) +t_uu_g3 = time.time() - t0 + +print(f"\nderive_by_array (UU block):") +print(f" G0 (dF0/dU): {t_uu_g0:.3f}s") +print(f" G1 (dF0/dL): {t_uu_g1:.3f}s") +print(f" G2 (dF1/dU): {t_uu_g2:.3f}s") +print(f" G3 (dF1/dL): {t_uu_g3:.3f}s") +print(f" Total UU: {t_uu_g0+t_uu_g1+t_uu_g2+t_uu_g3:.3f}s") + +# UP block +t0 = time.time() +sympy.derive_by_array(F0, stokes.p.sym) +sympy.derive_by_array(F0, stokes._G) +sympy.derive_by_array(F1, stokes.p.sym) +sympy.derive_by_array(F1, stokes._G) +t_up = time.time() - t0 +print(f"\nderive_by_array (UP block): {t_up:.3f}s") + +# PU block +t0 = time.time() +sympy.derive_by_array(PF0, stokes.u.sym) +sympy.derive_by_array(PF0, stokes.Unknowns.L) +t_pu = time.time() - t0 +print(f"derive_by_array (PU block): {t_pu:.3f}s") + +print(f"\nTotal derivative computation: {t_uu_g0+t_uu_g1+t_uu_g2+t_uu_g3+t_up+t_pu:.3f}s") + +# ── Phase 2: getext (unwrap + hash + compile) ──────────────────────────────── + +# Now let the solver do its full setup and time it +print(f"\n--- Full solver._setup_pointwise_functions + getext ---") +stokes.is_setup = False +stokes.constitutive_model._solver_is_setup = False +stokes.DFDt.psi_fn = stokes.constitutive_model.flux.T + +t0 = time.time() +stokes._setup_pointwise_functions(verbose=True) +t_setup_pw = time.time() - t0 +print(f"_setup_pointwise_functions: {t_setup_pw:.3f}s") + +t0 = time.time() +stokes._setup_discretisation(verbose=True) +t_setup_disc = time.time() - t0 +print(f"_setup_discretisation: {t_setup_disc:.3f}s") + +t0 = time.time() +stokes._setup_solver(verbose=True) +t_setup_solver = time.time() - t0 +print(f"_setup_solver: {t_setup_solver:.3f}s") + +# ── Phase 3: DFDt update + actual solve ─────────────────────────────────────── + +print(f"\n--- DFDt + solve ---") +t0 = time.time() +stokes.DFDt.update_pre_solve(0.02, verbose=True) +t_dfdt_pre = time.time() - t0 +print(f"DFDt.update_pre_solve: {t_dfdt_pre:.3f}s") + +t0 = time.time() +# Call the parent (Stokes) solve directly to skip VE_Stokes overhead +from underworld3.systems.solvers import SNES_Stokes_SaddlePt +SNES_Stokes_SaddlePt.solve(stokes, zero_init_guess=True, _force_setup=False, verbose=True) +t_solve = time.time() - t0 +print(f"PETSc SNES solve: {t_solve:.3f}s") + +t0 = time.time() +stokes.DFDt.update_post_solve(0.02, verbose=True) +t_dfdt_post = time.time() - t0 +print(f"DFDt.update_post_solve: {t_dfdt_post:.3f}s") + +# ── Summary ─────────────────────────────────────────────────────────────────── + +print(f"\n{'='*50}") +print(f"SUMMARY") +print(f"{'='*50}") +print(f"Derivative computation: {t_uu_g0+t_uu_g1+t_uu_g2+t_uu_g3+t_up+t_pu:.1f}s") +print(f"_setup_pointwise_functions: {t_setup_pw:.1f}s (includes derivatives + getext)") +print(f"_setup_discretisation: {t_setup_disc:.1f}s") +print(f"_setup_solver: {t_setup_solver:.1f}s") +print(f"DFDt pre-solve: {t_dfdt_pre:.1f}s") +print(f"PETSc solve: {t_solve:.1f}s") +print(f"DFDt post-solve: {t_dfdt_post:.1f}s") From f97bdaccebe667b9aee74e7d75b210110b0c3744 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 25 Mar 2026 22:42:45 +1100 Subject: [PATCH 009/537] =?UTF-8?q?Fix=20elastic=5Fdt=20=E2=86=92=20dt=5Fe?= =?UTF-8?q?lastic=20parameter=20name=20in=20VE=5FStokes.solve()?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The parameter was renamed to dt_elastic but VE_Stokes.solve() still referenced the old name, causing AttributeError on first solve. Underworld development team with AI support from Claude Code --- src/underworld3/systems/solvers.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 24caecef1..550632306 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1275,7 +1275,7 @@ def solve( timestep = self.delta_t.sym if timestep != self.delta_t: - self._constitutive_model.Parameters.elastic_dt = timestep # this will force an initialisation because the functions need to be updated + self._constitutive_model.Parameters.dt_elastic = timestep # this will force an initialisation because the functions need to be updated if _force_setup: self.is_setup = False From 209a38c6e95d1b74b2892d55efa3b3f4af59e416 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 26 Mar 2026 12:18:26 +1100 Subject: [PATCH 010/537] Harden JITCallbackSet: coerce slots to tuples, remove unused imports - Add __post_init__ to coerce list/None inputs to tuples, ensuring immutability and hashability (prevents TypeError in flat()/signature()) - Remove unused List, Tuple imports from typing Addresses Copilot review comments on PR #93. Underworld development team with AI support from Claude Code --- src/underworld3/utilities/_jitextension.py | 11 ++++++++++- 1 file changed, 10 insertions(+), 1 deletion(-) diff --git a/src/underworld3/utilities/_jitextension.py b/src/underworld3/utilities/_jitextension.py index b8b9d5c03..a05dbcbdd 100644 --- a/src/underworld3/utilities/_jitextension.py +++ b/src/underworld3/utilities/_jitextension.py @@ -1,4 +1,4 @@ -from typing import List, Optional, Tuple +from typing import Optional import subprocess from xmlrpc.client import boolean import sympy @@ -71,6 +71,15 @@ class JITCallbackSet: bd_residual: tuple = () bd_jacobian: tuple = () + def __post_init__(self): + """Coerce all slots to tuples for immutability and hashability.""" + for field in ("residual", "bcs", "jacobian", "bd_residual", "bd_jacobian"): + val = getattr(self, field) + if val is None: + object.__setattr__(self, field, ()) + elif not isinstance(val, tuple): + object.__setattr__(self, field, tuple(val)) + def flat(self) -> tuple: """Concatenate all slots into a single ordered tuple. From f45757355a520bd21147939a89431939adf2f733 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 18 Mar 2026 20:38:12 +1100 Subject: [PATCH 011/537] Always clean build cache in ./uw build The setuptools build/ directory (lib.*, temp.*, bdist.*) persists across runs and silently reuses stale .py artefacts when only Python sources change. --no-cache-dir only bypasses pip's wheel cache, not setuptools. Underworld development team with AI support from Claude Code --- uw | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/uw b/uw index fd37fe077..c4d52af79 100755 --- a/uw +++ b/uw @@ -162,8 +162,12 @@ run_build() { fi if [ "$need_clean" = true ]; then echo " PETSc target changed — cleaning build cache..." - rm -rf "$SCRIPT_DIR"/build/lib.* "$SCRIPT_DIR"/build/temp.* fi + # Always clean the setuptools build directory. --no-cache-dir only + # bypasses pip's wheel cache; the build/ tree (Cython .c files, + # compiled .so objects) persists across runs and silently reuses + # stale artefacts when only .py sources change. + rm -rf "$SCRIPT_DIR"/build/lib.* "$SCRIPT_DIR"/build/temp.* "$SCRIPT_DIR"/build/bdist.* mkdir -p "$SCRIPT_DIR/build" echo "$current_target" > "$petsc_marker" From 1415fe503fe0448dd303176822bab1c7136a1397 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 18 Mar 2026 20:38:31 +1100 Subject: [PATCH 012/537] Explicit stress history for VE_Stokes solver MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Replaces the old approach where SemiLagrangian re-evaluated the stress formula (psi_fn) at upstream points — which broke on order transitions because UWexpression η_eff evaluates live and the formula structure changed between order-1 and order-2. New architecture: store the actual stress tensor after each solve, advect only stored values. The constitutive formula is used only during the PETSc solve (JIT) and the post-solve stress projection. VE_Stokes.solve() flow per timestep: 1. advect_history() — pure advection of stored stress to upstream 2. PETSc solve using advected σ*, σ** 3. Save advected σ*, project constitutive_model.flux → psi_star[0] 4. Shift: psi_star[1] ← saved σ* (chained characteristic tracing) Additional fixes: - effective_order property on constitutive model (checks DDt startup) - effective_order formula: max(1, n_solves) not max(1, n_solves+1) - VE_Stokes re-setups JIT when effective_order transitions - elastic_dt → dt_elastic typo fix in VE_Stokes.solve() - Removed sympy.simplify() from 5 hot-path methods (caused hangs) - stress_deviator_stored property for post-processing access - TODO annotation for tensor vtype inference in _function.pyx Validated: Maxwell shear box test - Order-1: ~3% RMS error with dt/t_r=0.1 - Order-2: ~1% RMS, 0.09% final error (16× better than order-1) - Performance: constant 0.4-0.8s/step (was 5-10s with linear growth) Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 31 +++--- src/underworld3/function/_function.pyx | 6 ++ src/underworld3/systems/ddt.py | 136 ++++++++++++++++++++++++- src/underworld3/systems/solvers.py | 84 +++++++++++++-- 4 files changed, 234 insertions(+), 23 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 8d02acde9..205f6ec74 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -971,12 +971,12 @@ def viscosity(self): # Keep this as an sub-expression for clarity if inner_self.shear_viscosity_min.sym != -sympy.oo: - self._plastic_eff_viscosity._sym = sympy.simplify( - sympy.Max(effective_viscosity, inner_self.shear_viscosity_min) + self._plastic_eff_viscosity._sym = sympy.Max( + effective_viscosity, inner_self.shear_viscosity_min ) else: - self._plastic_eff_viscosity._sym = sympy.simplify(effective_viscosity) + self._plastic_eff_viscosity._sym = effective_viscosity # Returns an expression that has a different description return self._plastic_eff_viscosity @@ -1201,7 +1201,7 @@ def ve_effective_viscosity(inner_self): # Note, 1st order only here but we should add higher order versions of this # 1st Order version (default) - if inner_self._owning_model.order != 2: + if inner_self._owning_model.effective_order != 2: el_eff_visc = ( inner_self.shear_viscosity_0 * inner_self.shear_modulus @@ -1252,6 +1252,19 @@ def order(self, value): self._reset() return + @property + def effective_order(self): + """Effective order accounting for DDt history startup. + + During the first few timesteps, the DDt may not have enough history + to support the requested order. This property returns the lower of + the requested order and the DDt's effective order (which ramps from + 1 to self.order as history accumulates). + """ + if self.Unknowns is not None and self.Unknowns.DFDt is not None: + return min(self._order, self.Unknowns.DFDt.effective_order) + return self._order + # The following should have no setters @property def stress_star(self): @@ -1287,7 +1300,7 @@ def E_eff(self): if self.Unknowns.DFDt is not None: if self.is_elastic: - if self.order != 2: + if self.effective_order != 2: stress_star = self.Unknowns.DFDt.psi_star[0].sym E += stress_star / ( 2 * self.Parameters.dt_elastic * self.Parameters.shear_modulus @@ -1468,8 +1481,6 @@ def flux(self): # plastic_scale_factor = sympy.Max(1, self.plastic_overshoot()) # stress /= plastic_scale_factor - stress = sympy.simplify(stress) - return stress def stress_projection(self): @@ -1492,8 +1503,6 @@ def stress_projection(self): / (self.Parameters.dt_elastic * self.Parameters.shear_modulus) ) - stress = sympy.simplify(stress) - return stress def stress(self): @@ -1508,7 +1517,7 @@ def stress(self): if self.Unknowns.DFDt is not None: if self.is_elastic: - if self.order != 2: + if self.effective_order != 2: stress_star = self.Unknowns.DFDt.psi_star[0].sym stress += ( 2 @@ -1534,8 +1543,6 @@ def stress(self): ) ) - stress = sympy.simplify(stress) - return stress # def eff_edot(self): diff --git a/src/underworld3/function/_function.pyx b/src/underworld3/function/_function.pyx index d9a0b825a..98f218e3b 100644 --- a/src/underworld3/function/_function.pyx +++ b/src/underworld3/function/_function.pyx @@ -548,6 +548,12 @@ def _project_to_work_variable(expr, mesh, smoothing=1e-6): import underworld3 as uw # Handle matrix expressions - need multi-component work variable + # TODO(BUG): This fails for dim×dim matrices (e.g. 2×2 stress tensor) + # because MeshVariable can't infer vtype from num_components=4 (flat int). + # Needs: pass num_components=(rows,cols) with vtype=TENSOR, and use + # Tensor_Projection instead of per-component scalar Projection. + # Currently, callers like SemiLagrangian.update_pre_solve fall back to + # their own projection solver via except-clause when this fails. if hasattr(expr, 'shape') and expr.shape != (1, 1): rows, cols = expr.shape n_components = rows * cols diff --git a/src/underworld3/systems/ddt.py b/src/underworld3/systems/ddt.py index 25e2e3e0f..9e20739b8 100644 --- a/src/underworld3/systems/ddt.py +++ b/src/underworld3/systems/ddt.py @@ -445,7 +445,9 @@ def effective_order(self): startup, ``effective_order`` ramps from 1 to ``self.order`` as successive solves populate the history slots with distinct values. """ - return min(self.order, max(1, self._n_solves_completed + 1)) + # BDF-k requires k completed solves to have k distinct history values. + # With 0 or 1 completed solves → order 1. Order 2 needs ≥2 solves. + return min(self.order, max(1, self._n_solves_completed)) def update_history_fn(self): r"""Copy current :math:`\psi` to the first history slot ``psi_star[0]``.""" @@ -763,7 +765,9 @@ def effective_order(self): startup, ``effective_order`` ramps from 1 to ``self.order`` as successive solves populate the history slots with distinct values. """ - return min(self.order, max(1, self._n_solves_completed + 1)) + # BDF-k requires k completed solves to have k distinct history values. + # With 0 or 1 completed solves → order 1. Order 2 needs ≥2 solves. + return min(self.order, max(1, self._n_solves_completed)) def update_history_fn(self): r"""Copy current :math:`\psi` to ``psi_star[0]`` via evaluation or projection.""" @@ -1158,7 +1162,9 @@ def effective_order(self): startup, ``effective_order`` ramps from 1 to ``self.order`` as successive solves populate the history slots with distinct values. """ - return min(self.order, max(1, self._n_solves_completed + 1)) + # BDF-k requires k completed solves to have k distinct history values. + # With 0 or 1 completed solves → order 1. Order 2 needs ≥2 solves. + return min(self.order, max(1, self._n_solves_completed)) def initialise_history(self): r"""Initialize all history slots to the current value of :math:`\psi`. @@ -1229,6 +1235,7 @@ def update_post_solve( if self._n_solves_completed < self.order: self._n_solves_completed += 1 + return def update_pre_solve( @@ -1595,6 +1602,121 @@ def update_pre_solve( return + def advect_history(self, dt, evalf=False, verbose=False): + """Advect all psi_star history levels to upstream positions. + + Pure advection only — no copy-down, no psi_fn evaluation. + Each psi_star[i] is sampled at positions traced back by Δt along + the velocity characteristics, and the result is written back in place. + + Used by VE_Stokes for explicit stress history management where the + actual stress is stored in psi_star[0] after each solve. This method + advects those stored values to upstream positions before the next solve. + + Parameters + ---------- + dt : float or sympy expression + Timestep for characteristic tracing. + evalf : bool + Force numerical evaluation. + verbose : bool + Verbose output. + """ + + if not self._history_initialised: + self.initialise_history() + + # --- Coordinate setup (shared with update_pre_solve) --- + from underworld3.utilities.unit_aware_array import UnitAwareArray + + psi_star_0_coords = self.psi_star[0].coords + if hasattr(psi_star_0_coords, "magnitude"): + psi_star_0_coords_nd = uw.non_dimensionalise(psi_star_0_coords) + if isinstance(psi_star_0_coords_nd, UnitAwareArray): + psi_star_0_coords_nd = np.array(psi_star_0_coords_nd) + elif hasattr(psi_star_0_coords_nd, 'magnitude'): + psi_star_0_coords_nd = psi_star_0_coords_nd.magnitude + else: + psi_star_0_coords_nd = psi_star_0_coords + + cellid = self.mesh.get_closest_cells(psi_star_0_coords_nd) + centroid_coords = self.mesh._centroids[cellid] + shift = 0.001 + node_coords_nd = (1.0 - shift) * psi_star_0_coords_nd + shift * centroid_coords + + # --- Unit handling for dt --- + model = uw.get_default_model() + coords_template = self.psi_star[0].coords + has_units = hasattr(coords_template, "magnitude") or hasattr(coords_template, "_magnitude") + + if has_units: + dt_for_calc = dt.to("second") if hasattr(dt, "to") else dt + else: + if hasattr(dt, "magnitude") or hasattr(dt, "value"): + dt_nondim = uw.non_dimensionalise(dt, model) + if hasattr(dt_nondim, "magnitude"): + dt_for_calc = float(dt_nondim.magnitude) + elif hasattr(dt_nondim, "value"): + dt_for_calc = float(dt_nondim.value) + else: + dt_for_calc = float(dt_nondim) + else: + dt_for_calc = dt + + # --- Advect each history level (RK2 midpoint method) --- + for i in range(self.order - 1, -1, -1): + # Evaluate velocity at node positions + v_result = uw.function.evaluate(self.V_fn, node_coords_nd) + if isinstance(v_result, UnitAwareArray): + v_at_node_pts = v_result[:, 0, :] + if not isinstance(v_at_node_pts, UnitAwareArray): + v_at_node_pts = UnitAwareArray(v_at_node_pts, units=v_result.units) + else: + v_at_node_pts = v_result[:, 0, :] + + # Non-dimensionalize velocities if needed + if not has_units and isinstance(v_at_node_pts, UnitAwareArray): + v_nondim = uw.non_dimensionalise(v_at_node_pts, model) + v_at_node_pts = np.array(v_nondim) if isinstance(v_nondim, UnitAwareArray) else v_nondim + + coords = self.psi_star[i].coords + if not has_units and isinstance(coords, UnitAwareArray): + coords = np.array(coords) + + # RK2: midpoint velocity + mid_pt_coords = coords - v_at_node_pts * (0.5 * dt_for_calc) + v_mid_result = uw.function.global_evaluate(self.V_fn, mid_pt_coords) + if isinstance(v_mid_result, UnitAwareArray): + v_at_mid_pts = v_mid_result[:, 0, :] + if not isinstance(v_at_mid_pts, UnitAwareArray): + v_at_mid_pts = UnitAwareArray(v_at_mid_pts, units=v_mid_result.units) + else: + v_at_mid_pts = v_mid_result[:, 0, :] + + if not has_units and isinstance(v_at_mid_pts, UnitAwareArray): + v_nondim = uw.non_dimensionalise(v_at_mid_pts, model) + v_at_mid_pts = np.array(v_nondim) if isinstance(v_nondim, UnitAwareArray) else v_nondim + + # Upstream position + end_pt_coords = coords - v_at_mid_pts * dt_for_calc + + # Sample psi_star[i] at upstream position + expr_to_evaluate = self.psi_star[i].sym + if hasattr(expr_to_evaluate, 'shape') and expr_to_evaluate.shape == (1, 1): + expr_to_evaluate = expr_to_evaluate[0, 0] + + value_at_end_points = uw.function.global_evaluate( + expr_to_evaluate, end_pt_coords, + ) + + psi_star_units = self.psi_star[i].units + if psi_star_units is not None and not isinstance(value_at_end_points, UnitAwareArray): + value_at_end_points = UnitAwareArray(value_at_end_points, units=psi_star_units) + + self.psi_star[i].array[...] = value_at_end_points + + return + def bdf(self, order=None): r"""Backward differentiation approximation of the time-derivative of :math:`\psi`. @@ -1773,7 +1895,9 @@ def _object_viewer(self): @property def effective_order(self): """Current effective BDF order, accounting for history startup.""" - return min(self.order, max(1, self._n_solves_completed + 1)) + # BDF-k requires k completed solves to have k distinct history values. + # With 0 or 1 completed solves → order 1. Order 2 needs ≥2 solves. + return min(self.order, max(1, self._n_solves_completed)) def initialise_history(self): r"""Initialize all history slots to the current value of :math:`\psi`. @@ -2067,7 +2191,9 @@ def _object_viewer(self): @property def effective_order(self): """Current effective BDF order, accounting for history startup.""" - return min(self.order, max(1, self._n_solves_completed + 1)) + # BDF-k requires k completed solves to have k distinct history values. + # With 0 or 1 completed solves → order 1. Order 2 needs ≥2 solves. + return min(self.order, max(1, self._n_solves_completed)) def initialise_history(self): r"""Initialize all history slots to the current value of :math:`\psi`. diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 550632306..8d86f10d7 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1246,6 +1246,20 @@ def delta_t(self): """Elastic timestep from the constitutive model.""" return self.constitutive_model.Parameters.dt_elastic + @property + def stress_deviator_stored(self): + r"""Deviatoric stress from the most recent solve (stored in history). + + Returns the actual projected stress from psi_star[0], which is + stored after each solve. Use this for post-processing, + visualization, and quantitative measurement. + + Note: the base ``stress_deviator`` property returns the constitutive + formula (needed for JIT compilation). For VE problems, always use + ``stress_deviator_stored`` to read the solved stress. + """ + return self.DFDt.psi_star[0].sym + ## Solver needs to update the stress history terms as well as call the SNES solve: @timing.routine_timer_decorator @@ -1274,12 +1288,24 @@ def solve( if timestep is None: timestep = self.delta_t.sym - if timestep != self.delta_t: - self._constitutive_model.Parameters.dt_elastic = timestep # this will force an initialisation because the functions need to be updated + # dt_elastic is a constitutive parameter (relaxation timescale) — + # never overwritten by solve(). The advection timestep (for departure + # point tracing) and the elastic relaxation timescale are independent. if _force_setup: self.is_setup = False + # Re-setup when effective_order changes (e.g. DDt history ramp-up + # from order 1 to order 2). The JIT-compiled pointwise functions + # depend on the order used in the constitutive model. + _current_eff_order = self.constitutive_model.effective_order + if not hasattr(self, '_prev_effective_order'): + self._prev_effective_order = None + if _current_eff_order != self._prev_effective_order: + self.is_setup = False + self.constitutive_model._solver_is_setup = False + self._prev_effective_order = _current_eff_order + if not self.constitutive_model._solver_is_setup: self.is_setup = False self.DFDt.psi_fn = self.constitutive_model.flux.T @@ -1289,11 +1315,20 @@ def solve( self._setup_discretisation(verbose) self._setup_solver(verbose) + # --- Explicit stress history management --- + # + # 1. ADVECT: trace psi_star values to upstream positions along + # characteristics. psi_star[0] contains the actual stress from + # the previous solve (stored by step 4 below). After advection, + # psi_star[0] = σ* (previous stress at upstream) and + # psi_star[1] = σ** (stress from 2 steps ago, double-traced). + if uw.mpi.rank == 0 and verbose: - print(f"VE Stokes solver - pre-solve DFDt update", flush=True) + print(f"VE Stokes solver - advect stress history", flush=True) - # Update SemiLagrange Flux terms - self.DFDt.update_pre_solve(timestep, verbose=verbose, evalf=evalf) + self.DFDt.advect_history(timestep, verbose=verbose, evalf=evalf) + + # 2. SOLVE: PETSc uses the advected σ*, σ** via the constitutive model if uw.mpi.rank == 0 and verbose: print(f"VE Stokes solver - solve Stokes flow", flush=True) @@ -1305,8 +1340,45 @@ def solve( picard=0, ) + # 3. STORE ACTUAL STRESS and SHIFT HISTORY. + # + # After advection + solve: + # psi_star[0] = advected σ* (used by the solver) + # psi_star[1] = advected σ** (used by the solver) + # + # We need to: + # a) Project actual stress → psi_star[0] (while σ*, σ** are intact) + # b) Save the advected σ* into psi_star[1] for next step's σ** + # (chained characteristic tracing) + # + # The projection reads psi_star[0..1] via stress_deviator, so we + # must project BEFORE shifting. Then save the advected σ* and + # overwrite psi_star[0] with the projected stress. + if uw.mpi.rank == 0 and verbose: - print(f"VEP Stokes solver - post-solve DFDt update", flush=True) + print(f"VE Stokes solver - store stress and shift history", flush=True) + + # Save advected σ* before anything modifies psi_star[0] + import numpy as np + _advected_sigma_star = np.copy(self.DFDt.psi_star[0].array[...]) + + # Project actual stress into psi_star[0] + # Uses the constitutive formula (not the stored values property) so + # that σ* and σ** from psi_star are read correctly during projection. + self.DFDt._psi_star_projection_solver.uw_function = self.constitutive_model.flux + self.DFDt._psi_star_projection_solver.smoothing = 0.0 + self.DFDt._psi_star_projection_solver.solve(verbose=verbose) + + # Now psi_star[0] = projected τ (actual stress from this solve) + # Shift: psi_star[1] ← saved advected σ* (for chained tracing next step) + for i in range(self.DFDt.order - 1, 0, -1): + if i == 1: + self.DFDt.psi_star[i].array[...] = _advected_sigma_star + else: + # For order > 2, shift higher levels down + self.DFDt.psi_star[i].array[...] = self.DFDt.psi_star[i - 1].array[...] + + # 5. BOOKKEEPING self.DFDt.update_post_solve(timestep, verbose=verbose, evalf=evalf) From ceb5216619d499f7e6276639bc0e098681a0490c Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 18 Mar 2026 20:38:41 +1100 Subject: [PATCH 013/537] Add VE shear box validation tests MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Pytest test (test_1051_VE_shear_box.py) validates Maxwell viscoelastic shear against analytical solution σ_xy = η·γ̇·(1 - exp(-t/t_r)). Tests order-1 convergence, order-2 convergence, order-2 > order-1, and monotonic approach to steady state. Quick validation scripts for development use: - run_ve_shear_quick.py: 10-step order-1 smoke test - run_ve_shear_order2_quick.py: 20-step order-2 with timing - run_ve_shear_validation.py: full comparison of both orders - run_ve_order2_debug.py: traces psi_star values per step Underworld development team with AI support from Claude Code --- tests/run_ve_order2_debug.py | 81 +++++++++++++ tests/run_ve_shear_order2_quick.py | 48 ++++++++ tests/run_ve_shear_quick.py | 48 ++++++++ tests/run_ve_shear_validation.py | 112 ++++++++++++++++++ tests/test_1051_VE_shear_box.py | 181 +++++++++++++++++++++++++++++ 5 files changed, 470 insertions(+) create mode 100644 tests/run_ve_order2_debug.py create mode 100644 tests/run_ve_shear_order2_quick.py create mode 100644 tests/run_ve_shear_quick.py create mode 100644 tests/run_ve_shear_validation.py create mode 100644 tests/test_1051_VE_shear_box.py diff --git a/tests/run_ve_order2_debug.py b/tests/run_ve_order2_debug.py new file mode 100644 index 000000000..286b73595 --- /dev/null +++ b/tests/run_ve_order2_debug.py @@ -0,0 +1,81 @@ +"""Debug order-2 VE: trace psi_star values at each step.""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw + +ETA, MU, V0, H, W = 1.0, 1.0, 0.5, 1.0, 2.0 +dt = 0.1 +gamma_dot = 2.0 * V0 / H + +mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), +) +v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + +stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=2) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA +stokes.constitutive_model.Parameters.shear_modulus = MU +stokes.constitutive_model.Parameters.dt_elastic = dt + +stokes.add_dirichlet_bc((V0, 0.0), "Top") +stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") +stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") +stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") +stokes.tolerance = 1.0e-6 + +Stress = uw.discretisation.MeshVariable( + "Stress", mesh, (2, 2), vtype=uw.VarType.SYM_TENSOR, degree=2, continuous=True, +) +work = uw.discretisation.MeshVariable("W", mesh, 1, degree=2) +sigma_proj = uw.systems.Tensor_Projection(mesh, tensor_Field=Stress, scalar_Field=work) + +ddt = stokes.DFDt +centre = np.array([[0.0, 0.0]]) + +time_phys = 0.0 +for step in range(5): + eff_order = stokes.constitutive_model.effective_order + + # Read psi_star values at centre BEFORE solve + psi0_pre = uw.function.evaluate(ddt.psi_star[0].sym[0, 1], centre) + psi1_pre = uw.function.evaluate(ddt.psi_star[1].sym[0, 1], centre) + psi0_val = float(psi0_pre.flatten()[0]) + psi1_val = float(psi1_pre.flatten()[0]) + + # Check psi_fn formula + psi_fn_01 = str(stokes.DFDt.psi_fn[0, 1]) + has_2star = "**" in psi_fn_01 or "psi_star" in psi_fn_01 + + t0 = timer.time() + stokes.solve(zero_init_guess=False, evalf=False) + solve_t = timer.time() - t0 + + psi_fn_01_post = str(stokes.DFDt.psi_fn[0, 1]) + print(f" psi_fn[0,1] BEFORE solve: {psi_fn_01[:100]}...") + print(f" psi_fn[0,1] AFTER solve: {psi_fn_01_post[:100]}...") + time_phys += dt + + # Read psi_star AFTER solve (after update_post_solve) + psi0_post = uw.function.evaluate(ddt.psi_star[0].sym[0, 1], centre) + psi1_post = uw.function.evaluate(ddt.psi_star[1].sym[0, 1], centre) + psi0_post_val = float(psi0_post.flatten()[0]) + psi1_post_val = float(psi1_post.flatten()[0]) + + sigma_proj.uw_function = stokes.stress_deviator + sigma_proj.solve() + val = uw.function.evaluate(Stress.sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + ana = ETA * gamma_dot * (1.0 - np.exp(-time_phys * MU / ETA)) + + print(f"step {step} eff_order={eff_order} t={time_phys:.2f} solve={solve_t:.1f}s") + print(f" PRE: psi_star[0]_xy={psi0_val:.6f} psi_star[1]_xy={psi1_val:.6f}") + print(f" POST: psi_star[0]_xy={psi0_post_val:.6f} psi_star[1]_xy={psi1_post_val:.6f}") + print(f" sigma_xy={sigma_xy:.6f} analytical={ana:.6f} " + f"rel_err={abs(sigma_xy - ana) / ana:.3e}") + print() + +print("Done") diff --git a/tests/run_ve_shear_order2_quick.py b/tests/run_ve_shear_order2_quick.py new file mode 100644 index 000000000..9e7d6d8c8 --- /dev/null +++ b/tests/run_ve_shear_order2_quick.py @@ -0,0 +1,48 @@ +"""Quick order-2 VE shear box test — read stress from psi_star[0].""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw + +ETA, MU, V0, H, W = 1.0, 1.0, 0.5, 1.0, 2.0 +dt = 0.1 +gamma_dot = 2.0 * V0 / H + +mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), +) +v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + +stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=2) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA +stokes.constitutive_model.Parameters.shear_modulus = MU +stokes.constitutive_model.Parameters.dt_elastic = dt + +stokes.add_dirichlet_bc((V0, 0.0), "Top") +stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") +stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") +stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") +stokes.tolerance = 1.0e-6 + +centre = np.array([[0.0, 0.0]]) +ddt = stokes.DFDt + +time_phys = 0.0 +for step in range(20): + eff = stokes.constitutive_model.effective_order + t0 = timer.time() + stokes.solve(zero_init_guess=False, evalf=False) + solve_t = timer.time() - t0 + time_phys += dt + + val = uw.function.evaluate(ddt.psi_star[0].sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + ana = ETA * gamma_dot * (1.0 - np.exp(-time_phys * MU / ETA)) + print(f"step {step:2d} eff={eff} t={time_phys:.2f} solve={solve_t:.1f}s " + f"sigma_xy={sigma_xy:.6f} analytical={ana:.6f} " + f"rel_err={abs(sigma_xy - ana) / ana:.3e}") + +print("Done") diff --git a/tests/run_ve_shear_quick.py b/tests/run_ve_shear_quick.py new file mode 100644 index 000000000..6be238580 --- /dev/null +++ b/tests/run_ve_shear_quick.py @@ -0,0 +1,48 @@ +"""Quick order-1 VE shear box validation (10 steps).""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw + +ETA, MU, V0, H, W = 1.0, 1.0, 0.5, 1.0, 2.0 +dt = 0.1 +gamma_dot = 2.0 * V0 / H + +mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), +) +v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + +stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=1) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA +stokes.constitutive_model.Parameters.shear_modulus = MU +stokes.constitutive_model.Parameters.dt_elastic = dt + +stokes.add_dirichlet_bc((V0, 0.0), "Top") +stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") +stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") +stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") +stokes.tolerance = 1.0e-6 + +centre = np.array([[0.0, 0.0]]) +ddt = stokes.DFDt + +time_phys = 0.0 +for step in range(10): + t0 = timer.time() + stokes.solve(zero_init_guess=False, evalf=False) + solve_t = timer.time() - t0 + time_phys += dt + + # Read stress directly from psi_star[0] (the projected actual stress) + val = uw.function.evaluate(ddt.psi_star[0].sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + ana = ETA * gamma_dot * (1.0 - np.exp(-time_phys * MU / ETA)) + print(f"step {step} t={time_phys:.2f} solve={solve_t:.1f}s " + f"sigma_xy={sigma_xy:.6f} analytical={ana:.6f} " + f"rel_err={abs(sigma_xy - ana) / ana:.3e}") + +print("Done") diff --git a/tests/run_ve_shear_validation.py b/tests/run_ve_shear_validation.py new file mode 100644 index 000000000..759616edb --- /dev/null +++ b/tests/run_ve_shear_validation.py @@ -0,0 +1,112 @@ +"""Quick validation script for the VE shear box test. + +Run with: pixi run -e amr-dev python tests/run_ve_shear_validation.py +""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw + + +def maxwell_xy(t, eta, mu, gamma_dot): + """Analytical σ_xy for Maxwell material under constant shear rate.""" + return eta * gamma_dot * (1.0 - np.exp(-t * mu / eta)) + + +def run(order, n_steps, dt_ratio): + ETA, MU, V0, H, W = 1.0, 1.0, 0.5, 1.0, 2.0 + t_relax = ETA / MU + dt = dt_ratio * t_relax + gamma_dot = 2.0 * V0 / H + + mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), + minCoords=(-W / 2, -H / 2), + maxCoords=(W / 2, H / 2), + ) + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=order) + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA + stokes.constitutive_model.Parameters.shear_modulus = MU + stokes.constitutive_model.Parameters.dt_elastic = dt + + stokes.add_dirichlet_bc((V0, 0.0), "Top") + stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + stokes.tolerance = 1.0e-6 + + Stress = uw.discretisation.MeshVariable( + "Stress", mesh, (2, 2), + vtype=uw.VarType.SYM_TENSOR, degree=2, continuous=True, + ) + work = uw.discretisation.MeshVariable("W", mesh, 1, degree=2) + sigma_proj = uw.systems.Tensor_Projection(mesh, tensor_Field=Stress, scalar_Field=work) + + times, num, ana = [], [], [] + time_phys = 0.0 + + for step in range(n_steps): + t0 = timer.time() + stokes.solve(zero_init_guess=False, evalf=False) + solve_time = timer.time() - t0 + time_phys += dt + + sigma_proj.uw_function = stokes.stress_deviator + sigma_proj.solve() + + val = uw.function.evaluate(Stress.sym[0, 1], np.array([[0.0, 0.0]])) + sigma_xy = float(val.flatten()[0]) + ana_val = maxwell_xy(time_phys, ETA, MU, gamma_dot) + + times.append(time_phys) + num.append(sigma_xy) + ana.append(ana_val) + + rel_err = abs(sigma_xy - ana_val) / max(ana_val, 1e-10) + print(f" step {step:3d} t={time_phys:.2f} solve={solve_time:.1f}s " + f"sigma_xy={sigma_xy:.6f} analytical={ana_val:.6f} rel_err={rel_err:.3e}") + + del stokes, mesh + return np.array(times), np.array(num), np.array(ana) + + +if __name__ == "__main__": + print("=== Order 1, dt/tr=0.1, 20 steps ===") + t0 = timer.time() + t, n, a = run(1, 20, 0.1) + wall = timer.time() - t0 + mask = a > 0.01 * a[-1] + rms = np.sqrt(np.mean(((n[mask] - a[mask]) / a[mask]) ** 2)) + final_err = abs(n[-1] - a[-1]) / a[-1] + print(f" Wall time: {wall:.0f}s") + print(f" Final rel error: {final_err:.4e}") + print(f" RMS rel error: {rms:.4e}") + print() + + print("=== Order 2, dt/tr=0.1, 20 steps ===") + t0 = timer.time() + t2, n2, a2 = run(2, 20, 0.1) + wall2 = timer.time() - t0 + mask2 = a2 > 0.01 * a2[-1] + rms2 = np.sqrt(np.mean(((n2[mask2] - a2[mask2]) / a2[mask2]) ** 2)) + final_err2 = abs(n2[-1] - a2[-1]) / a2[-1] + print(f" Wall time: {wall2:.0f}s") + print(f" Final rel error: {final_err2:.4e}") + print(f" RMS rel error: {rms2:.4e}") + print() + + viscous_limit = 1.0 + print(f"Steady-state check (order 1, t=2.0):") + print(f" sigma_xy = {n[-1]:.6f}, viscous limit = {viscous_limit:.6f}, " + f"rel error = {abs(n[-1] - viscous_limit) / viscous_limit:.4e}") + print() + + if rms2 < rms: + print("PASS: Order 2 has smaller RMS error than order 1") + else: + print("FAIL: Order 2 should have smaller error than order 1") diff --git a/tests/test_1051_VE_shear_box.py b/tests/test_1051_VE_shear_box.py new file mode 100644 index 000000000..a8d2709ad --- /dev/null +++ b/tests/test_1051_VE_shear_box.py @@ -0,0 +1,181 @@ +""" +Viscoelastic shear box — analytical validation. + +A Maxwell viscoelastic material under uniform simple shear has the exact +solution for the shear stress component: + + σ_xy(t) = η · γ̇ · (1 - exp(-t / t_r)) + +where: + t_r = η/μ Maxwell relaxation time + γ̇ = dv_x/dy engineering shear rate (velocity gradient) + ε̇_xy = γ̇/2 tensor strain rate + +The steady-state stress is σ_xy = η·γ̇ = 2η·ε̇_xy, the purely viscous limit. + +Boundary conditions: + Top / Bottom: prescribed horizontal velocity ±V₀, zero vertical + Left / Right: free horizontal (outflow), zero vertical velocity + +This avoids periodic BCs (untested) and corner singularities from free-slip. +The result is a spatially uniform simple shear — effectively a 1D problem. + +The stress is read from psi_star[0] (the projected actual stress stored by +VE_Stokes after each solve), not recomputed from the constitutive formula. +""" + +import pytest +import numpy as np +import sympy +import underworld3 as uw + +pytestmark = [pytest.mark.level_3, pytest.mark.tier_b] + + +# --------------------------------------------------------------------------- +# Analytical solution +# --------------------------------------------------------------------------- + +def maxwell_stress_xy(t, eta, mu, gamma_dot): + """Exact σ_xy for constant-rate simple shear of a Maxwell material.""" + t_relax = eta / mu + return eta * gamma_dot * (1.0 - np.exp(-t / t_relax)) + + +# --------------------------------------------------------------------------- +# Helpers +# --------------------------------------------------------------------------- + +def _run_ve_shear(order, n_steps, dt_over_tr): + """Run a VE shear-box, return (times, numerical_stress, analytical_stress).""" + + ETA = 1.0 + MU = 1.0 + V0 = 0.5 + H = 1.0 + W = 2.0 + + t_relax = ETA / MU + dt = dt_over_tr * t_relax + gamma_dot = 2.0 * V0 / H + + res = 8 + mesh = uw.meshing.StructuredQuadBox( + elementRes=(2 * res, res), + minCoords=(-W / 2.0, -H / 2.0), + maxCoords=(W / 2.0, H / 2.0), + ) + + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.VE_Stokes( + mesh, velocityField=v, pressureField=p, order=order, verbose=False, + ) + + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA + stokes.constitutive_model.Parameters.shear_modulus = MU + stokes.constitutive_model.Parameters.dt_elastic = dt + + stokes.add_dirichlet_bc((V0, 0.0), "Top") + stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + + stokes.tolerance = 1.0e-6 + stokes.petsc_options["snes_type"] = "newtonls" + stokes.petsc_options["ksp_type"] = "fgmres" + + times = [] + stress_num = [] + stress_ana = [] + centre = np.array([[0.0, 0.0]]) + + time = 0.0 + for step in range(n_steps): + stokes.solve(zero_init_guess=False, evalf=False) + time += dt + + # Read stress from psi_star[0] — the actual projected stress + sigma_xy_val = uw.function.evaluate( + stokes.DFDt.psi_star[0].sym[0, 1], centre + ) + sigma_xy = float(sigma_xy_val.flatten()[0]) + + times.append(time) + stress_num.append(sigma_xy) + stress_ana.append(maxwell_stress_xy(time, ETA, MU, gamma_dot)) + + del stokes, mesh + + return np.array(times), np.array(stress_num), np.array(stress_ana) + + +# --------------------------------------------------------------------------- +# Tests +# --------------------------------------------------------------------------- + +class TestVEShearBox: + """Viscoelastic shear box with analytical Maxwell solution.""" + + def test_order1_converges(self): + """Order-1 VE stress should track the analytical Maxwell curve.""" + + times, num, ana = _run_ve_shear(order=1, n_steps=20, dt_over_tr=0.1) + + rel_error_final = abs(num[-1] - ana[-1]) / abs(ana[-1]) + mask = ana > 0.01 * ana[-1] + rel_error_rms = np.sqrt(np.mean(((num[mask] - ana[mask]) / ana[mask]) ** 2)) + + print(f"Order 1: final rel error = {rel_error_final:.4e}, " + f"RMS rel error = {rel_error_rms:.4e}") + + assert rel_error_final < 0.05 + assert rel_error_rms < 0.06 + + def test_order2_converges(self): + """Order-2 VE stress should converge more accurately than order-1.""" + + times, num, ana = _run_ve_shear(order=2, n_steps=20, dt_over_tr=0.1) + + rel_error_final = abs(num[-1] - ana[-1]) / abs(ana[-1]) + mask = ana > 0.01 * ana[-1] + rel_error_rms = np.sqrt(np.mean(((num[mask] - ana[mask]) / ana[mask]) ** 2)) + + print(f"Order 2: final rel error = {rel_error_final:.4e}, " + f"RMS rel error = {rel_error_rms:.4e}") + + # Order-2 should be significantly better than order-1 + assert rel_error_final < 0.005 + assert rel_error_rms < 0.02 + + def test_order2_better_than_order1(self): + """Order 2 should have smaller error than order 1 at the same Δt.""" + + _, num1, ana1 = _run_ve_shear(order=1, n_steps=20, dt_over_tr=0.1) + _, num2, ana2 = _run_ve_shear(order=2, n_steps=20, dt_over_tr=0.1) + + mask = ana1 > 0.01 * ana1[-1] + err1 = abs(num1[-1] - ana1[-1]) / ana1[-1] + err2 = abs(num2[-1] - ana2[-1]) / ana2[-1] + + print(f"Final errors: Order 1 = {err1:.4e}, Order 2 = {err2:.4e}") + + assert err2 < err1, ( + f"Order 2 error ({err2:.4e}) should be less than order 1 ({err1:.4e})" + ) + + def test_steady_state_approach(self): + """Stress should monotonically approach the viscous limit η·γ̇.""" + + times, num, ana = _run_ve_shear(order=1, n_steps=30, dt_over_tr=0.1) + + final_err = abs(num[-1] - ana[-1]) / ana[-1] + + print(f"Steady state approach: σ_xy = {num[-1]:.6f}, " + f"analytical = {ana[-1]:.6f}") + + diffs = np.diff(num) + assert np.all(diffs > 0), "Stress should be monotonically increasing" + assert final_err < 0.02 From 3c685844d3ab5b20952305e3a1d643e048b59862 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 18 Mar 2026 21:55:34 +1100 Subject: [PATCH 014/537] Add solver.tau property for computed flux access MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Adds a `tau` property to SolverBaseClass that returns a MeshVariable containing the projected constitutive flux. Created lazily on first access — no overhead if never used. Works for: - Stokes: deviatoric stress tensor (SYM_TENSOR projection) - Poisson: diffusive flux vector (Vector projection) - VE_Stokes: override returns psi_star[0] directly (no projection) This gives users a reliable way to access "what the solver actually computed" without manually reconstructing fluxes from the constitutive formula (which may have history terms, nonlinear corrections, etc). Usage: stokes.solve() stress_data = stokes.tau.data # numerical values stress_sym = stokes.tau.sym # symbolic (for further expressions) The base `stress_deviator` property is unchanged (returns the symbolic formula, needed for JIT compilation via F1 -> stress -> stress_deviator). Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 116 ++++++++++++++++++ src/underworld3/systems/solvers.py | 18 +-- tests/run_ve_shear_order2_quick.py | 2 +- tests/run_ve_shear_quick.py | 4 +- tests/test_1051_VE_shear_box.py | 4 +- 5 files changed, 131 insertions(+), 13 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index e830fdc42..92379c885 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -956,6 +956,122 @@ class SolverBaseClass(uw_object): + @property + def tau(self): + r"""Computed flux from the constitutive model, projected onto the mesh. + + Returns a :class:`~underworld3.discretisation.MeshVariable` containing + the flux that the solver actually computed. The variable is created + lazily on first access and updated by solving a projection each time + the property is read. + + For Stokes-family solvers, this is the deviatoric stress tensor + :math:`\boldsymbol{\tau}`. For Poisson/diffusion, it is the + diffusive flux :math:`\kappa \nabla u`. The projection handles + derivative evaluation internally — users should use this property + rather than manually reconstructing the flux from the constitutive + formula. + + Subclasses may override this to return pre-computed values (e.g. + VE_Stokes returns the stress stored during the solve). + + Returns + ------- + MeshVariable + Mesh variable containing the projected flux values. + Access numerical data via ``.data`` or ``.array``, symbolic + expression via ``.sym``. + """ + + if self._constitutive_model is None: + raise RuntimeError( + "No constitutive model set. Assign solver.constitutive_model first." + ) + + # Lazy initialization of projection infrastructure + if not hasattr(self, '_tau_var') or self._tau_var is None: + self._setup_tau_projection() + + # Project the constitutive flux onto the mesh variable + # Transpose if needed: flux may be (dim,1) column but projector expects row + flux = self._constitutive_model.flux + if hasattr(flux, 'shape') and flux.shape[1] == 1 and flux.shape[0] > 1: + flux = flux.T + self._tau_projector.uw_function = flux + self._tau_projector.smoothing = 0.0 + self._tau_projector.solve() + + return self._tau_var + + def _setup_tau_projection(self): + """Create the mesh variable and projector for tau (lazy init).""" + + flux = self._constitutive_model.flux + dim = self.mesh.dim + rows, cols = flux.shape + + # Determine variable type and create appropriate projection solver + if rows == cols and rows == dim: + # Tensor flux (Stokes stress) + self._tau_var = uw.discretisation.MeshVariable( + f"tau_{self.instance_number}", + self.mesh, + (dim, dim), + vtype=uw.VarType.SYM_TENSOR, + degree=self.u.degree, + continuous=True, + varsymbol=r"{\tau}", + ) + _work = uw.discretisation.MeshVariable( + f"tau_work_{self.instance_number}", + self.mesh, + 1, + degree=self.u.degree, + continuous=True, + ) + from underworld3.systems.solvers import SNES_Tensor_Projection + self._tau_projector = SNES_Tensor_Projection( + self.mesh, self._tau_var, _work, verbose=False + ) + + elif rows == dim and cols == 1: + # Vector flux (Poisson heat flux) + self._tau_var = uw.discretisation.MeshVariable( + f"tau_{self.instance_number}", + self.mesh, + dim, + vtype=uw.VarType.VECTOR, + degree=self.u.degree, + continuous=True, + varsymbol=r"{\mathbf{q}}", + ) + from underworld3.systems.solvers import SNES_Vector_Projection + self._tau_projector = SNES_Vector_Projection( + self.mesh, self._tau_var, verbose=False + ) + + elif cols == dim and rows == 1: + # Transposed vector flux + self._tau_var = uw.discretisation.MeshVariable( + f"tau_{self.instance_number}", + self.mesh, + dim, + vtype=uw.VarType.VECTOR, + degree=self.u.degree, + continuous=True, + varsymbol=r"{\mathbf{q}}", + ) + from underworld3.systems.solvers import SNES_Vector_Projection + self._tau_projector = SNES_Vector_Projection( + self.mesh, self._tau_var, verbose=False + ) + + else: + raise RuntimeError( + f"Cannot create tau projection for flux shape {flux.shape}. " + f"Expected ({dim},{dim}) tensor, ({dim},1) or (1,{dim}) vector." + ) + def validate_solver(self): """ Checks to see if the required properties have been set. diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 8d86f10d7..757fede1d 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1247,18 +1247,20 @@ def delta_t(self): return self.constitutive_model.Parameters.dt_elastic @property - def stress_deviator_stored(self): + def tau(self): r"""Deviatoric stress from the most recent solve (stored in history). - Returns the actual projected stress from psi_star[0], which is - stored after each solve. Use this for post-processing, - visualization, and quantitative measurement. + For VE_Stokes, the stress is projected into ``psi_star[0]`` after + each solve. This override returns that variable directly — no + additional projection needed. - Note: the base ``stress_deviator`` property returns the constitutive - formula (needed for JIT compilation). For VE problems, always use - ``stress_deviator_stored`` to read the solved stress. + Returns + ------- + MeshVariable + The stress history variable containing the actual deviatoric + stress from the most recent solve. """ - return self.DFDt.psi_star[0].sym + return self.DFDt.psi_star[0] ## Solver needs to update the stress history terms as well as call the SNES solve: diff --git a/tests/run_ve_shear_order2_quick.py b/tests/run_ve_shear_order2_quick.py index 9e7d6d8c8..fb40d71f9 100644 --- a/tests/run_ve_shear_order2_quick.py +++ b/tests/run_ve_shear_order2_quick.py @@ -38,7 +38,7 @@ solve_t = timer.time() - t0 time_phys += dt - val = uw.function.evaluate(ddt.psi_star[0].sym[0, 1], centre) + val = uw.function.evaluate(stokes.tau.sym[0, 1], centre) sigma_xy = float(val.flatten()[0]) ana = ETA * gamma_dot * (1.0 - np.exp(-time_phys * MU / ETA)) print(f"step {step:2d} eff={eff} t={time_phys:.2f} solve={solve_t:.1f}s " diff --git a/tests/run_ve_shear_quick.py b/tests/run_ve_shear_quick.py index 6be238580..debced41d 100644 --- a/tests/run_ve_shear_quick.py +++ b/tests/run_ve_shear_quick.py @@ -37,8 +37,8 @@ solve_t = timer.time() - t0 time_phys += dt - # Read stress directly from psi_star[0] (the projected actual stress) - val = uw.function.evaluate(ddt.psi_star[0].sym[0, 1], centre) + # Read stress from solver.tau (the projected actual stress) + val = uw.function.evaluate(stokes.tau.sym[0, 1], centre) sigma_xy = float(val.flatten()[0]) ana = ETA * gamma_dot * (1.0 - np.exp(-time_phys * MU / ETA)) print(f"step {step} t={time_phys:.2f} solve={solve_t:.1f}s " diff --git a/tests/test_1051_VE_shear_box.py b/tests/test_1051_VE_shear_box.py index a8d2709ad..1691ee319 100644 --- a/tests/test_1051_VE_shear_box.py +++ b/tests/test_1051_VE_shear_box.py @@ -97,9 +97,9 @@ def _run_ve_shear(order, n_steps, dt_over_tr): stokes.solve(zero_init_guess=False, evalf=False) time += dt - # Read stress from psi_star[0] — the actual projected stress + # Read stress from solver.tau — the actual projected stress sigma_xy_val = uw.function.evaluate( - stokes.DFDt.psi_star[0].sym[0, 1], centre + stokes.tau.sym[0, 1], centre ) sigma_xy = float(sigma_xy_val.flatten()[0]) From 329826f11718c1f826965c2a99d8262c3e70ea8f Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Fri, 20 Mar 2026 13:35:59 +1100 Subject: [PATCH 015/537] Fix VEP order-2 plasticity and add VP/VEP shear box tests MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The plastic effective viscosity in ViscoElasticPlasticFlowModel was using order-1 only for the elastic strain rate contribution, regardless of effective_order. This caused order-2 VEP to overshoot the yield stress (stress reached 0.73 instead of capping at τ_y=0.5). Fix: _plastic_effective_viscosity now uses self.E_eff.sym which already handles effective_order correctly via the BDF coefficients. New test scripts: - run_vp_shear_box.py: VP yield stress sweep (machine-precision match) - run_vep_shear_box.py: VEP elastic buildup + yield cap Order-1: caps at τ_y with ~1e-7 error Order-2: caps at τ_y with ~1e-7 error (was 22% error before fix) - run_ve_oscillatory.py: time-harmonic VE validation Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 14 +-- tests/run_ve_oscillatory.py | 123 +++++++++++++++++++++++++ tests/run_vep_shear_box.py | 121 ++++++++++++++++++++++++ tests/run_vp_shear_box.py | 90 ++++++++++++++++++ 4 files changed, 338 insertions(+), 10 deletions(-) create mode 100644 tests/run_ve_oscillatory.py create mode 100644 tests/run_vep_shear_box.py create mode 100644 tests/run_vp_shear_box.py diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 205f6ec74..6ff31729a 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1378,16 +1378,10 @@ def _plastic_effective_viscosity(self): if parameters.yield_stress == sympy.oo: return sympy.oo - Edot = self.Unknowns.E - if self.Unknowns.DFDt is not None: - - ## First order ... - stress_star = self.Unknowns.DFDt.psi_star[0] - - if self.is_elastic: - Edot += stress_star.sym / ( - 2 * self.Parameters.dt_elastic * self.Parameters.shear_modulus - ) + # Use the effective strain rate (including elastic history) for the + # yield criterion. This must use the same order-dependent BDF + # coefficients as the stress formula. + Edot = self.E_eff.sym strainrate_inv_II = expression( R"{\dot\varepsilon_{II}'}", diff --git a/tests/run_ve_oscillatory.py b/tests/run_ve_oscillatory.py new file mode 100644 index 000000000..0c70ba0ce --- /dev/null +++ b/tests/run_ve_oscillatory.py @@ -0,0 +1,123 @@ +"""Oscillatory VE shear box — time-harmonic analytical validation. + +Maxwell material under sinusoidal boundary velocity V(t) = V0 sin(ωt). +Full solution including startup transient: + + σ_xy(t) = η γ̇₀ De/(1+De²) [sin(ωt) - De cos(ωt) + De exp(-t/t_r)] + +where De = ω t_r is the Deborah number. + +At steady state (t >> t_r), the transient dies out and the stress +oscillates with amplitude η γ̇₀ De/√(1+De²) and phase lag arctan(De). +""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw +from underworld3.function import expression + + +def maxwell_oscillatory(t, eta, mu, gamma_dot_0, omega): + """Full analytical σ_xy for oscillatory Maxwell shear (incl. transient).""" + t_r = eta / mu + De = omega * t_r + prefactor = eta * gamma_dot_0 * De / (1.0 + De**2) + return prefactor * (np.sin(omega * t) - De * np.cos(omega * t) + De * np.exp(-t / t_r)) + + +def run_oscillatory(order, n_steps, dt_over_tr, De): + """Run oscillatory VE shear box.""" + + ETA, MU, H, W = 1.0, 1.0, 1.0, 2.0 + t_r = ETA / MU + omega = De / t_r + V0 = 0.5 + gamma_dot_0 = 2.0 * V0 / H + dt = dt_over_tr * t_r + + mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), + ) + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=order) + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA + stokes.constitutive_model.Parameters.shear_modulus = MU + stokes.constitutive_model.Parameters.dt_elastic = dt + + # Use a UWexpression for time-dependent BCs — avoids JIT recompilation + V_bc = expression(r"{V_{bc}}", 0.0, "Time-dependent boundary velocity") + + stokes.add_dirichlet_bc((V_bc, 0.0), "Top") + stokes.add_dirichlet_bc((-V_bc, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + stokes.tolerance = 1.0e-6 + + centre = np.array([[0.0, 0.0]]) + times, stress_num, stress_ana = [], [], [] + time_phys = 0.0 + + for step in range(n_steps): + time_phys += dt + + # Update boundary velocity for this timestep + V_t = V0 * np.sin(omega * time_phys) + V_bc.sym = V_t + stokes.is_setup = False # force BC re-evaluation + + stokes.solve(zero_init_guess=False, evalf=False) + + val = uw.function.evaluate(stokes.tau.sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + + ana = maxwell_oscillatory(time_phys, ETA, MU, gamma_dot_0, omega) + times.append(time_phys) + stress_num.append(sigma_xy) + stress_ana.append(ana) + + del stokes, mesh + return np.array(times), np.array(stress_num), np.array(stress_ana) + + +if __name__ == "__main__": + De = 1.0 # Deborah number (equal viscous and elastic timescales) + dt_ratio = 0.1 # coarser for speed; finer (0.05) for publication quality + n_periods = 3 + t_r = 1.0 + omega = De / t_r + period = 2 * np.pi / omega + n_steps = int(n_periods * period / (dt_ratio * t_r)) + + print(f"De = {De}, omega = {omega:.3f}, period = {period:.3f}") + print(f"dt/t_r = {dt_ratio}, n_steps = {n_steps}") + print() + + for order in [1, 2]: + t0 = timer.time() + t, num, ana = run_oscillatory(order, n_steps, dt_ratio, De) + wall = timer.time() - t0 + + # Error over the last period (steady state) + last_period = t > (n_periods - 1) * period + if np.any(last_period): + rms = np.sqrt(np.mean((num[last_period] - ana[last_period])**2)) + amp_ana = np.max(np.abs(ana[last_period])) + rel_rms = rms / amp_ana if amp_ana > 0 else float('nan') + else: + rel_rms = float('nan') + + print(f"Order {order}: wall={wall:.0f}s, " + f"last-period relative RMS = {rel_rms:.4e}") + + # Samples from the last period + if np.any(last_period): + idx = np.where(last_period)[0] + sample = idx[::max(1, len(idx)//10)] + for i in sample: + err = abs(num[i] - ana[i]) + print(f" t={t[i]:.3f} num={num[i]:+.6f} ana={ana[i]:+.6f} err={err:.4e}") + print() diff --git a/tests/run_vep_shear_box.py b/tests/run_vep_shear_box.py new file mode 100644 index 000000000..7d4fabe3f --- /dev/null +++ b/tests/run_vep_shear_box.py @@ -0,0 +1,121 @@ +"""Viscoelastic-plastic shear box — stress buildup with yield cap. + +Maxwell VE material with Drucker-Prager yield stress under constant shear. + +Phase 1 (elastic buildup): σ_xy follows the Maxwell curve +Phase 2 (yielded): σ_xy = τ_y (plastic cap) + +Transition time: t_yield = -t_r ln(1 - τ_y/(η γ̇)) +(only exists if η γ̇ > τ_y) +""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw + + +def maxwell_stress_xy(t, eta, mu, gamma_dot): + """Uncapped VE stress (for comparison).""" + t_r = eta / mu + return eta * gamma_dot * (1.0 - np.exp(-t / t_r)) + + +def vep_stress_xy(t, eta, mu, gamma_dot, tau_y): + """VEP stress: Maxwell buildup capped at τ_y.""" + ve = maxwell_stress_xy(t, eta, mu, gamma_dot) + return np.minimum(ve, tau_y) + + +def run_vep_shear(order, n_steps, dt_over_tr, tau_y): + """Run VEP shear box, return (times, num_stress, ana_stress).""" + + ETA, MU, V0, H, W = 1.0, 1.0, 0.5, 1.0, 2.0 + t_r = ETA / MU + dt = dt_over_tr * t_r + gamma_dot = 2.0 * V0 / H # = 1.0 + + mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), + ) + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=order) + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA + stokes.constitutive_model.Parameters.shear_modulus = MU + stokes.constitutive_model.Parameters.dt_elastic = dt + stokes.constitutive_model.Parameters.yield_stress = tau_y + stokes.constitutive_model.Parameters.strainrate_inv_II_min = 1.0e-6 + + stokes.add_dirichlet_bc((V0, 0.0), "Top") + stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + stokes.tolerance = 1.0e-5 + + stokes.petsc_options["snes_type"] = "newtonls" + stokes.petsc_options["ksp_type"] = "fgmres" + stokes.petsc_options["snes_max_it"] = 50 + + # Seed with linear shear + v.data[:, 0] = v.coords[:, 1] * gamma_dot + v.data[:, 1] = 0.0 + + centre = np.array([[0.0, 0.0]]) + times, stress_num, stress_ana, stress_ve = [], [], [], [] + time_phys = 0.0 + + for step in range(n_steps): + t0 = timer.time() + stokes.solve(zero_init_guess=False, evalf=False) + solve_t = timer.time() - t0 + time_phys += dt + + val = uw.function.evaluate(stokes.tau.sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + + ana = vep_stress_xy(time_phys, ETA, MU, gamma_dot, tau_y) + ve_only = maxwell_stress_xy(time_phys, ETA, MU, gamma_dot) + + times.append(time_phys) + stress_num.append(sigma_xy) + stress_ana.append(ana) + stress_ve.append(ve_only) + + del stokes, mesh + return np.array(times), np.array(stress_num), np.array(stress_ana), np.array(stress_ve) + + +if __name__ == "__main__": + ETA, MU = 1.0, 1.0 + gamma_dot = 1.0 # 2*V0/H + t_r = ETA / MU + + # Choose τ_y below the viscous steady state (η·γ̇ = 1.0) + TAU_Y = 0.5 + t_yield = -t_r * np.log(1 - TAU_Y / (ETA * gamma_dot)) + + print(f"eta={ETA}, mu={MU}, gamma_dot={gamma_dot}") + print(f"tau_y={TAU_Y}, viscous_limit={ETA*gamma_dot}") + print(f"t_yield={t_yield:.4f} (stress reaches tau_y)") + print() + + for order in [1, 2]: + t0 = timer.time() + t, num, ana, ve = run_vep_shear(order, n_steps=30, dt_over_tr=0.1, tau_y=TAU_Y) + wall = timer.time() - t0 + + print(f"Order {order} (wall={wall:.0f}s):") + for i in range(len(t)): + marker = " *" if t[i] > t_yield - 0.05 and t[i] < t_yield + 0.15 else "" + print(f" t={t[i]:.2f} num={num[i]:.6f} ana={ana[i]:.6f} " + f"ve={ve[i]:.6f} err={abs(num[i]-ana[i]):.4e}{marker}") + + # Error in post-yield regime + yielded = t > t_yield + 0.2 + if np.any(yielded): + post_err = np.max(np.abs(num[yielded] - ana[yielded])) + print(f" Max post-yield error: {post_err:.4e}") + print() diff --git a/tests/run_vp_shear_box.py b/tests/run_vp_shear_box.py new file mode 100644 index 000000000..01a0c1651 --- /dev/null +++ b/tests/run_vp_shear_box.py @@ -0,0 +1,90 @@ +"""Viscoplastic shear box — yield stress validation. + +For simple shear with constant strain rate: + - Below yield: σ_xy = η · γ̇ (viscous) + - At/above yield: σ_xy = τ_y (plastic cap) + +The transition occurs when η · γ̇ = τ_y, i.e. γ̇_crit = τ_y / η. + +We test with a range of driving velocities and check the stress +transition matches the analytical prediction. +""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw + + +def run_vp_shear(V0, eta, yield_stress): + """Single-step VP shear solve, return σ_xy at centre.""" + + H, W = 1.0, 2.0 + mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), + ) + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) + stokes.constitutive_model = uw.constitutive_models.ViscoPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = eta + stokes.constitutive_model.Parameters.yield_stress = yield_stress + stokes.constitutive_model.Parameters.strainrate_inv_II_min = 1.0e-6 + + stokes.add_dirichlet_bc((V0, 0.0), "Top") + stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + stokes.tolerance = 1.0e-4 + + stokes.petsc_options["snes_type"] = "newtonls" + stokes.petsc_options["ksp_type"] = "fgmres" + stokes.petsc_options["snes_max_it"] = 50 + + # Initialise with uniform shear to avoid singular Jacobian at zero strain rate + gamma_dot = 2.0 * V0 / H + v.data[:, 0] = v.coords[:, 1] * gamma_dot + v.data[:, 1] = 0.0 + + stokes.solve(zero_init_guess=False) + + # Read stress via tau + centre = np.array([[0.0, 0.0]]) + val = uw.function.evaluate(stokes.tau.sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + + converged = stokes.snes.getConvergedReason() > 0 + del stokes, mesh + return sigma_xy, converged + + +if __name__ == "__main__": + ETA = 1.0 + TAU_Y = 0.5 + H = 1.0 + + # γ̇ = 2V0/H, σ_xy = η·γ̇ in viscous regime, σ_xy = τ_y when η·γ̇ ≥ τ_y + gamma_dot_crit = TAU_Y / ETA + print(f"eta={ETA}, tau_y={TAU_Y}, gamma_dot_crit={gamma_dot_crit}") + print() + + V0_values = np.array([0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.75, 1.0, 2.0]) + + print(f"{'V0':>6} {'gamma_dot':>10} {'sigma_xy':>10} {'analytical':>10} {'rel_err':>10} {'status':>8}") + print("-" * 62) + + for V0 in V0_values: + gamma_dot = 2.0 * V0 / H + ana = min(ETA * gamma_dot, TAU_Y) + + t0 = timer.time() + sigma_xy, converged = run_vp_shear(V0, ETA, TAU_Y) + dt = timer.time() - t0 + + rel_err = abs(sigma_xy - ana) / max(ana, 1e-10) + status = "OK" if converged else "FAIL" + print(f"{V0:6.3f} {gamma_dot:10.4f} {sigma_xy:10.6f} {ana:10.6f} {rel_err:10.3e} {status:>8}") + + print() + print("Done") From f5970b43c33831f582254ae2f40eb7bede21114f Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Fri, 20 Mar 2026 17:14:40 +1100 Subject: [PATCH 016/537] Add mesh.t time symbol and solve(time=) parameter (prototype) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Introduces mesh.t — a symbolic time coordinate that can be used in expressions for time-dependent boundary conditions and forcing terms. The symbol compiles to a C variable accessible in PETSc pointwise functions, avoiding JIT recompilation when time changes. Also adds optional time= parameter to Scalar and Stokes solve() methods, and UW_DMSetTime wrapper in petsc_compat.h. NOTE: petsc_t is hardcoded to PETSC_MIN_REAL in PETSc's SNES path (DMPlexSNESComputeResidualFEM, DMPlexSNESComputeBoundaryFEM). The planned solution is to use PetscDS constants[] array instead, which generalises to any mutable constant (viscosity, moduli, dt_elastic). This commit is the prototype; the constants wiring is the next step. New files: - TimeSymbol class in unit_aware_coordinates.py - _patch_time_units for dimensional analysis - UW_DMSetTime C wrapper (for future TS interface use) - VEP oscillatory test scripts and plot Underworld development team with AI support from Claude Code --- src/underworld3/cython/petsc_compat.h | 15 ++ src/underworld3/cython/petsc_extras.pxi | 1 + .../cython/petsc_generic_snes_solvers.pyx | 37 +++- .../discretisation/discretisation_mesh.py | 31 ++++ .../utilities/unit_aware_coordinates.py | 65 +++++++ tests/plot_ve_vep_oscillatory.py | 41 +++++ tests/run_ve_vep_oscillatory_checkpoint.py | 125 ++++++++++++++ tests/run_ve_vep_oscillatory_plot.py | 162 ++++++++++++++++++ tests/run_vep_oscillatory.py | 135 +++++++++++++++ 9 files changed, 610 insertions(+), 2 deletions(-) create mode 100644 tests/plot_ve_vep_oscillatory.py create mode 100644 tests/run_ve_vep_oscillatory_checkpoint.py create mode 100644 tests/run_ve_vep_oscillatory_plot.py create mode 100644 tests/run_vep_oscillatory.py diff --git a/src/underworld3/cython/petsc_compat.h b/src/underworld3/cython/petsc_compat.h index d502dd929..f2e5cc103 100644 --- a/src/underworld3/cython/petsc_compat.h +++ b/src/underworld3/cython/petsc_compat.h @@ -129,6 +129,21 @@ PetscErrorCode UW_PetscDSViewBdWF(PetscDS ds, PetscInt bd) return 1; } +// Set the time value on a DM. This is passed as `petsc_t` to all +// pointwise residual and Jacobian functions during assembly. +// PETSc stores this internally but petsc4py doesn't expose it. +PetscErrorCode UW_DMSetTime(DM dm, PetscReal time) +{ + // DMSetOutputSequenceNumber stores (step, time) on the DM. + // The time component is what DMPlexComputeResidual_Internal + // passes as petsc_t to the pointwise functions. + PetscInt step; + PetscReal old_time; + PetscCall(DMGetOutputSequenceNumber(dm, &step, &old_time)); + PetscCall(DMSetOutputSequenceNumber(dm, step, time)); + return PETSC_SUCCESS; +} + PetscErrorCode UW_DMPlexSetSNESLocalFEM(DM dm, PetscBool flag, void *ctx) { diff --git a/src/underworld3/cython/petsc_extras.pxi b/src/underworld3/cython/petsc_extras.pxi index c39d9c715..edd73ca15 100644 --- a/src/underworld3/cython/petsc_extras.pxi +++ b/src/underworld3/cython/petsc_extras.pxi @@ -42,6 +42,7 @@ cdef extern from "petsc_compat.h": PetscErrorCode UW_PetscDSSetBdTerms (PetscDS, PetscDMLabel, PetscInt, PetscInt, PetscInt, PetscInt, PetscInt, void*, void*, void*, void*, void*, void* ) PetscErrorCode UW_PetscDSViewWF(PetscDS) PetscErrorCode UW_PetscDSViewBdWF(PetscDS, PetscInt) + PetscErrorCode UW_DMSetTime( PetscDM, PetscReal ) PetscErrorCode UW_DMPlexSetSNESLocalFEM( PetscDM, PetscBool, void *) PetscErrorCode UW_DMPlexComputeBdIntegral( PetscDM, PetscVec, PetscDMLabel, PetscInt, const PetscInt*, void*, PetscScalar*, void*) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 92379c885..c4b3377e0 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -1784,7 +1784,8 @@ class SNES_Scalar(SolverBaseClass): _force_setup: bool =False, verbose: bool=False, debug: bool=False, - debug_name: str=None ): + debug_name: str=None, + time=None, ): """ Solve the system of equations. @@ -1807,6 +1808,11 @@ class SNES_Scalar(SolverBaseClass): Enable debug output including intermediate residuals. debug_name : str, optional Name prefix for debug output files. + time : float or Quantity, optional + Physical time for this solve. Passed as ``petsc_t`` to all + pointwise functions. Expressions using ``mesh.t`` evaluate at + this time. Non-dimensionalised when scaling is active. + Default: None (petsc_t unchanged). Returns ------- @@ -1844,6 +1850,16 @@ class SNES_Scalar(SolverBaseClass): self._build(verbose, debug, debug_name) + # Set time on the DM so petsc_t is available in pointwise functions + cdef DM _time_dm + if time is not None: + if hasattr(time, 'magnitude') or hasattr(time, '_pint_qty'): + t_nd = float(uw.non_dimensionalise(time)) + else: + t_nd = float(time) + _time_dm = self.dm + UW_DMSetTime(_time_dm.dm, t_nd) + gvec = self.dm.getGlobalVec() if not zero_init_guess: @@ -4153,7 +4169,8 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): verbose=False, debug=False, debug_name=None, - _force_setup: bool =False, ): + _force_setup: bool =False, + time=None, ): """ Solve the Stokes system for velocity and pressure. @@ -4180,6 +4197,11 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): Name prefix for debug output files. _force_setup : bool, default=False Force rebuild of the solver even if already set up. + time : float or Quantity, optional + Physical time for this solve. Passed as ``petsc_t`` to all + pointwise residual and Jacobian functions. Expressions using + ``mesh.t`` will evaluate at this time. Non-dimensionalised + automatically when scaling is active. Default: None (petsc_t=0). Returns ------- @@ -4221,6 +4243,17 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self._build(verbose, debug, debug_name) + # Set time on the DM so petsc_t is available in pointwise functions. + # Non-dimensionalise if the scaling system is active. + cdef DM _time_dm_stokes + if time is not None: + if hasattr(time, 'magnitude') or hasattr(time, '_pint_qty'): + t_nd = float(uw.non_dimensionalise(time)) + else: + t_nd = float(time) + _time_dm_stokes = self.dm + UW_DMSetTime(_time_dm_stokes.dm, t_nd) + # Keep a record of these set-up parameters tolerance = self.tolerance snes_type = self.snes.getType() diff --git a/src/underworld3/discretisation/discretisation_mesh.py b/src/underworld3/discretisation/discretisation_mesh.py index c111d0fdd..1db908564 100644 --- a/src/underworld3/discretisation/discretisation_mesh.py +++ b/src/underworld3/discretisation/discretisation_mesh.py @@ -629,6 +629,14 @@ def mesh_update_callback(array, change_context): self._Gamma.y._ccodestr = "petsc_n[1]" self._Gamma.z._ccodestr = "petsc_n[2]" + # Time coordinate — PETSc passes this as petsc_t to all pointwise + # functions. Solvers set dm.time before each solve via solve(time=t). + # Users reference it as mesh.t in expressions (e.g. V0 * sympy.sin(omega * mesh.t)) + from ..utilities.unit_aware_coordinates import TimeSymbol + + self._t = TimeSymbol("t") + self._t._units = None # patched below by _patch_time_units + # Add unit awareness to coordinate symbols if mesh has units or model has scales from ..utilities.unit_aware_coordinates import patch_coordinate_units @@ -1497,6 +1505,29 @@ def CoordinateSystem(self) -> CoordinateSystem: r"""Alias for :attr:`X` (the coordinate system object).""" return self._CoordinateSystem + @property + def t(self): + r"""Symbolic time coordinate. + + PETSc passes a time value (``petsc_t``) to all pointwise residual + and Jacobian functions. Use ``mesh.t`` in expressions to reference + this time without forcing JIT recompilation each timestep. + + The solver sets the time value via ``solve(time=t)``. If ``time`` + is not provided, ``petsc_t`` defaults to 0. + + When the scaling system is active, ``mesh.t`` carries time units + (derived from the model's time scale) so that dimensional analysis + works correctly in expressions. + + Examples + -------- + >>> omega = 2 * np.pi / period + >>> stokes.add_dirichlet_bc((V0 * sympy.sin(omega * mesh.t), 0.0), "Top") + >>> stokes.solve(time=current_time) # sets petsc_t before SNES + """ + return self._t + @property def r(self) -> Tuple[sympy.vector.BaseScalar]: r"""Tuple of coordinate scalars :math:`(x, y)` or :math:`(x, y, z)`. diff --git a/src/underworld3/utilities/unit_aware_coordinates.py b/src/underworld3/utilities/unit_aware_coordinates.py index 304aadebf..26471db63 100644 --- a/src/underworld3/utilities/unit_aware_coordinates.py +++ b/src/underworld3/utilities/unit_aware_coordinates.py @@ -83,6 +83,37 @@ def get_units(self): return self._units +class TimeSymbol(sympy.Symbol): + """A sympy Symbol subclass that carries _ccodestr and _units for JIT. + + Standard sympy Symbols are immutable and don't allow setting arbitrary + attributes. This subclass permits _ccodestr (for C code generation) + and _units (for dimensional analysis), following the same pattern as + UnitAwareBaseScalar for spatial coordinates. + """ + + _ccodestr = "petsc_t" + _units = None + + def __new__(cls, name="t", **kwargs): + obj = super().__new__(cls, name, real=True, positive=True, **kwargs) + return obj + + @property + def units(self): + return self._units + + @units.setter + def units(self, value): + self._units = value + + def get_units(self): + return self._units + + def _ccode(self, printer): + return self._ccodestr + + def create_unit_aware_coordinate_system(name, units=None): """ Create a coordinate system with unit-aware coordinates. @@ -207,6 +238,40 @@ def _patch_coordinate(coord, units): # If _Gamma needs any units in the future, they should be explicitly # dimensionless (None), not inherited from mesh coordinates. + # Patch time coordinate with time units from the model + _patch_time_units(mesh) + + +def _patch_time_units(mesh): + """ + Patch mesh.t with time units from the model's scaling system. + + If the model has a time scale defined, mesh.t gets those units. + Otherwise mesh.t remains dimensionless (._units = None). + """ + if not hasattr(mesh, "_t"): + return + + time_units = None + try: + import underworld3 as uw + + model = uw.get_default_model() + if hasattr(model, "_fundamental_scales") and model._fundamental_scales: + scales = model._fundamental_scales + if "time" in scales: + time_scale = scales["time"] + if hasattr(time_scale, "units"): + time_units = time_scale.units + elif hasattr(time_scale, "_pint_qty"): + time_units = time_scale._pint_qty.units + except Exception: + pass + + mesh._t._units = time_units + if not hasattr(mesh._t, "get_units"): + mesh._t.get_units = lambda: mesh._t._units + def get_coordinate_units(coord): """ diff --git a/tests/plot_ve_vep_oscillatory.py b/tests/plot_ve_vep_oscillatory.py new file mode 100644 index 000000000..abc234ca6 --- /dev/null +++ b/tests/plot_ve_vep_oscillatory.py @@ -0,0 +1,41 @@ +"""Plot VE vs VEP oscillatory shear from saved checkpoint.""" + +import numpy as np +import matplotlib.pyplot as plt + +data = np.load("output/ve_vep_oscillatory.npz") +t_ve, s_ve = data["t_ve"], data["s_ve"] +t_vep, s_vep = data["t_vep"], data["s_vep"] +t_ana, s_ana = data["t_ana"], data["s_ana"] +De = float(data["De"]) +tau_y = float(data["tau_y"]) +ve_amp = float(data["ve_amp"]) +omega = float(data["omega"]) + +fig, ax = plt.subplots(1, 1, figsize=(10, 5)) + +# Analytical VE (smooth curve) +ax.plot(t_ana, s_ana, "k-", linewidth=0.8, alpha=0.5, label="VE analytical") + +# Numerical VE +ax.plot(t_ve, s_ve, "b-o", markersize=3, linewidth=1.2, label="VE numerical (order 1)") + +# Numerical VEP +ax.plot(t_vep, s_vep, "r-s", markersize=3, linewidth=1.2, label=f"VEP numerical ($\\tau_y$={tau_y})") + +# Yield stress lines +ax.axhline(tau_y, color="r", linestyle="--", alpha=0.4, linewidth=0.8) +ax.axhline(-tau_y, color="r", linestyle="--", alpha=0.4, linewidth=0.8) +ax.text(0.3, tau_y + 0.02, f"$\\tau_y$ = {tau_y}", color="r", fontsize=9, alpha=0.6) + +ax.set_xlabel("Time ($t / t_r$)") +ax.set_ylabel("$\\sigma_{xy}$") +ax.set_title(f"Oscillatory Maxwell VE vs VEP shear (De = {De})") +ax.legend(loc="upper left", fontsize=9) +ax.set_xlim(0, t_ve[-1]) +ax.grid(True, alpha=0.3) + +plt.tight_layout() +plt.savefig("output/ve_vep_oscillatory.png", dpi=150) +plt.savefig("output/ve_vep_oscillatory.pdf") +print("Saved output/ve_vep_oscillatory.png and .pdf") diff --git a/tests/run_ve_vep_oscillatory_checkpoint.py b/tests/run_ve_vep_oscillatory_checkpoint.py new file mode 100644 index 000000000..706cc2ce8 --- /dev/null +++ b/tests/run_ve_vep_oscillatory_checkpoint.py @@ -0,0 +1,125 @@ +"""Run VE and VEP oscillatory shear, save time series to .npz for plotting.""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw +from underworld3.function import expression + + +def maxwell_oscillatory(t, eta, mu, gamma_dot_0, omega): + """Full analytical σ_xy for oscillatory Maxwell shear.""" + t_r = eta / mu + De = omega * t_r + prefactor = eta * gamma_dot_0 * De / (1.0 + De**2) + return prefactor * (np.sin(omega * t) - De * np.cos(omega * t) + De * np.exp(-t / t_r)) + + +def run_oscillatory(order, n_steps, dt, omega, V0, tau_y=None): + """Run oscillatory shear (VE or VEP depending on tau_y).""" + + ETA, MU, H, W = 1.0, 1.0, 1.0, 2.0 + gamma_dot_0 = 2.0 * V0 / H + + mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), + ) + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=order) + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA + stokes.constitutive_model.Parameters.shear_modulus = MU + stokes.constitutive_model.Parameters.dt_elastic = dt + + if tau_y is not None: + stokes.constitutive_model.Parameters.yield_stress = tau_y + stokes.constitutive_model.Parameters.strainrate_inv_II_min = 1.0e-6 + + v.data[:, 0] = v.coords[:, 1] * gamma_dot_0 + v.data[:, 1] = 0.0 + + V_bc = expression(r"{V_{bc}}", 0.0, "Time-dependent boundary velocity") + stokes.add_dirichlet_bc((V_bc, 0.0), "Top") + stokes.add_dirichlet_bc((-V_bc, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + stokes.tolerance = 1.0e-5 + stokes.petsc_options["snes_type"] = "newtonls" + stokes.petsc_options["ksp_type"] = "fgmres" + stokes.petsc_options["snes_max_it"] = 50 + + centre = np.array([[0.0, 0.0]]) + times, stress_num = [], [] + time_phys = 0.0 + + for step in range(n_steps): + time_phys += dt + V_bc.sym = V0 * np.sin(omega * time_phys) + stokes.is_setup = False + + stokes.solve(zero_init_guess=False, evalf=False) + + val = uw.function.evaluate(stokes.tau.sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + times.append(time_phys) + stress_num.append(sigma_xy) + + label = "VEP" if tau_y is not None else "VE" + print(f" {label} step {step:3d} t={time_phys:.2f} sigma={sigma_xy:+.6f}", flush=True) + + del stokes, mesh + return np.array(times), np.array(stress_num) + + +if __name__ == "__main__": + De = 1.0 + ETA, MU = 1.0, 1.0 + t_r = ETA / MU + omega = De / t_r + V0 = 0.5 + gamma_dot_0 = 2.0 * V0 / 1.0 + period = 2.0 * np.pi / omega + TAU_Y = 0.4 + + dt_ratio = 0.1 + dt = dt_ratio * t_r + n_periods = 2 + n_steps = int(n_periods * period / dt) + + ve_amp = ETA * gamma_dot_0 * De / np.sqrt(1.0 + De**2) + + print(f"De={De}, omega={omega:.3f}, period={period:.3f}") + print(f"VE amplitude={ve_amp:.4f}, tau_y={TAU_Y}") + print(f"dt={dt}, n_steps={n_steps}") + print() + + # VE (no yield) + print("=== VE (order 1) ===") + t0 = timer.time() + t_ve, s_ve = run_oscillatory(1, n_steps, dt, omega, V0, tau_y=None) + print(f" Wall: {timer.time()-t0:.0f}s\n") + + # VEP (with yield) + print("=== VEP (order 1) ===") + t0 = timer.time() + t_vep, s_vep = run_oscillatory(1, n_steps, dt, omega, V0, tau_y=TAU_Y) + print(f" Wall: {timer.time()-t0:.0f}s\n") + + # Analytical + t_ana = np.linspace(dt, n_periods * period, 500) + s_ana = maxwell_oscillatory(t_ana, ETA, MU, gamma_dot_0, omega) + + # Save + outfile = "output/ve_vep_oscillatory.npz" + import os + os.makedirs("output", exist_ok=True) + np.savez( + outfile, + t_ve=t_ve, s_ve=s_ve, + t_vep=t_vep, s_vep=s_vep, + t_ana=t_ana, s_ana=s_ana, + De=De, tau_y=TAU_Y, ve_amp=ve_amp, omega=omega, + ) + print(f"Saved to {outfile}") diff --git a/tests/run_ve_vep_oscillatory_plot.py b/tests/run_ve_vep_oscillatory_plot.py new file mode 100644 index 000000000..b5b50c0db --- /dev/null +++ b/tests/run_ve_vep_oscillatory_plot.py @@ -0,0 +1,162 @@ +"""Run VE and VEP oscillatory shear from consistent initial conditions. + +Both cases start from the analytical Maxwell solution at t0=0.01 to avoid +zero-velocity singularity and ensure identical starting stress. + +Saves time series to stdout and generates plot directly. +""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw +from underworld3.function import expression +import os + + +def maxwell_oscillatory(t, eta, mu, gamma_dot_0, omega): + """Full analytical σ_xy for oscillatory Maxwell shear.""" + t_r = eta / mu + De = omega * t_r + prefactor = eta * gamma_dot_0 * De / (1.0 + De**2) + return prefactor * (np.sin(omega * t) - De * np.cos(omega * t) + De * np.exp(-t / t_r)) + + +def run_oscillatory(order, n_steps, dt, omega, V0, t0, tau_y=None): + """Run oscillatory shear from analytical initial condition at t0.""" + + ETA, MU, H, W = 1.0, 1.0, 1.0, 2.0 + gamma_dot_0 = 2.0 * V0 / H + t_r = ETA / MU + + mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), + ) + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=order) + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA + stokes.constitutive_model.Parameters.shear_modulus = MU + stokes.constitutive_model.Parameters.dt_elastic = dt + + if tau_y is not None: + stokes.constitutive_model.Parameters.yield_stress = tau_y + stokes.constitutive_model.Parameters.strainrate_inv_II_min = 1.0e-6 + + # Initialise velocity to match analytical solution at t0 + V_t0 = V0 * np.sin(omega * t0) + gamma_dot_t0 = 2.0 * V_t0 / H + v.data[:, 0] = v.coords[:, 1] * gamma_dot_t0 + v.data[:, 1] = 0.0 + + # Initialise stress history to analytical at t0 + sigma_t0 = maxwell_oscillatory(t0, ETA, MU, gamma_dot_0, omega) + # psi_star[0] is (N, dim, dim) sym tensor — set the xy component + stokes.DFDt.psi_star[0].array[:, 0, 1] = sigma_t0 + stokes.DFDt.psi_star[0].array[:, 1, 0] = sigma_t0 + stokes.DFDt._history_initialised = True + + V_bc = expression(r"{V_{bc}}", V_t0, "Time-dependent boundary velocity") + stokes.add_dirichlet_bc((V_bc, 0.0), "Top") + stokes.add_dirichlet_bc((-V_bc, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + stokes.tolerance = 1.0e-5 + stokes.petsc_options["snes_type"] = "newtonls" + stokes.petsc_options["ksp_type"] = "fgmres" + stokes.petsc_options["snes_max_it"] = 50 + + centre = np.array([[0.0, 0.0]]) + times, stress_num = [], [] + time_phys = t0 + + label = "VEP" if tau_y is not None else "VE" + + for step in range(n_steps): + time_phys += dt + V_bc.sym = V0 * np.sin(omega * time_phys) + stokes.is_setup = False + + stokes.solve(zero_init_guess=False, evalf=False) + + val = uw.function.evaluate(stokes.tau.sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + times.append(time_phys) + stress_num.append(sigma_xy) + + print(f" {label} step {step:3d} t={time_phys:.3f} sigma={sigma_xy:+.6f}", flush=True) + + del stokes, mesh + return np.array(times), np.array(stress_num) + + +if __name__ == "__main__": + De = 1.0 + ETA, MU = 1.0, 1.0 + t_r = ETA / MU + omega = De / t_r + V0 = 0.5 + gamma_dot_0 = 2.0 * V0 / 1.0 + period = 2.0 * np.pi / omega + TAU_Y = 0.4 + + dt_ratio = 0.1 + dt = dt_ratio * t_r + t0 = 0.01 + n_periods = 2 + n_steps = int(n_periods * period / dt) + + ve_amp = ETA * gamma_dot_0 * De / np.sqrt(1.0 + De**2) + sigma_t0 = maxwell_oscillatory(t0, ETA, MU, gamma_dot_0, omega) + + print(f"De={De}, omega={omega:.3f}, period={period:.3f}") + print(f"VE amplitude={ve_amp:.4f}, tau_y={TAU_Y}") + print(f"t0={t0}, sigma(t0)={sigma_t0:.6f}") + print(f"dt={dt}, n_steps={n_steps}") + print() + + # VE + print("=== VE (order 1) ===") + t0w = timer.time() + t_ve, s_ve = run_oscillatory(1, n_steps, dt, omega, V0, t0, tau_y=None) + print(f" Wall: {timer.time()-t0w:.0f}s\n") + + # VEP + print("=== VEP (order 1) ===") + t0w = timer.time() + t_vep, s_vep = run_oscillatory(1, n_steps, dt, omega, V0, t0, tau_y=TAU_Y) + print(f" Wall: {timer.time()-t0w:.0f}s\n") + + # Analytical + t_ana = np.linspace(t0, t_ve[-1], 500) + s_ana = maxwell_oscillatory(t_ana, ETA, MU, gamma_dot_0, omega) + + # Plot + import matplotlib + matplotlib.use("Agg") + import matplotlib.pyplot as plt + + fig, ax = plt.subplots(1, 1, figsize=(10, 5)) + + ax.plot(t_ana, s_ana, "k-", linewidth=0.8, alpha=0.5, label="VE analytical") + ax.plot(t_ve, s_ve, "b-o", markersize=3, linewidth=1.2, label="VE numerical (order 1)") + ax.plot(t_vep, s_vep, "r-s", markersize=3, linewidth=1.2, label=f"VEP numerical ($\\tau_y$={TAU_Y})") + + ax.axhline(TAU_Y, color="r", linestyle="--", alpha=0.4, linewidth=0.8) + ax.axhline(-TAU_Y, color="r", linestyle="--", alpha=0.4, linewidth=0.8) + ax.text(0.3, TAU_Y + 0.02, f"$\\tau_y$ = {TAU_Y}", color="r", fontsize=9, alpha=0.6) + + ax.set_xlabel("Time ($t / t_r$)") + ax.set_ylabel("$\\sigma_{xy}$") + ax.set_title(f"Oscillatory Maxwell VE vs VEP shear (De = {De})") + ax.legend(loc="upper left", fontsize=9) + ax.set_xlim(0, t_ve[-1]) + ax.grid(True, alpha=0.3) + + plt.tight_layout() + os.makedirs("output", exist_ok=True) + plt.savefig("output/ve_vep_oscillatory.png", dpi=150) + plt.savefig("output/ve_vep_oscillatory.pdf") + print("Saved output/ve_vep_oscillatory.png and .pdf") diff --git a/tests/run_vep_oscillatory.py b/tests/run_vep_oscillatory.py new file mode 100644 index 000000000..3f767579e --- /dev/null +++ b/tests/run_vep_oscillatory.py @@ -0,0 +1,135 @@ +"""Oscillatory VEP shear box — does the yield stress cap the oscillation? + +Same setup as the VE oscillatory test but with a yield stress. +The VE amplitude at steady state is η γ̇₀ De/√(1+De²). +If τ_y is below this amplitude, the stress should be clipped. +""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw +from underworld3.function import expression + + +def maxwell_oscillatory(t, eta, mu, gamma_dot_0, omega): + """Full analytical σ_xy for oscillatory Maxwell shear (incl. transient).""" + t_r = eta / mu + De = omega * t_r + prefactor = eta * gamma_dot_0 * De / (1.0 + De**2) + return prefactor * (np.sin(omega * t) - De * np.cos(omega * t) + De * np.exp(-t / t_r)) + + +def run_vep_oscillatory(order, n_steps, dt_over_tr, De, tau_y): + """Run oscillatory VEP shear box.""" + + ETA, MU, H, W = 1.0, 1.0, 1.0, 2.0 + t_r = ETA / MU + omega = De / t_r + V0 = 0.5 + gamma_dot_0 = 2.0 * V0 / H + dt = dt_over_tr * t_r + + # VE steady-state amplitude + ve_amplitude = ETA * gamma_dot_0 * De / np.sqrt(1 + De**2) + + mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), + ) + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=order) + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA + stokes.constitutive_model.Parameters.shear_modulus = MU + stokes.constitutive_model.Parameters.dt_elastic = dt + stokes.constitutive_model.Parameters.yield_stress = tau_y + stokes.constitutive_model.Parameters.strainrate_inv_II_min = 1.0e-6 + + # Seed with linear shear + v.data[:, 0] = v.coords[:, 1] * gamma_dot_0 + v.data[:, 1] = 0.0 + + V_bc = expression(r"{V_{bc}}", 0.0, "Time-dependent boundary velocity") + stokes.add_dirichlet_bc((V_bc, 0.0), "Top") + stokes.add_dirichlet_bc((-V_bc, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + stokes.tolerance = 1.0e-5 + + stokes.petsc_options["snes_type"] = "newtonls" + stokes.petsc_options["ksp_type"] = "fgmres" + stokes.petsc_options["snes_max_it"] = 50 + + centre = np.array([[0.0, 0.0]]) + times, stress_num, stress_ve = [], [], [] + time_phys = 0.0 + + for step in range(n_steps): + time_phys += dt + V_t = V0 * np.sin(omega * time_phys) + V_bc.sym = V_t + stokes.is_setup = False + + t0s = __import__('time').time() + stokes.solve(zero_init_guess=False, evalf=False) + solve_t = __import__('time').time() - t0s + + val = uw.function.evaluate(stokes.tau.sym[0, 1], centre) + sigma_xy = float(val.flatten()[0]) + ve_stress = maxwell_oscillatory(time_phys, ETA, MU, gamma_dot_0, omega) + + times.append(time_phys) + stress_num.append(sigma_xy) + stress_ve.append(ve_stress) + print(f" step {step:3d} t={time_phys:.2f} solve={solve_t:.1f}s " + f"vep={sigma_xy:+.6f} ve={ve_stress:+.6f}", flush=True) + + del stokes, mesh + return np.array(times), np.array(stress_num), np.array(stress_ve), ve_amplitude + + +if __name__ == "__main__": + De = 1.0 + dt_ratio = 0.1 + n_periods = 2 + t_r = 1.0 + omega = De / t_r + period = 2 * np.pi / omega + n_steps = int(n_periods * period / (dt_ratio * t_r)) + + ETA, gamma_dot_0 = 1.0, 1.0 + ve_amp = ETA * gamma_dot_0 * De / np.sqrt(1 + De**2) + + # Set τ_y below the VE amplitude so we see clipping + TAU_Y = 0.4 + + print(f"De={De}, VE amplitude={ve_amp:.4f}, tau_y={TAU_Y}") + print(f"Expect clipping at ±{TAU_Y}") + print(f"dt/t_r={dt_ratio}, n_steps={n_steps}") + print() + + for order in [1]: + t0 = timer.time() + t, num, ve, amp = run_vep_oscillatory(order, n_steps, dt_ratio, De, TAU_Y) + wall = timer.time() - t0 + + print(f"Order {order} (wall={wall:.0f}s):") + print(f" VE amplitude: {amp:.4f}") + print(f" Max |σ_xy|: {np.max(np.abs(num)):.6f}") + print(f" Min σ_xy: {np.min(num):.6f}") + print(f" Max σ_xy: {np.max(num):.6f}") + print(f" Clipped at τ_y={TAU_Y}? {np.max(np.abs(num)) <= TAU_Y + 0.01}") + print() + + # Print last period + last_period = t > (n_periods - 1) * period + if np.any(last_period): + idx = np.where(last_period)[0] + sample = idx[::max(1, len(idx)//12)] + print(f" Last period samples:") + for i in sample: + clipped = " CLIPPED" if abs(num[i]) > TAU_Y - 0.01 else "" + print(f" t={t[i]:.3f} vep={num[i]:+.6f} ve={ve[i]:+.6f}{clipped}") + print() From 7cd6a43b8040025d3a08efa3d8b4a242aa9a1d7c Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Sat, 21 Mar 2026 21:56:20 +1100 Subject: [PATCH 017/537] Add BDF-3 VE constitutive formulae, fix dt_elastic handling Constitutive model changes: - Add effective_order property that delegates to DDt's ramp-up counter - ve_effective_viscosity: three-way branch for BDF-1/2/3 effective viscosity (eta_eff = eta*mu*dt / (c0*eta + mu*dt) where c0 = 1, 3/2, 11/6) - E_eff: three-way branch with correct BDF coefficients for history terms - stress(): three-way branch matching the BDF discretisation VE_Stokes.solve() changes: - Fix elastic_dt -> dt_elastic parameter name bug - Remove dt_elastic overwrite: solve(timestep=) no longer clobbers the constitutive relaxation parameter with the advection timestep - Improved docstring clarifying timestep vs dt_elastic semantics Convergence verified against Maxwell analytical solution: dt=0.2 O1: 3.0e-2 O2: 4.0e-3 O3: 6.4e-3 dt=0.1 O1: 1.5e-2 O2: 9.3e-4 O3: 1.7e-3 dt=0.05 O1: 7.8e-3 O2: 2.3e-4 O3: 4.3e-4 Order 2 converges at 2nd order, Order 3 at ~2nd order (BDF-3 error constant larger for this stiffness ratio). Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- src/underworld3/constitutive_models.py | 100 +++++++++++-------------- src/underworld3/systems/solvers.py | 44 ++++++++--- 2 files changed, 76 insertions(+), 68 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 6ff31729a..df7c26b3d 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1198,32 +1198,19 @@ def ve_effective_viscosity(inner_self): if inner_self.shear_modulus == sympy.oo: return inner_self.shear_viscosity_0 - # Note, 1st order only here but we should add higher order versions of this - - # 1st Order version (default) - if inner_self._owning_model.effective_order != 2: - el_eff_visc = ( - inner_self.shear_viscosity_0 - * inner_self.shear_modulus - * inner_self.dt_elastic - / ( - inner_self.shear_viscosity_0 - + inner_self.dt_elastic * inner_self.shear_modulus - ) - ) - - # 2nd Order version (need to ask for this one) + # BDF-k effective viscosity: eta_eff = eta*mu*dt / (c0*eta + mu*dt) + # c0: 1 (BDF-1), 3/2 (BDF-2), 11/6 (BDF-3) + eta = inner_self.shear_viscosity_0 + mu = inner_self.shear_modulus + dt_e = inner_self.dt_elastic + eff_order = inner_self._owning_model.effective_order + + if eff_order == 2: + el_eff_visc = 2 * eta * mu * dt_e / (3 * eta + 2 * mu * dt_e) + elif eff_order >= 3: + el_eff_visc = 6 * eta * mu * dt_e / (11 * eta + 6 * mu * dt_e) else: - el_eff_visc = ( - 2 - * inner_self.shear_viscosity_0 - * inner_self.shear_modulus - * inner_self.dt_elastic - / ( - 3 * inner_self.shear_viscosity_0 - + 2 * inner_self.dt_elastic * inner_self.shear_modulus - ) - ) + el_eff_visc = eta * mu * dt_e / (eta + mu * dt_e) inner_self._ve_effective_viscosity.sym = el_eff_visc @@ -1300,20 +1287,23 @@ def E_eff(self): if self.Unknowns.DFDt is not None: if self.is_elastic: - if self.effective_order != 2: - stress_star = self.Unknowns.DFDt.psi_star[0].sym - E += stress_star / ( - 2 * self.Parameters.dt_elastic * self.Parameters.shear_modulus - ) + mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus + eff_order = self.effective_order - else: + if eff_order == 2: stress_star = self.Unknowns.DFDt.psi_star[0].sym stress_2star = self.Unknowns.DFDt.psi_star[1].sym - E += stress_star / ( - self.Parameters.dt_elastic * self.Parameters.shear_modulus - ) - stress_2star / ( - 4 * self.Parameters.dt_elastic * self.Parameters.shear_modulus - ) + E += stress_star / mu_dt - stress_2star / (4 * mu_dt) + elif eff_order >= 3: + stress_star = self.Unknowns.DFDt.psi_star[0].sym + stress_2star = self.Unknowns.DFDt.psi_star[1].sym + stress_3star = self.Unknowns.DFDt.psi_star[2].sym + E += (3 * stress_star / (2 * mu_dt) + - 3 * stress_2star / (4 * mu_dt) + + stress_3star / (6 * mu_dt)) + else: + stress_star = self.Unknowns.DFDt.psi_star[0].sym + E += stress_star / (2 * mu_dt) self._E_eff.sym = E @@ -1511,30 +1501,28 @@ def stress(self): if self.Unknowns.DFDt is not None: if self.is_elastic: - if self.effective_order != 2: + mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus + eff_order = self.effective_order + + if eff_order == 2: stress_star = self.Unknowns.DFDt.psi_star[0].sym - stress += ( - 2 - * self.viscosity - * ( - stress_star - / (2 * self.Parameters.dt_elastic * self.Parameters.shear_modulus) - ) + stress_2star = self.Unknowns.DFDt.psi_star[1].sym + stress += 2 * self.viscosity * ( + stress_star / mu_dt - stress_2star / (4 * mu_dt) ) - - else: + elif eff_order >= 3: stress_star = self.Unknowns.DFDt.psi_star[0].sym stress_2star = self.Unknowns.DFDt.psi_star[1].sym - - stress += ( - 2 - * self.viscosity - * ( - stress_star - / (self.Parameters.dt_elastic * self.Parameters.shear_modulus) - - stress_2star - / (4 * self.Parameters.dt_elastic * self.Parameters.shear_modulus) - ) + stress_3star = self.Unknowns.DFDt.psi_star[2].sym + stress += 2 * self.viscosity * ( + 3 * stress_star / (2 * mu_dt) + - 3 * stress_2star / (4 * mu_dt) + + stress_3star / (6 * mu_dt) + ) + else: + stress_star = self.Unknowns.DFDt.psi_star[0].sym + stress += 2 * self.viscosity * ( + stress_star / (2 * mu_dt) ) return stress diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 757fede1d..12c60a90d 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1360,25 +1360,45 @@ def solve( if uw.mpi.rank == 0 and verbose: print(f"VE Stokes solver - store stress and shift history", flush=True) - # Save advected σ* before anything modifies psi_star[0] import numpy as np - _advected_sigma_star = np.copy(self.DFDt.psi_star[0].array[...]) + import sympy as _sympy - # Project actual stress into psi_star[0] - # Uses the constitutive formula (not the stored values property) so - # that σ* and σ** from psi_star are read correctly during projection. + # Running average blending factor. + # When timestep == dt_elastic: phi = 1 → hard copy (standard behaviour). + # When timestep < dt_elastic: phi < 1 → gradual accumulation so each + # history slot represents approximately one dt_elastic of elapsed time. + dt_elastic_value = self.delta_t.sym + try: + _phi = float(_sympy.Min(1, timestep / dt_elastic_value)) + except (TypeError, ValueError): + _phi = 1.0 + + # Save advected psi_star values before projection modifies psi_star[0]. + # We need psi_star[i-1] for the running average shift. + _saved = [] + for i in range(self.DFDt.order): + _saved.append(np.copy(self.DFDt.psi_star[i].array[...])) + + # Project actual stress into psi_star[0]. + # Uses the constitutive formula so that σ* and σ** from psi_star + # are read correctly during projection. self.DFDt._psi_star_projection_solver.uw_function = self.constitutive_model.flux self.DFDt._psi_star_projection_solver.smoothing = 0.0 self.DFDt._psi_star_projection_solver.solve(verbose=verbose) - # Now psi_star[0] = projected τ (actual stress from this solve) - # Shift: psi_star[1] ← saved advected σ* (for chained tracing next step) + # Now psi_star[0] = projected τ (actual stress from this solve). + # + # Shift history with running average: + # psi_star[i] ← phi * saved[i-1] + (1-phi) * saved[i] + # + # When phi=1 (dt==dt_elastic): straight copy (classical behaviour). + # When phi<1 (dt 2, shift higher levels down - self.DFDt.psi_star[i].array[...] = self.DFDt.psi_star[i - 1].array[...] + self.DFDt.psi_star[i].array[...] = ( + _phi * _saved[i - 1] + (1 - _phi) * _saved[i] + ) # 5. BOOKKEEPING From 5cd5580e8dfa6fdf2043e57f7040e4b639699b0d Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Sun, 22 Mar 2026 14:12:55 +1100 Subject: [PATCH 018/537] Fix analytical formula, add oscillatory benchmark docs, remove running average MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Fix Maxwell analytical solution: remove spurious De factor in prefactor. Was η γ̇₀ De/(1+De²), correct is η γ̇₀/(1+De²). The bug was invisible at De=1 (factor cancels) but caused apparent "amplitude error" at other De. - Add oscillatory shear benchmark documentation (docs/advanced/benchmarks/) with convergence tables and resolution study description. - Add plot_ve_oscillatory_validation.py: generates validation figures for De=1.5 (phase lag, amplitude) with --replot support for saved .npz data. - Remove running-average history smoothing from VE_Stokes.solve(): the BDF constitutive formula couples dt_elastic to the time between evaluations, so the exponential moving average cannot compensate for dt << dt_elastic. Reverted to simple history shift (direct copy-down). Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- docs/advanced/benchmarks/index.md | 13 + .../benchmarks/ve-oscillatory-shear.md | 109 ++++++++ src/underworld3/systems/solvers.py | 36 +-- tests/plot_ve_oscillatory_validation.py | 239 ++++++++++++++++++ tests/run_ve_oscillatory.py | 2 +- 5 files changed, 371 insertions(+), 28 deletions(-) create mode 100644 docs/advanced/benchmarks/index.md create mode 100644 docs/advanced/benchmarks/ve-oscillatory-shear.md create mode 100644 tests/plot_ve_oscillatory_validation.py diff --git a/docs/advanced/benchmarks/index.md b/docs/advanced/benchmarks/index.md new file mode 100644 index 000000000..774102ea4 --- /dev/null +++ b/docs/advanced/benchmarks/index.md @@ -0,0 +1,13 @@ +--- +title: "Benchmarks" +--- + +# Solver Benchmarks + +Validation benchmarks comparing Underworld3 solvers against analytical solutions. + +```{toctree} +:maxdepth: 1 + +ve-oscillatory-shear +``` diff --git a/docs/advanced/benchmarks/ve-oscillatory-shear.md b/docs/advanced/benchmarks/ve-oscillatory-shear.md new file mode 100644 index 000000000..a7663bcde --- /dev/null +++ b/docs/advanced/benchmarks/ve-oscillatory-shear.md @@ -0,0 +1,109 @@ +--- +title: "Viscoelastic Oscillatory Shear Benchmark" +--- + +# Maxwell Oscillatory Shear + +This benchmark validates the viscoelastic Stokes solver against the analytical +solution for a Maxwell material under oscillatory simple shear. + +## Problem Setup + +A box with height $H$ and width $2H$ is sheared by imposing time-dependent +velocities on the top and bottom boundaries: + +$$v_x(y=\pm H/2, t) = \pm V_0 \sin(\omega t)$$ + +The left and right boundaries are free-slip (no vertical velocity). The shear +rate is $\dot\gamma(t) = \dot\gamma_0 \sin(\omega t)$ where $\dot\gamma_0 = 2V_0/H$. + +## Analytical Solution + +The Maxwell constitutive law gives: + +$$\dot\sigma_{xy} + \frac{\sigma_{xy}}{t_r} = \mu \dot\gamma_0 \sin(\omega t)$$ + +where $t_r = \eta/\mu$ is the relaxation time. With $\sigma(0) = 0$, the full +solution (including the startup transient) is: + +$$\sigma_{xy}(t) = \frac{\eta \dot\gamma_0}{1 + \text{De}^2} +\left[\sin(\omega t) - \text{De}\cos(\omega t) + \text{De}\,e^{-t/t_r}\right]$$ + +where $\text{De} = \omega t_r$ is the Deborah number. + +**Steady-state properties** (after transient decays): + +- Amplitude: $A = \eta \dot\gamma_0 / \sqrt{1 + \text{De}^2}$ +- Phase lag: $\delta = \arctan(\text{De})$ + +At $\text{De} = 0$ (viscous limit): $A = \eta\dot\gamma_0$, $\delta = 0$. +At $\text{De} \to \infty$ (elastic limit): $A \to 0$, $\delta \to 90°$. + +## Convergence with BDF Order + +The VE solver uses BDF-$k$ time integration ($k = 1, 2, 3$). The convergence +study (constant shear, $\text{De} = 1$) shows: + +| $\Delta t / t_r$ | BDF-1 error | BDF-2 error | BDF-3 error | +|-------------------|-------------|-------------|-------------| +| 0.200 | 3.0e-02 | 4.0e-03 | 6.4e-03 | +| 0.100 | 1.5e-02 | 9.3e-04 | 1.7e-03 | +| 0.050 | 7.8e-03 | 2.3e-04 | 4.3e-04 | +| 0.020 | 3.1e-03 | 3.7e-05 | — | + +BDF-2 achieves second-order convergence (~4x error reduction per halving) and +is the recommended default. BDF-1 is first-order. BDF-3 converges at nearly +second order but with a larger error constant. + +## Resolution Study (Oscillatory, De = 5) + +At high Deborah number, the oscillation period is short relative to the +relaxation time, requiring fine time resolution. The plot below shows the +effect of timestep size at $\text{De} = 5$ ($\omega t_r = 5$, phase lag = 79°): + +- **63 pts/period** ($\Delta t/t_r = 0.02$): both orders match analytical +- **31 pts/period** ($\Delta t/t_r = 0.04$): O1 shows slight amplitude reduction, O2 still accurate +- **16 pts/period** ($\Delta t/t_r = 0.08$): O1 amplitude visibly damped, O2 remains good + +```{note} +The amplitude reduction at coarse timesteps is numerical dissipation from +the BDF-1 discrete transfer function, not a cumulative error. The discrete +steady-state amplitude is a fixed fraction of the analytical amplitude, +determined by $\omega \Delta t$. +``` + +## Running the Benchmarks + +```bash +# Oscillatory validation (De=1.5, order 1 and 2) +python tests/plot_ve_oscillatory_validation.py + +# Resolution study (De=5, three timestep sizes) +# Saves .npz data files for re-analysis +python tests/plot_ve_oscillatory_validation.py + +# Replot from saved data (no re-running) +python tests/plot_ve_oscillatory_validation.py --replot +``` + +## Notes on `dt_elastic` + +The parameter `dt_elastic` on the constitutive model is the elastic relaxation +timescale used in the BDF discretisation. It controls the effective viscosity +$\eta_{\text{eff}}$ and the stress history weighting: + +- BDF-1: $\eta_{\text{eff}} = \eta\mu\Delta t_e / (\eta + \mu\Delta t_e)$ +- BDF-2: $\eta_{\text{eff}} = 2\eta\mu\Delta t_e / (3\eta + 2\mu\Delta t_e)$ +- BDF-3: $\eta_{\text{eff}} = 6\eta\mu\Delta t_e / (11\eta + 6\mu\Delta t_e)$ + +When `timestep` is passed to `VE_Stokes.solve()`, it controls the advection +step for semi-Lagrangian history transport. It does **not** overwrite +`dt_elastic` — these are independent parameters. + +A running-average approach for accumulating history when $\Delta t \ll \Delta t_e$ +was investigated but found to be inaccurate: the BDF constitutive formula +inherently couples `dt_elastic` to the time between stress evaluations, so +the history smoothing cannot compensate for the mismatch. For problems requiring +small advection steps with a longer relaxation scale, viscosity clamping +(flooring $\eta_{\text{eff}}$ at the `dt_elastic`-derived value) is the +recommended approach. diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 12c60a90d..e6f51dd87 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1361,23 +1361,9 @@ def solve( print(f"VE Stokes solver - store stress and shift history", flush=True) import numpy as np - import sympy as _sympy - # Running average blending factor. - # When timestep == dt_elastic: phi = 1 → hard copy (standard behaviour). - # When timestep < dt_elastic: phi < 1 → gradual accumulation so each - # history slot represents approximately one dt_elastic of elapsed time. - dt_elastic_value = self.delta_t.sym - try: - _phi = float(_sympy.Min(1, timestep / dt_elastic_value)) - except (TypeError, ValueError): - _phi = 1.0 - - # Save advected psi_star values before projection modifies psi_star[0]. - # We need psi_star[i-1] for the running average shift. - _saved = [] - for i in range(self.DFDt.order): - _saved.append(np.copy(self.DFDt.psi_star[i].array[...])) + # Save advected σ* before projection modifies psi_star[0] + _advected_sigma_star = np.copy(self.DFDt.psi_star[0].array[...]) # Project actual stress into psi_star[0]. # Uses the constitutive formula so that σ* and σ** from psi_star @@ -1387,18 +1373,14 @@ def solve( self.DFDt._psi_star_projection_solver.solve(verbose=verbose) # Now psi_star[0] = projected τ (actual stress from this solve). - # - # Shift history with running average: - # psi_star[i] ← phi * saved[i-1] + (1-phi) * saved[i] - # - # When phi=1 (dt==dt_elastic): straight copy (classical behaviour). - # When phi<1 (dt Date: Sun, 22 Mar 2026 14:19:37 +1100 Subject: [PATCH 019/537] Update dt_elastic guidance: running average is diffusive, advise viscosity limiting Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- docs/advanced/benchmarks/ve-oscillatory-shear.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/docs/advanced/benchmarks/ve-oscillatory-shear.md b/docs/advanced/benchmarks/ve-oscillatory-shear.md index a7663bcde..03e95c437 100644 --- a/docs/advanced/benchmarks/ve-oscillatory-shear.md +++ b/docs/advanced/benchmarks/ve-oscillatory-shear.md @@ -101,9 +101,8 @@ step for semi-Lagrangian history transport. It does **not** overwrite `dt_elastic` — these are independent parameters. A running-average approach for accumulating history when $\Delta t \ll \Delta t_e$ -was investigated but found to be inaccurate: the BDF constitutive formula -inherently couples `dt_elastic` to the time between stress evaluations, so -the history smoothing cannot compensate for the mismatch. For problems requiring -small advection steps with a longer relaxation scale, viscosity clamping -(flooring $\eta_{\text{eff}}$ at the `dt_elastic`-derived value) is the -recommended approach. +was investigated but found to be extremely diffusive for semi-Lagrangian +transport and is not implemented. To prevent runaway or unstable behaviour +when timesteps become small (e.g. due to CFL constraints or failure events), +we advise limiting the minimum effective viscosity, in line with the physics +of the problem. From 0cab29357e9614a366aa1290dd73cf1915a3f447 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 23 Mar 2026 13:23:45 +1100 Subject: [PATCH 020/537] Fix stale analytical formulas and minor issues from PR review MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - Remove spurious De factor from Maxwell oscillatory prefactor and steady-state amplitude in 5 test/validation scripts (code and docstrings). The corrected formula is η γ̇₀/(1+De²), not η γ̇₀ De/(1+De²). - TimeSymbol: change positive=True to nonnegative=True (t=0 is valid) - test_1051: relax strict monotonicity check (diffs > 0 → >= -1e-10) to avoid flaky failures from solver roundoff - mesh.t docstring: clarify that high-level Python solve() wrappers do not yet pass time= through to PETSc Underworld development team with AI support from Claude Code --- src/underworld3/discretisation/discretisation_mesh.py | 7 +++++-- src/underworld3/utilities/unit_aware_coordinates.py | 2 +- tests/plot_ve_oscillatory_validation.py | 4 ++-- tests/run_ve_oscillatory.py | 4 ++-- tests/run_ve_vep_oscillatory_checkpoint.py | 4 ++-- tests/run_ve_vep_oscillatory_plot.py | 4 ++-- tests/run_vep_oscillatory.py | 8 ++++---- tests/test_1051_VE_shear_box.py | 2 +- 8 files changed, 19 insertions(+), 16 deletions(-) diff --git a/src/underworld3/discretisation/discretisation_mesh.py b/src/underworld3/discretisation/discretisation_mesh.py index 1db908564..4b11dbd6e 100644 --- a/src/underworld3/discretisation/discretisation_mesh.py +++ b/src/underworld3/discretisation/discretisation_mesh.py @@ -1513,8 +1513,11 @@ def t(self): and Jacobian functions. Use ``mesh.t`` in expressions to reference this time without forcing JIT recompilation each timestep. - The solver sets the time value via ``solve(time=t)``. If ``time`` - is not provided, ``petsc_t`` defaults to 0. + The low-level PETSc solver accepts ``time=t`` to set the value + of ``petsc_t`` for pointwise functions. If not provided, ``petsc_t`` + defaults to 0. Note: the high-level Python ``solve()`` wrappers + do not yet pass ``time=`` through — set it directly via + ``UW_DMSetTime`` at the Cython level if needed. When the scaling system is active, ``mesh.t`` carries time units (derived from the model's time scale) so that dimensional analysis diff --git a/src/underworld3/utilities/unit_aware_coordinates.py b/src/underworld3/utilities/unit_aware_coordinates.py index 26471db63..0073f2830 100644 --- a/src/underworld3/utilities/unit_aware_coordinates.py +++ b/src/underworld3/utilities/unit_aware_coordinates.py @@ -96,7 +96,7 @@ class TimeSymbol(sympy.Symbol): _units = None def __new__(cls, name="t", **kwargs): - obj = super().__new__(cls, name, real=True, positive=True, **kwargs) + obj = super().__new__(cls, name, real=True, nonnegative=True, **kwargs) return obj @property diff --git a/tests/plot_ve_oscillatory_validation.py b/tests/plot_ve_oscillatory_validation.py index d4dbf5255..f3ac103f7 100644 --- a/tests/plot_ve_oscillatory_validation.py +++ b/tests/plot_ve_oscillatory_validation.py @@ -5,7 +5,7 @@ - Bottom panel: stress σ_xy(t) for order 1 and order 2 vs analytical Maxwell analytical solution including startup transient: - σ_xy(t) = η γ̇₀ De/(1+De²) [sin(ωt) - De cos(ωt) + De exp(-t/t_r)] + σ_xy(t) = η γ̇₀/(1+De²) [sin(ωt) - De cos(ωt) + De exp(-t/t_r)] Results are saved as .npz checkpoint files for re-analysis. @@ -137,7 +137,7 @@ def make_plot(results, params, output_path): shear_rate = gamma_dot_0 * np.sin(omega * t_fine) phase_lag_deg = np.degrees(np.arctan(De)) - steady_amp = ETA * gamma_dot_0 * De / np.sqrt(1 + De**2) + steady_amp = ETA * gamma_dot_0 / np.sqrt(1 + De**2) period = 2.0 * np.pi / omega fig, (ax1, ax2) = plt.subplots( diff --git a/tests/run_ve_oscillatory.py b/tests/run_ve_oscillatory.py index be5c996be..98242026e 100644 --- a/tests/run_ve_oscillatory.py +++ b/tests/run_ve_oscillatory.py @@ -3,12 +3,12 @@ Maxwell material under sinusoidal boundary velocity V(t) = V0 sin(ωt). Full solution including startup transient: - σ_xy(t) = η γ̇₀ De/(1+De²) [sin(ωt) - De cos(ωt) + De exp(-t/t_r)] + σ_xy(t) = η γ̇₀/(1+De²) [sin(ωt) - De cos(ωt) + De exp(-t/t_r)] where De = ω t_r is the Deborah number. At steady state (t >> t_r), the transient dies out and the stress -oscillates with amplitude η γ̇₀ De/√(1+De²) and phase lag arctan(De). +oscillates with amplitude η γ̇₀/√(1+De²) and phase lag arctan(De). """ import time as timer diff --git a/tests/run_ve_vep_oscillatory_checkpoint.py b/tests/run_ve_vep_oscillatory_checkpoint.py index 706cc2ce8..b14529d51 100644 --- a/tests/run_ve_vep_oscillatory_checkpoint.py +++ b/tests/run_ve_vep_oscillatory_checkpoint.py @@ -11,7 +11,7 @@ def maxwell_oscillatory(t, eta, mu, gamma_dot_0, omega): """Full analytical σ_xy for oscillatory Maxwell shear.""" t_r = eta / mu De = omega * t_r - prefactor = eta * gamma_dot_0 * De / (1.0 + De**2) + prefactor = eta * gamma_dot_0 / (1.0 + De**2) return prefactor * (np.sin(omega * t) - De * np.cos(omega * t) + De * np.exp(-t / t_r)) @@ -88,7 +88,7 @@ def run_oscillatory(order, n_steps, dt, omega, V0, tau_y=None): n_periods = 2 n_steps = int(n_periods * period / dt) - ve_amp = ETA * gamma_dot_0 * De / np.sqrt(1.0 + De**2) + ve_amp = ETA * gamma_dot_0 / np.sqrt(1.0 + De**2) print(f"De={De}, omega={omega:.3f}, period={period:.3f}") print(f"VE amplitude={ve_amp:.4f}, tau_y={TAU_Y}") diff --git a/tests/run_ve_vep_oscillatory_plot.py b/tests/run_ve_vep_oscillatory_plot.py index b5b50c0db..79ba8dcf5 100644 --- a/tests/run_ve_vep_oscillatory_plot.py +++ b/tests/run_ve_vep_oscillatory_plot.py @@ -18,7 +18,7 @@ def maxwell_oscillatory(t, eta, mu, gamma_dot_0, omega): """Full analytical σ_xy for oscillatory Maxwell shear.""" t_r = eta / mu De = omega * t_r - prefactor = eta * gamma_dot_0 * De / (1.0 + De**2) + prefactor = eta * gamma_dot_0 / (1.0 + De**2) return prefactor * (np.sin(omega * t) - De * np.cos(omega * t) + De * np.exp(-t / t_r)) @@ -108,7 +108,7 @@ def run_oscillatory(order, n_steps, dt, omega, V0, t0, tau_y=None): n_periods = 2 n_steps = int(n_periods * period / dt) - ve_amp = ETA * gamma_dot_0 * De / np.sqrt(1.0 + De**2) + ve_amp = ETA * gamma_dot_0 / np.sqrt(1.0 + De**2) sigma_t0 = maxwell_oscillatory(t0, ETA, MU, gamma_dot_0, omega) print(f"De={De}, omega={omega:.3f}, period={period:.3f}") diff --git a/tests/run_vep_oscillatory.py b/tests/run_vep_oscillatory.py index 3f767579e..9831b3e80 100644 --- a/tests/run_vep_oscillatory.py +++ b/tests/run_vep_oscillatory.py @@ -1,7 +1,7 @@ """Oscillatory VEP shear box — does the yield stress cap the oscillation? Same setup as the VE oscillatory test but with a yield stress. -The VE amplitude at steady state is η γ̇₀ De/√(1+De²). +The VE amplitude at steady state is η γ̇₀/√(1+De²). If τ_y is below this amplitude, the stress should be clipped. """ @@ -16,7 +16,7 @@ def maxwell_oscillatory(t, eta, mu, gamma_dot_0, omega): """Full analytical σ_xy for oscillatory Maxwell shear (incl. transient).""" t_r = eta / mu De = omega * t_r - prefactor = eta * gamma_dot_0 * De / (1.0 + De**2) + prefactor = eta * gamma_dot_0 / (1.0 + De**2) return prefactor * (np.sin(omega * t) - De * np.cos(omega * t) + De * np.exp(-t / t_r)) @@ -31,7 +31,7 @@ def run_vep_oscillatory(order, n_steps, dt_over_tr, De, tau_y): dt = dt_over_tr * t_r # VE steady-state amplitude - ve_amplitude = ETA * gamma_dot_0 * De / np.sqrt(1 + De**2) + ve_amplitude = ETA * gamma_dot_0 / np.sqrt(1 + De**2) mesh = uw.meshing.StructuredQuadBox( elementRes=(16, 8), minCoords=(-W/2, -H/2), maxCoords=(W/2, H/2), @@ -100,7 +100,7 @@ def run_vep_oscillatory(order, n_steps, dt_over_tr, De, tau_y): n_steps = int(n_periods * period / (dt_ratio * t_r)) ETA, gamma_dot_0 = 1.0, 1.0 - ve_amp = ETA * gamma_dot_0 * De / np.sqrt(1 + De**2) + ve_amp = ETA * gamma_dot_0 / np.sqrt(1 + De**2) # Set τ_y below the VE amplitude so we see clipping TAU_Y = 0.4 diff --git a/tests/test_1051_VE_shear_box.py b/tests/test_1051_VE_shear_box.py index 1691ee319..1608a7291 100644 --- a/tests/test_1051_VE_shear_box.py +++ b/tests/test_1051_VE_shear_box.py @@ -177,5 +177,5 @@ def test_steady_state_approach(self): f"analytical = {ana[-1]:.6f}") diffs = np.diff(num) - assert np.all(diffs > 0), "Stress should be monotonically increasing" + assert np.all(diffs >= -1.0e-10), "Stress should be monotonically increasing" assert final_err < 0.02 From ae8066b2074ac78a1331cebca77b6c3c27028af9 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Mar 2026 09:14:51 +1100 Subject: [PATCH 021/537] Variable-dt BDF coefficients for viscoelastic constitutive model The DDt system already computes correct variable-timestep BDF coefficients via _bdf_coefficients(order, dt_n, dt_history), but the constitutive model hardcoded uniform-step values (c0 = 3/2 for BDF-2, 11/6 for BDF-3). When dt varies between timesteps, the hardcoded coefficients are wrong, silently degrading accuracy. This commit: - Adds bdf_coefficients property to all DDt classes (SemiLagrangian, Eulerian, Lagrangian, Lagrangian_Swarm) exposing the current coefficients - Adds _get_bdf_coefficients() helper to ViscoElasticPlasticFlowModel that pulls from DDt when available, falls back to uniform otherwise - Rewrites ve_effective_viscosity, E_eff, and stress() to use DDt coefficients instead of hardcoded order-based branching - Adds square-wave forcing benchmark (tests/run_ve_square_wave.py) for validating variable-dt accuracy via Fourier superposition of Maxwell analytical solutions For uniform dt, results are identical (same coefficient values). Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 63 ++----- src/underworld3/systems/ddt.py | 25 +++ tests/run_ve_square_wave.py | 249 +++++++++++++++++++++++++ 3 files changed, 294 insertions(+), 43 deletions(-) create mode 100644 tests/run_ve_square_wave.py diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index df7c26b3d..b50687fe8 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -48,6 +48,7 @@ from underworld3.swarm import IndexSwarmVariable from underworld3.discretisation import MeshVariable from underworld3.systems.ddt import SemiLagrangian as SemiLagrangian_DDt +from underworld3.systems.ddt import _bdf_coefficients from underworld3.function.quantities import UWQuantity from underworld3.systems.ddt import Lagrangian as Lagrangian_DDt @@ -1199,18 +1200,14 @@ def ve_effective_viscosity(inner_self): return inner_self.shear_viscosity_0 # BDF-k effective viscosity: eta_eff = eta*mu*dt / (c0*eta + mu*dt) - # c0: 1 (BDF-1), 3/2 (BDF-2), 11/6 (BDF-3) + # c0 from DDt's BDF coefficients (variable-dt aware) eta = inner_self.shear_viscosity_0 mu = inner_self.shear_modulus dt_e = inner_self.dt_elastic - eff_order = inner_self._owning_model.effective_order + coeffs = inner_self._owning_model._get_bdf_coefficients() + c0 = coeffs[0] - if eff_order == 2: - el_eff_visc = 2 * eta * mu * dt_e / (3 * eta + 2 * mu * dt_e) - elif eff_order >= 3: - el_eff_visc = 6 * eta * mu * dt_e / (11 * eta + 6 * mu * dt_e) - else: - el_eff_visc = eta * mu * dt_e / (eta + mu * dt_e) + el_eff_visc = eta * mu * dt_e / (c0 * eta + mu * dt_e) inner_self._ve_effective_viscosity.sym = el_eff_visc @@ -1252,6 +1249,12 @@ def effective_order(self): return min(self._order, self.Unknowns.DFDt.effective_order) return self._order + def _get_bdf_coefficients(self): + """Get BDF coefficients from DDt (variable-dt aware) or fall back to uniform.""" + if self.Unknowns is not None and self.Unknowns.DFDt is not None: + return self.Unknowns.DFDt.bdf_coefficients + return _bdf_coefficients(self.effective_order, None, []) + # The following should have no setters @property def stress_star(self): @@ -1288,22 +1291,11 @@ def E_eff(self): if self.is_elastic: mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus - eff_order = self.effective_order - - if eff_order == 2: - stress_star = self.Unknowns.DFDt.psi_star[0].sym - stress_2star = self.Unknowns.DFDt.psi_star[1].sym - E += stress_star / mu_dt - stress_2star / (4 * mu_dt) - elif eff_order >= 3: - stress_star = self.Unknowns.DFDt.psi_star[0].sym - stress_2star = self.Unknowns.DFDt.psi_star[1].sym - stress_3star = self.Unknowns.DFDt.psi_star[2].sym - E += (3 * stress_star / (2 * mu_dt) - - 3 * stress_2star / (4 * mu_dt) - + stress_3star / (6 * mu_dt)) - else: - stress_star = self.Unknowns.DFDt.psi_star[0].sym - E += stress_star / (2 * mu_dt) + coeffs = self._get_bdf_coefficients() + + # History contribution: -Σ cᵢ·σ_star[i-1] / (2·μ·dt) + for i in range(1, len(coeffs)): + E += -coeffs[i] * self.Unknowns.DFDt.psi_star[i - 1].sym / (2 * mu_dt) self._E_eff.sym = E @@ -1502,27 +1494,12 @@ def stress(self): if self.is_elastic: mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus - eff_order = self.effective_order + coeffs = self._get_bdf_coefficients() - if eff_order == 2: - stress_star = self.Unknowns.DFDt.psi_star[0].sym - stress_2star = self.Unknowns.DFDt.psi_star[1].sym - stress += 2 * self.viscosity * ( - stress_star / mu_dt - stress_2star / (4 * mu_dt) - ) - elif eff_order >= 3: - stress_star = self.Unknowns.DFDt.psi_star[0].sym - stress_2star = self.Unknowns.DFDt.psi_star[1].sym - stress_3star = self.Unknowns.DFDt.psi_star[2].sym - stress += 2 * self.viscosity * ( - 3 * stress_star / (2 * mu_dt) - - 3 * stress_2star / (4 * mu_dt) - + stress_3star / (6 * mu_dt) - ) - else: - stress_star = self.Unknowns.DFDt.psi_star[0].sym + # History contribution: 2·η_eff · (-Σ cᵢ·σ_star[i-1]) / (2·μ·dt) + for i in range(1, len(coeffs)): stress += 2 * self.viscosity * ( - stress_star / (2 * mu_dt) + -coeffs[i] * self.Unknowns.DFDt.psi_star[i - 1].sym / (2 * mu_dt) ) return stress diff --git a/src/underworld3/systems/ddt.py b/src/underworld3/systems/ddt.py index 9e20739b8..27705b914 100644 --- a/src/underworld3/systems/ddt.py +++ b/src/underworld3/systems/ddt.py @@ -526,6 +526,11 @@ def update_post_solve( return + @property + def bdf_coefficients(self): + """Current BDF coefficients [c0, c1, ...] accounting for variable timesteps.""" + return _bdf_coefficients(self.effective_order, self._dt, self._dt_history) + def bdf(self, order: Optional[int] = None): r"""Backward differentiation approximation of the time-derivative of ψ. @@ -894,6 +899,11 @@ def update_post_solve( return + @property + def bdf_coefficients(self): + """Current BDF coefficients [c0, c1, ...] accounting for variable timesteps.""" + return _bdf_coefficients(self.effective_order, self._dt, self._dt_history) + def bdf(self, order=None): r"""Backward differentiation approximation of the time-derivative of :math:`\psi`. @@ -1717,6 +1727,11 @@ def advect_history(self, dt, evalf=False, verbose=False): return + @property + def bdf_coefficients(self): + """Current BDF coefficients [c0, c1, ...] accounting for variable timesteps.""" + return _bdf_coefficients(self.effective_order, self._dt, self._dt_history) + def bdf(self, order=None): r"""Backward differentiation approximation of the time-derivative of :math:`\psi`. @@ -2010,6 +2025,11 @@ def update_post_solve( if self._n_solves_completed < self.order: self._n_solves_completed += 1 + @property + def bdf_coefficients(self): + """Current BDF coefficients [c0, c1, ...] accounting for variable timesteps.""" + return _bdf_coefficients(self.effective_order, self._dt, self._dt_history) + def bdf(self, order=None): r"""Backward differentiation approximation of the time-derivative of :math:`\psi`. @@ -2307,6 +2327,11 @@ def update_post_solve( return + @property + def bdf_coefficients(self): + """Current BDF coefficients [c0, c1, ...] accounting for variable timesteps.""" + return _bdf_coefficients(self.effective_order, self._dt, self._dt_history) + def bdf(self, order=None): r"""Backward differentiation approximation of the time-derivative of :math:`\psi`. diff --git a/tests/run_ve_square_wave.py b/tests/run_ve_square_wave.py new file mode 100644 index 000000000..788b7551e --- /dev/null +++ b/tests/run_ve_square_wave.py @@ -0,0 +1,249 @@ +"""Variable-timestep VE benchmark: square-wave forcing. + +Maxwell material under square-wave shear rate (Fourier series, N harmonics): + + γ̇(t) = (4γ̇₀/π) Σ_{k=1..N} sin((2k-1)ωt) / (2k-1) + +Since the Maxwell equation is linear, the analytical stress is the +superposition of single-frequency solutions: + + σ(t) = Σ_{k=1..N} maxwell_oscillatory(t, η, μ, aₖ, ωₖ) + +where aₖ = 4γ̇₀/(π(2k-1)) and ωₖ = (2k-1)ω. + +The sharp transitions demand small dt at the edges, large dt in the +flat regions — testing variable-dt BDF correctness. + +Usage: + python tests/run_ve_square_wave.py +""" + +import time as timer +import numpy as np +import sympy +import underworld3 as uw +from underworld3.function import expression + + +def maxwell_oscillatory(t, eta, mu, gamma_dot_0, omega): + """Full analytical σ_xy for single-frequency oscillatory Maxwell shear.""" + t_r = eta / mu + De = omega * t_r + prefactor = eta * gamma_dot_0 / (1.0 + De**2) + return prefactor * (np.sin(omega * t) - De * np.cos(omega * t) + De * np.exp(-t / t_r)) + + +def square_wave_analytical(t, eta, mu, gamma_dot_0, omega, n_harmonics=20): + """Analytical stress for square-wave forcing via Fourier superposition.""" + sigma = np.zeros_like(t) + for k in range(1, n_harmonics + 1): + n = 2 * k - 1 # odd harmonics: 1, 3, 5, ... + a_k = 4.0 * gamma_dot_0 / (np.pi * n) + omega_k = n * omega + sigma += maxwell_oscillatory(t, eta, mu, a_k, omega_k) + return sigma + + +def square_wave_shear_rate(t, gamma_dot_0, omega, n_harmonics=20): + """Square-wave shear rate via truncated Fourier series.""" + rate = np.zeros_like(t) + for k in range(1, n_harmonics + 1): + n = 2 * k - 1 + rate += 4.0 * gamma_dot_0 / (np.pi * n) * np.sin(n * omega * t) + return rate + + +def adaptive_dt(t_current, omega, dt_min, dt_max): + """Adaptive timestep: small near square-wave transitions, large on plateaux. + + Transitions occur at t = (2m+1)·π/(2ω) for integer m, i.e. at odd + multiples of quarter-period. We use distance to nearest transition + to interpolate between dt_min and dt_max. + """ + half_period = np.pi / omega + # Phase within half-period [0, half_period) + phase = t_current % half_period + # Distance to nearest transition (0 or half_period boundary) + dist = min(phase, half_period - phase) + # Normalise to [0, 1] where 0 = at transition, 1 = mid-plateau + frac = dist / (half_period / 2.0) + # Smooth interpolation + return dt_min + (dt_max - dt_min) * frac**2 + + +def run_square_wave(order, De, n_periods, dt_min_over_tr, dt_max_over_tr, + n_harmonics=20, uniform=False): + """Run VE square-wave shear box with adaptive or uniform timestep.""" + + ETA, MU, H, W = 1.0, 1.0, 1.0, 2.0 + t_r = ETA / MU + omega = De / t_r + V0 = 0.5 + gamma_dot_0 = 2.0 * V0 / H + dt_min = dt_min_over_tr * t_r + dt_max = dt_max_over_tr * t_r + T = 2.0 * np.pi / omega + t_end = n_periods * T + + mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 8), minCoords=(-W / 2, -H / 2), maxCoords=(W / 2, H / 2), + ) + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.VE_Stokes(mesh, velocityField=v, pressureField=p, order=order) + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA + stokes.constitutive_model.Parameters.shear_modulus = MU + + # Boundary conditions: oscillatory shear with square-wave envelope + x, y = mesh.X + t_sym = sympy.Symbol("t_sim") + t_expr = expression(R"t_{\mathrm{sim}}", t_sym, "Simulation time") + + # Build the Fourier-series velocity symbolically (truncated) + v_top_sym = sympy.Integer(0) + for k in range(1, n_harmonics + 1): + n = 2 * k - 1 + a_k = sympy.Rational(4, 1) / (sympy.pi * n) + v_top_sym += a_k * sympy.sin(n * omega * t_sym) + v_top_sym *= V0 + + v_bc_sym = v_top_sym * (y / (H / 2)) + v_bc = expression(R"v_{\mathrm{bc}}", v_bc_sym, "Square-wave shear velocity") + + stokes.add_dirichlet_bc((v_bc.sym, 0.0), "Top") + stokes.add_dirichlet_bc((-v_bc.sym, 0.0), "Bottom") + stokes.add_dirichlet_bc((None, 0.0), "Left") + stokes.add_dirichlet_bc((None, 0.0), "Right") + + # Time loop + times = [] + numerical_stress = [] + timesteps_used = [] + t_current = 0.0 + step = 0 + + while t_current < t_end: + # Determine timestep + if uniform: + dt = dt_min + else: + dt = adaptive_dt(t_current, omega, dt_min, dt_max) + + # Update simulation time and dt_elastic + t_expr.sym = t_current + dt + stokes.constitutive_model.Parameters.dt_elastic = dt + + stokes.solve(timestep=dt) + + t_current += dt + step += 1 + + # Extract stress at mesh centre + tau = stokes.tau + centre = np.array([[0.0, 0.0]]) + tau_xy = uw.function.evaluate(tau.sym[0, 1], centre, mesh) + sigma_xy = float(tau_xy.flatten()[0]) + + times.append(t_current) + numerical_stress.append(sigma_xy) + timesteps_used.append(dt) + + if step % 50 == 0: + ana = square_wave_analytical( + np.array([t_current]), ETA, MU, gamma_dot_0, omega, n_harmonics + )[0] + print(f" Step {step:4d}: t/t_r = {t_current / t_r:.3f}, " + f"dt/t_r = {dt / t_r:.4f}, " + f"σ_xy = {sigma_xy:.6f}, ana = {ana:.6f}") + + times = np.array(times) + numerical_stress = np.array(numerical_stress) + timesteps_used = np.array(timesteps_used) + + # Analytical solution + analytical_stress = square_wave_analytical(times, ETA, MU, gamma_dot_0, omega, n_harmonics) + + # Error metrics (skip first period for startup transient) + mask = times > T + if mask.sum() > 0: + l2_err = np.sqrt(np.mean((numerical_stress[mask] - analytical_stress[mask]) ** 2)) + linf_err = np.max(np.abs(numerical_stress[mask] - analytical_stress[mask])) + else: + l2_err = linf_err = np.nan + + return { + "times": times, + "numerical": numerical_stress, + "analytical": analytical_stress, + "timesteps": timesteps_used, + "l2_error": l2_err, + "linf_error": linf_err, + "n_steps": step, + } + + +if __name__ == "__main__": + De = 1.5 + order = 2 + n_periods = 3 + n_harmonics = 15 + + print("=" * 60) + print(f"Square-wave VE benchmark: De={De}, order={order}") + print(f" {n_harmonics} Fourier harmonics, {n_periods} periods") + print("=" * 60) + + # Run with adaptive dt + print("\n--- Adaptive timestep ---") + t0 = timer.time() + result_adaptive = run_square_wave( + order=order, De=De, n_periods=n_periods, + dt_min_over_tr=0.02, dt_max_over_tr=0.15, + n_harmonics=n_harmonics, uniform=False, + ) + t_adaptive = timer.time() - t0 + print(f" {result_adaptive['n_steps']} steps in {t_adaptive:.1f}s") + print(f" L2 error: {result_adaptive['l2_error']:.6e}") + print(f" Linf error: {result_adaptive['linf_error']:.6e}") + print(f" dt range: [{result_adaptive['timesteps'].min():.4f}, " + f"{result_adaptive['timesteps'].max():.4f}]") + + # Run with uniform dt (reference) + print("\n--- Uniform timestep (dt_min) ---") + t0 = timer.time() + result_uniform = run_square_wave( + order=order, De=De, n_periods=n_periods, + dt_min_over_tr=0.02, dt_max_over_tr=0.02, + n_harmonics=n_harmonics, uniform=True, + ) + t_uniform = timer.time() - t0 + print(f" {result_uniform['n_steps']} steps in {t_uniform:.1f}s") + print(f" L2 error: {result_uniform['l2_error']:.6e}") + print(f" Linf error: {result_uniform['linf_error']:.6e}") + + # Summary + print("\n" + "=" * 60) + print("Summary:") + print(f" Adaptive: {result_adaptive['n_steps']} steps, " + f"L2 = {result_adaptive['l2_error']:.2e}") + print(f" Uniform: {result_uniform['n_steps']} steps, " + f"L2 = {result_uniform['l2_error']:.2e}") + ratio = result_adaptive['l2_error'] / result_uniform['l2_error'] + print(f" Error ratio (adaptive/uniform): {ratio:.2f}") + print(f" Step savings: {1 - result_adaptive['n_steps'] / result_uniform['n_steps']:.0%}") + + # Save results + np.savez( + "tests/ve_square_wave_benchmark.npz", + adaptive_times=result_adaptive["times"], + adaptive_numerical=result_adaptive["numerical"], + adaptive_analytical=result_adaptive["analytical"], + adaptive_timesteps=result_adaptive["timesteps"], + uniform_times=result_uniform["times"], + uniform_numerical=result_uniform["numerical"], + uniform_analytical=result_uniform["analytical"], + uniform_timesteps=result_uniform["timesteps"], + ) + print("\nResults saved to tests/ve_square_wave_benchmark.npz") From 8bc3b6662f13868a0bccea4a00ad6665de6031cf Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Mar 2026 14:00:12 +1100 Subject: [PATCH 022/537] Fix time-varying BCs: pass UWexpression directly, not .sym MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Passing expr.sym to add_dirichlet_bc strips the UWexpression wrapper, causing the value to be baked as a C literal in the JIT. The PetscDS constants mechanism only works when the UWexpression atom is visible to _extract_constants during compilation. - Square-wave benchmark: pass V_top (not V_top.sym) to BCs - Remove is_setup=False workaround from 4 oscillatory test scripts (run_ve_oscillatory, run_vep_oscillatory, run_ve_vep_oscillatory_plot, run_ve_vep_oscillatory_checkpoint) — unnecessary when UWexpression is passed directly Underworld development team with AI support from Claude Code --- tests/run_ve_oscillatory.py | 1 - tests/run_ve_square_wave.py | 43 ++++++++++------------ tests/run_ve_vep_oscillatory_checkpoint.py | 1 - tests/run_ve_vep_oscillatory_plot.py | 1 - tests/run_vep_oscillatory.py | 1 - 5 files changed, 19 insertions(+), 28 deletions(-) diff --git a/tests/run_ve_oscillatory.py b/tests/run_ve_oscillatory.py index 98242026e..2cf7e21da 100644 --- a/tests/run_ve_oscillatory.py +++ b/tests/run_ve_oscillatory.py @@ -67,7 +67,6 @@ def run_oscillatory(order, n_steps, dt_over_tr, De): # Update boundary velocity for this timestep V_t = V0 * np.sin(omega * time_phys) V_bc.sym = V_t - stokes.is_setup = False # force BC re-evaluation stokes.solve(zero_init_guess=False, evalf=False) diff --git a/tests/run_ve_square_wave.py b/tests/run_ve_square_wave.py index 788b7551e..36b2a8336 100644 --- a/tests/run_ve_square_wave.py +++ b/tests/run_ve_square_wave.py @@ -96,26 +96,15 @@ def run_square_wave(order, De, n_periods, dt_min_over_tr, dt_max_over_tr, stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA stokes.constitutive_model.Parameters.shear_modulus = MU - # Boundary conditions: oscillatory shear with square-wave envelope - x, y = mesh.X - t_sym = sympy.Symbol("t_sim") - t_expr = expression(R"t_{\mathrm{sim}}", t_sym, "Simulation time") + # Boundary conditions: simple shear driven by top/bottom velocity + # V_top updated numerically each timestep to produce square-wave γ̇ + V_top = expression(R"V_{\mathrm{top}}", sympy.Float(0.0), "Top boundary velocity") - # Build the Fourier-series velocity symbolically (truncated) - v_top_sym = sympy.Integer(0) - for k in range(1, n_harmonics + 1): - n = 2 * k - 1 - a_k = sympy.Rational(4, 1) / (sympy.pi * n) - v_top_sym += a_k * sympy.sin(n * omega * t_sym) - v_top_sym *= V0 - - v_bc_sym = v_top_sym * (y / (H / 2)) - v_bc = expression(R"v_{\mathrm{bc}}", v_bc_sym, "Square-wave shear velocity") - - stokes.add_dirichlet_bc((v_bc.sym, 0.0), "Top") - stokes.add_dirichlet_bc((-v_bc.sym, 0.0), "Bottom") - stokes.add_dirichlet_bc((None, 0.0), "Left") - stokes.add_dirichlet_bc((None, 0.0), "Right") + stokes.add_dirichlet_bc((V_top, 0.0), "Top") + stokes.add_dirichlet_bc((-V_top, 0.0), "Bottom") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Left") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Right") + stokes.tolerance = 1.0e-6 # Time loop times = [] @@ -131,19 +120,25 @@ def run_square_wave(order, De, n_periods, dt_min_over_tr, dt_max_over_tr, else: dt = adaptive_dt(t_current, omega, dt_min, dt_max) - # Update simulation time and dt_elastic - t_expr.sym = t_current + dt + t_next = t_current + dt + + # Update boundary velocity: V_top(t) such that γ̇ = 2·V_top/H = square wave + # square_wave_shear_rate returns the actual γ̇, so V_top = γ̇ · H/2 + gamma_dot_t = square_wave_shear_rate( + np.array([t_next]), gamma_dot_0, omega, n_harmonics + )[0] + V_top.sym = sympy.Float(gamma_dot_t * H / 2.0) + stokes.constitutive_model.Parameters.dt_elastic = dt - stokes.solve(timestep=dt) + stokes.solve(zero_init_guess=False, timestep=dt) t_current += dt step += 1 # Extract stress at mesh centre - tau = stokes.tau centre = np.array([[0.0, 0.0]]) - tau_xy = uw.function.evaluate(tau.sym[0, 1], centre, mesh) + tau_xy = uw.function.evaluate(stokes.tau.sym[0, 1], centre) sigma_xy = float(tau_xy.flatten()[0]) times.append(t_current) diff --git a/tests/run_ve_vep_oscillatory_checkpoint.py b/tests/run_ve_vep_oscillatory_checkpoint.py index b14529d51..8ae07f015 100644 --- a/tests/run_ve_vep_oscillatory_checkpoint.py +++ b/tests/run_ve_vep_oscillatory_checkpoint.py @@ -57,7 +57,6 @@ def run_oscillatory(order, n_steps, dt, omega, V0, tau_y=None): for step in range(n_steps): time_phys += dt V_bc.sym = V0 * np.sin(omega * time_phys) - stokes.is_setup = False stokes.solve(zero_init_guess=False, evalf=False) diff --git a/tests/run_ve_vep_oscillatory_plot.py b/tests/run_ve_vep_oscillatory_plot.py index 79ba8dcf5..b5ee4907c 100644 --- a/tests/run_ve_vep_oscillatory_plot.py +++ b/tests/run_ve_vep_oscillatory_plot.py @@ -77,7 +77,6 @@ def run_oscillatory(order, n_steps, dt, omega, V0, t0, tau_y=None): for step in range(n_steps): time_phys += dt V_bc.sym = V0 * np.sin(omega * time_phys) - stokes.is_setup = False stokes.solve(zero_init_guess=False, evalf=False) diff --git a/tests/run_vep_oscillatory.py b/tests/run_vep_oscillatory.py index 9831b3e80..e76e212e5 100644 --- a/tests/run_vep_oscillatory.py +++ b/tests/run_vep_oscillatory.py @@ -70,7 +70,6 @@ def run_vep_oscillatory(order, n_steps, dt_over_tr, De, tau_y): time_phys += dt V_t = V0 * np.sin(omega * time_phys) V_bc.sym = V_t - stokes.is_setup = False t0s = __import__('time').time() stokes.solve(zero_init_guess=False, evalf=False) From f2204537d280b75c160bac2cc457a9c43e7c89dc Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Mar 2026 15:22:59 +1100 Subject: [PATCH 023/537] Replace advect_history() with standard DDt update_pre_solve pathway The VE_Stokes solver now uses update_pre_solve(advect_only=True) instead of the custom advect_history() method. This reuses the battle-tested advection code (coordinate handling, global_evaluate, return_coords_to_bounds) rather than reimplementing it. advect_only=True skips the history shift and psi_fn evaluation steps, since the VE solver manages those in its post-solve sequence. Only the upstream advection of existing psi_star levels is performed. The old advect_history() is parked as _advect_history_PARKED for reference. Also fixes: return_coords_to_bounds calls in advect path, benchmark BC pattern (pass UWexpression directly, 3 harmonics). Regression: 4/4 VE shear box tests pass (order 1 + order 2). Underworld development team with AI support from Claude Code --- src/underworld3/systems/ddt.py | 67 +++++++++++++++++++----------- src/underworld3/systems/solvers.py | 17 ++++---- tests/run_ve_square_wave.py | 2 +- 3 files changed, 53 insertions(+), 33 deletions(-) diff --git a/src/underworld3/systems/ddt.py b/src/underworld3/systems/ddt.py index 27705b914..7ef2f4d94 100644 --- a/src/underworld3/systems/ddt.py +++ b/src/underworld3/systems/ddt.py @@ -1254,11 +1254,21 @@ def update_pre_solve( evalf: Optional[bool] = False, verbose: Optional[bool] = False, dt_physical: Optional[float] = None, + advect_only: Optional[bool] = False, ): """Sample upstream values along characteristics before solve. On the first call, automatically initialises history from the current field values so that bdf() returns zero on the first step. + + Parameters + ---------- + advect_only : bool, optional + If True, skip the psi_fn evaluation into psi_star[0] (step 2) + and only perform history shift (step 1) and upstream advection + (step 3). Used by VE_Stokes where psi_star[0] already contains + the projected actual stress from the previous solve — we want to + advect that stored stress, not overwrite it with the flux expression. """ self._dt = dt @@ -1292,15 +1302,19 @@ def update_pre_solve( else: phi = sympy.sympify(1) - for i in range(self.order - 1, 0, -1): - self.psi_star[i].array[...] = ( - phi * self.psi_star[i - 1].array[...] + (1 - phi) * self.psi_star[i].array[...] - ) + if not advect_only: + for i in range(self.order - 1, 0, -1): + self.psi_star[i].array[...] = ( + phi * self.psi_star[i - 1].array[...] + (1 - phi) * self.psi_star[i].array[...] + ) # 2. Compute the current value of psi_fn which we store in psi_star[0] # Note the need to do a try/except to handle unsupported evaluations # (e.g. of derivatives) # + # When advect_only=True (VE stress history), skip this step — + # psi_star[0] already contains the projected actual stress from + # the previous solve and we want to advect *that*, not the flux. # CRITICAL FIX (2025-11-28): Handle coordinates correctly for unit-aware mode. # Previous bug: extracting .magnitude gives METERS (e.g., 1000000), but: @@ -1339,28 +1353,29 @@ def update_pre_solve( :, : ] - try: - # Use shifted ND coords to avoid quad mesh boundary issues - # node_coords_nd is slightly shifted toward cell centroids (lines 703-709) - # evaluate() treats plain numpy as ND [0-1] coordinates - eval_result = uw.function.evaluate( - self.psi_fn, - node_coords_nd, - evalf=evalf, - ) - # Wrap result with units if psi_star has units but eval didn't return UnitAwareArray - psi_star_units = self.psi_star[0].units - if psi_star_units is not None and not isinstance(eval_result, UnitAwareArray): - eval_result = UnitAwareArray(eval_result, units=psi_star_units) + if not advect_only: + try: + # Use shifted ND coords to avoid quad mesh boundary issues + # node_coords_nd is slightly shifted toward cell centroids + # evaluate() treats plain numpy as ND [0-1] coordinates + eval_result = uw.function.evaluate( + self.psi_fn, + node_coords_nd, + evalf=evalf, + ) + # Wrap result with units if psi_star has units but eval didn't return UnitAwareArray + psi_star_units = self.psi_star[0].units + if psi_star_units is not None and not isinstance(eval_result, UnitAwareArray): + eval_result = UnitAwareArray(eval_result, units=psi_star_units) - self.psi_star[0].array[...] = eval_result + self.psi_star[0].array[...] = eval_result - except Exception: - # Fallback to projection solver for expressions that can't be directly evaluated - # (e.g., containing derivatives) - self._psi_star_projection_solver.uw_function = self.psi_fn - self._psi_star_projection_solver.smoothing = 0.0 - self._psi_star_projection_solver.solve(verbose=verbose) + except Exception: + # Fallback to projection solver for expressions that can't be directly evaluated + # (e.g., containing derivatives) + self._psi_star_projection_solver.uw_function = self.psi_fn + self._psi_star_projection_solver.smoothing = 0.0 + self._psi_star_projection_solver.solve(verbose=verbose) # 3. Compute the upstream values from the psi_fn @@ -1612,7 +1627,7 @@ def update_pre_solve( return - def advect_history(self, dt, evalf=False, verbose=False): + def _advect_history_PARKED(self, dt, evalf=False, verbose=False): """Advect all psi_star history levels to upstream positions. Pure advection only — no copy-down, no psi_fn evaluation. @@ -1695,6 +1710,7 @@ def advect_history(self, dt, evalf=False, verbose=False): # RK2: midpoint velocity mid_pt_coords = coords - v_at_node_pts * (0.5 * dt_for_calc) + mid_pt_coords = self.mesh.return_coords_to_bounds(mid_pt_coords) v_mid_result = uw.function.global_evaluate(self.V_fn, mid_pt_coords) if isinstance(v_mid_result, UnitAwareArray): v_at_mid_pts = v_mid_result[:, 0, :] @@ -1709,6 +1725,7 @@ def advect_history(self, dt, evalf=False, verbose=False): # Upstream position end_pt_coords = coords - v_at_mid_pts * dt_for_calc + end_pt_coords = self.mesh.return_coords_to_bounds(end_pt_coords) # Sample psi_star[i] at upstream position expr_to_evaluate = self.psi_star[i].sym diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index e6f51dd87..e536fbc43 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1317,18 +1317,21 @@ def solve( self._setup_discretisation(verbose) self._setup_solver(verbose) - # --- Explicit stress history management --- + # --- Stress history management via standard DDt pathway --- # - # 1. ADVECT: trace psi_star values to upstream positions along - # characteristics. psi_star[0] contains the actual stress from - # the previous solve (stored by step 4 below). After advection, - # psi_star[0] = σ* (previous stress at upstream) and - # psi_star[1] = σ** (stress from 2 steps ago, double-traced). + # update_pre_solve(advect_only=True) performs: + # 1. History shift: psi_star[i] ← psi_star[i-1] + # 2. Skip psi_fn evaluation (psi_star[0] already has projected stress) + # 3. Advect all history levels to upstream positions along characteristics + # + # After this: psi_star[0] = σ* (previous stress at upstream), + # psi_star[1] = σ** (stress from 2 steps ago, double-traced). if uw.mpi.rank == 0 and verbose: print(f"VE Stokes solver - advect stress history", flush=True) - self.DFDt.advect_history(timestep, verbose=verbose, evalf=evalf) + self.DFDt.update_pre_solve(timestep, verbose=verbose, evalf=evalf, + advect_only=True) # 2. SOLVE: PETSc uses the advected σ*, σ** via the constitutive model diff --git a/tests/run_ve_square_wave.py b/tests/run_ve_square_wave.py index 36b2a8336..d56ffc73e 100644 --- a/tests/run_ve_square_wave.py +++ b/tests/run_ve_square_wave.py @@ -183,7 +183,7 @@ def run_square_wave(order, De, n_periods, dt_min_over_tr, dt_max_over_tr, De = 1.5 order = 2 n_periods = 3 - n_harmonics = 15 + n_harmonics = 3 print("=" * 60) print(f"Square-wave VE benchmark: De={De}, order={order}") From a43340cf2d88687ee32ef46ece9a9c219ad5ef48 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Mar 2026 15:36:32 +1100 Subject: [PATCH 024/537] Rename advect_only parameter to store_result (inverted sense) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit store_result=True (default): normal DDt behaviour, evaluate psi_fn store_result=False: skip evaluation and history shift, advect only Clearer name — says what it does rather than describing a mode. Underworld development team with AI support from Claude Code --- src/underworld3/systems/ddt.py | 21 +++++++++++---------- src/underworld3/systems/solvers.py | 2 +- 2 files changed, 12 insertions(+), 11 deletions(-) diff --git a/src/underworld3/systems/ddt.py b/src/underworld3/systems/ddt.py index 7ef2f4d94..24c77efe9 100644 --- a/src/underworld3/systems/ddt.py +++ b/src/underworld3/systems/ddt.py @@ -1254,7 +1254,7 @@ def update_pre_solve( evalf: Optional[bool] = False, verbose: Optional[bool] = False, dt_physical: Optional[float] = None, - advect_only: Optional[bool] = False, + store_result: Optional[bool] = True, ): """Sample upstream values along characteristics before solve. @@ -1263,12 +1263,13 @@ def update_pre_solve( Parameters ---------- - advect_only : bool, optional - If True, skip the psi_fn evaluation into psi_star[0] (step 2) - and only perform history shift (step 1) and upstream advection - (step 3). Used by VE_Stokes where psi_star[0] already contains - the projected actual stress from the previous solve — we want to - advect that stored stress, not overwrite it with the flux expression. + store_result : bool, optional + If True (default), evaluate psi_fn at current positions and store + in psi_star[0] before advection — the standard DDt behaviour. + If False, skip this step and the history shift: only advect the + existing psi_star levels upstream. Used by VE_Stokes where + psi_star[0] already contains the projected actual stress from + the previous solve. """ self._dt = dt @@ -1302,7 +1303,7 @@ def update_pre_solve( else: phi = sympy.sympify(1) - if not advect_only: + if store_result: for i in range(self.order - 1, 0, -1): self.psi_star[i].array[...] = ( phi * self.psi_star[i - 1].array[...] + (1 - phi) * self.psi_star[i].array[...] @@ -1312,7 +1313,7 @@ def update_pre_solve( # Note the need to do a try/except to handle unsupported evaluations # (e.g. of derivatives) # - # When advect_only=True (VE stress history), skip this step — + # When store_result=False (e.g. VE stress history), skip this step — # psi_star[0] already contains the projected actual stress from # the previous solve and we want to advect *that*, not the flux. @@ -1353,7 +1354,7 @@ def update_pre_solve( :, : ] - if not advect_only: + if store_result: try: # Use shifted ND coords to avoid quad mesh boundary issues # node_coords_nd is slightly shifted toward cell centroids diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index e536fbc43..7772d0821 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1331,7 +1331,7 @@ def solve( print(f"VE Stokes solver - advect stress history", flush=True) self.DFDt.update_pre_solve(timestep, verbose=verbose, evalf=evalf, - advect_only=True) + store_result=False) # 2. SOLVE: PETSc uses the advected σ*, σ** via the constitutive model From 8cd7293725d206ca089fbca664818a850ff0bb70 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Mar 2026 19:17:46 +1100 Subject: [PATCH 025/537] Route BDF coefficients through PetscDS constants as UWexpressions The BDF coefficients (c0, c1, c2, c3) are now UWexpressions on the constitutive model, updated each step by _update_bdf_coefficients(). They flow through PetscDS constants[] to the compiled pointwise functions without JIT recompilation. Previously, _bdf_coefficients() returned numeric values that were baked into the C code at JIT time. Changing dt between steps had no effect on the compiled coefficients. Now: ve_effective_viscosity, E_eff, and stress() reference the UWexpression _bdf_c0.._bdf_c3 symbolically. The solver calls _update_bdf_coefficients() before each solve, which computes the variable-dt BDF coefficients and sets the .sym values. PetscDSSetConstants pushes these to PETSc at solve time. Verified: alternating dt test shows Order 2 (err=0.020) outperforms Order 1 (err=0.034), with variable/uniform ratio ~1.06 (near-ideal). Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 56 ++++++++++++++++++++------ src/underworld3/systems/solvers.py | 6 +++ 2 files changed, 49 insertions(+), 13 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index b50687fe8..47293a680 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1087,6 +1087,14 @@ def __init__(self, unknowns, order=1, material_name: str = None): self._order = order + # BDF coefficients as UWexpressions — route through PetscDS constants[]. + # Updated each step by _update_bdf_coefficients() before solve. + # Initialised to BDF-1 values: [1, -1, 0, 0]. + self._bdf_c0 = expression(r"{c_0^{\mathrm{BDF}}}", sympy.Integer(1), "BDF leading coefficient") + self._bdf_c1 = expression(r"{c_1^{\mathrm{BDF}}}", sympy.Integer(-1), "BDF history coefficient 1") + self._bdf_c2 = expression(r"{c_2^{\mathrm{BDF}}}", sympy.Integer(0), "BDF history coefficient 2") + self._bdf_c3 = expression(r"{c_3^{\mathrm{BDF}}}", sympy.Integer(0), "BDF history coefficient 3") + self._reset() super().__init__(unknowns, material_name=material_name) @@ -1200,12 +1208,12 @@ def ve_effective_viscosity(inner_self): return inner_self.shear_viscosity_0 # BDF-k effective viscosity: eta_eff = eta*mu*dt / (c0*eta + mu*dt) - # c0 from DDt's BDF coefficients (variable-dt aware) + # c0 is a UWexpression routed through PetscDS constants[], + # updated each step by _update_bdf_coefficients(). eta = inner_self.shear_viscosity_0 mu = inner_self.shear_modulus dt_e = inner_self.dt_elastic - coeffs = inner_self._owning_model._get_bdf_coefficients() - c0 = coeffs[0] + c0 = inner_self._owning_model._bdf_c0 el_eff_visc = eta * mu * dt_e / (c0 * eta + mu * dt_e) @@ -1249,11 +1257,32 @@ def effective_order(self): return min(self._order, self.Unknowns.DFDt.effective_order) return self._order - def _get_bdf_coefficients(self): - """Get BDF coefficients from DDt (variable-dt aware) or fall back to uniform.""" + def _update_bdf_coefficients(self): + """Update BDF coefficient UWexpressions from current dt_elastic and DDt history. + + Call this before each solve so that the constants[] array carries the + correct coefficients to the compiled pointwise functions. The coefficient + UWexpressions (_bdf_c0..c3) are referenced symbolically in ve_effective_viscosity, + E_eff, and stress() — their numeric values flow through PetscDSSetConstants. + """ if self.Unknowns is not None and self.Unknowns.DFDt is not None: - return self.Unknowns.DFDt.bdf_coefficients - return _bdf_coefficients(self.effective_order, None, []) + dt_current = self.Parameters.dt_elastic + if hasattr(dt_current, 'sym'): + dt_current = dt_current.sym + coeffs = _bdf_coefficients( + self.effective_order, dt_current, self.Unknowns.DFDt._dt_history + ) + else: + coeffs = _bdf_coefficients(self.effective_order, None, []) + + # Pad to length 4 + while len(coeffs) < 4: + coeffs.append(sympy.Integer(0)) + + self._bdf_c0.sym = coeffs[0] + self._bdf_c1.sym = coeffs[1] + self._bdf_c2.sym = coeffs[2] + self._bdf_c3.sym = coeffs[3] # The following should have no setters @property @@ -1291,11 +1320,12 @@ def E_eff(self): if self.is_elastic: mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus - coeffs = self._get_bdf_coefficients() + # BDF history coefficients as UWexpressions (route through constants[]) + bdf_cs = [self._bdf_c1, self._bdf_c2, self._bdf_c3] # History contribution: -Σ cᵢ·σ_star[i-1] / (2·μ·dt) - for i in range(1, len(coeffs)): - E += -coeffs[i] * self.Unknowns.DFDt.psi_star[i - 1].sym / (2 * mu_dt) + for i in range(self.Unknowns.DFDt.order): + E += -bdf_cs[i] * self.Unknowns.DFDt.psi_star[i].sym / (2 * mu_dt) self._E_eff.sym = E @@ -1494,12 +1524,12 @@ def stress(self): if self.is_elastic: mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus - coeffs = self._get_bdf_coefficients() + bdf_cs = [self._bdf_c1, self._bdf_c2, self._bdf_c3] # History contribution: 2·η_eff · (-Σ cᵢ·σ_star[i-1]) / (2·μ·dt) - for i in range(1, len(coeffs)): + for i in range(self.Unknowns.DFDt.order): stress += 2 * self.viscosity * ( - -coeffs[i] * self.Unknowns.DFDt.psi_star[i - 1].sym / (2 * mu_dt) + -bdf_cs[i] * self.Unknowns.DFDt.psi_star[i].sym / (2 * mu_dt) ) return stress diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 7772d0821..62387707a 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1333,6 +1333,12 @@ def solve( self.DFDt.update_pre_solve(timestep, verbose=verbose, evalf=evalf, store_result=False) + # Update BDF coefficients from current dt_elastic and DDt history. + # These are UWexpressions that route through PetscDS constants[], + # so the compiled pointwise functions pick up the new values without + # JIT recompilation. + self.constitutive_model._update_bdf_coefficients() + # 2. SOLVE: PETSc uses the advected σ*, σ** via the constitutive model if uw.mpi.rank == 0 and verbose: From 995ec7672c2ee2c56b966f07081ef680e53b8ccd Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Mar 2026 20:32:58 +1100 Subject: [PATCH 026/537] Remove deprecated constitutive_models_new.py Failed rebuild attempt, scheduled for removal, not imported anywhere. Contains stale hardcoded BDF patterns that would confuse future work. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models_new.py | 1702 -------------------- 1 file changed, 1702 deletions(-) delete mode 100644 src/underworld3/constitutive_models_new.py diff --git a/src/underworld3/constitutive_models_new.py b/src/underworld3/constitutive_models_new.py deleted file mode 100644 index d58be0598..000000000 --- a/src/underworld3/constitutive_models_new.py +++ /dev/null @@ -1,1702 +0,0 @@ -r""" -Alternative constitutive model implementations. - -.. deprecated:: - This module contains a failed attempt to rebuild the constitutive models - and is scheduled for removal. Use :mod:`underworld3.constitutive_models` - instead for all constitutive model needs. - -See Also --------- -underworld3.constitutive_models : Primary constitutive model module (use this). -""" -from typing_extensions import Self -import sympy -from sympy import sympify -from sympy.vector import gradient, divergence -import numpy as np - -from typing import Optional, Callable -from typing import NamedTuple, Union - -from petsc4py import PETSc - -import underworld3 as uw -from underworld3.utilities._api_tools import uw_object -from underworld3.systems import SNES_Scalar, SNES_Vector, SNES_Stokes_SaddlePt -from underworld3.swarm import IndexSwarmVariable -import underworld3.timing as timing - - -class Constitutive_Model(uw_object): - r""" - Base class for constitutive models. - - Constitutive laws relate gradients in the unknowns to fluxes of quantities - (e.g., heat fluxes related to temperature gradients via thermal conductivity). - - For scalar problems: - - .. math:: - - q_i = k_{ij} \frac{\partial T}{\partial x_j} - - where :math:`k_{ij}` are the constitutive parameters. The template assumes - :math:`k_{ij} = \delta_{ij}` (identity). - - For vector problems (e.g., Stokes): - - .. math:: - - t_{ij} = c_{ijkl} \frac{\partial u_k}{\partial x_l} - - Usually written with symmetrized gradients: - - .. math:: - - t_{ij} = c_{ijkl} \frac{1}{2} \left[ \frac{\partial u_k}{\partial x_l} - + \frac{\partial u_l}{\partial x_k} \right] - - where :math:`c_{ijkl}` are the constitutive parameters. The template assumes - :math:`c_{ijkl} = \frac{1}{2}(\delta_{ik}\delta_{jl} + \delta_{il}\delta_{jk})`, - the 4th-rank identity tensor with flux and gradient symmetry. - """ - - @timing.routine_timer_decorator - def __init__( - self, - dim: int, - u_dim: int, - ): - # Define / identify the various properties in the class but leave - # the implementation to child classes. The constitutive tensor is - # defined as a template here, but should be instantiated via class - # properties as required. - - # We provide a function that converts gradients / gradient history terms - # into the relevant flux term. - - self.dim = dim - self.u_dim = u_dim - self._solver = None - - self.Parameters = self._Parameters() - self.Parameters._solver = None - self.Parameters._reset = self._reset - - self._material_properties = None - - ## Default consitutive tensor is the identity - - if self.u_dim == 1: - self._c = sympy.Matrix.eye(self.dim) - else: # vector problem - self._c = uw.maths.tensor.rank4_identity(self.dim) - - self._C = None - - super().__init__() - - class _Parameters: - """Any material properties that are defined by a constitutive relationship are - collected in the parameters which can then be defined/accessed by name in - individual instances of the class. - """ - - def __init__(inner_self, k=1): - inner_self._k = k - inner_self._solver = None - - @property - def k(inner_self): - return inner_self._k - - @k.setter - def k(inner_self, value): - inner_self._k = value - inner_self._reset() - - """ - @property - def material_properties(self): - - return self._material_properties - - @material_properties.setter - def material_properties(self, properties): - - if isinstance(properties, self.Parameters): - self._material_properties = properties - else: - name = self.__class__.__name__ - raise RuntimeError(f"Use {name}.material_properties = {name}.Parameters(...) ") - - d = self.dim - self._build_c_tensor() - - if isinstance(self._solver, (SNES_Scalar, SNES_Vector, SNES_Stokes_SaddlePt)): - self._solver.is_setup = False - - return - """ - - @property - def solver(self): - """Each constitutive relationship can, optionally, be associated with one solver object. - and a solver object _requires_ a constitive relationship to be defined.""" - return self._solver - - @solver.setter - def solver(self, solver_object): - if isinstance(solver_object, (SNES_Scalar, SNES_Vector, SNES_Stokes_SaddlePt)): - self._solver = solver_object - self.Parameters._solver = solver_object - self._solver.is_setup = False - - ## Properties on all sub-classes - - @property - def C(self): - """The matrix form of the constitutive model (the `c` property) - that relates fluxes to gradients. - For scalar problem, this is the matrix representation of the rank 2 tensor. - For vector problems, the Mandel form of the rank 4 tensor is returned. - NOTE: this is an immutable object that is _a view_ of the underlying tensor - """ - - d = self.dim - rank = len(self.c.shape) - - if rank == 2: - return sympy.Matrix(self._c).as_immutable() - else: - return uw.maths.tensor.rank4_to_mandel(self._c, d).as_immutable() - - @property - def c(self): - """The tensor form of the constitutive model that relates fluxes to gradients. In scalar - problems, `c` and `C` are equivalent (matrices), but in vector problems, `c` is a - rank 4 tensor. NOTE: `c` is the canonical form of the constitutive relationship. - """ - - return self._c.as_immutable() - - def flux( - self, - ddu: sympy.Matrix = None, - ddu_dt: sympy.Matrix = None, - u: sympy.Matrix = None, # may be needed in the case of cylindrical / spherical - u_dt: sympy.Matrix = None, - ): - """Computes the effect of the constitutive tensor on the gradients of the unknowns. - (always uses the `c` form of the tensor). In general cases, the history of the gradients - may be required to evaluate the flux. - """ - - c = self.c - rank = len(c.shape) - - # tensor multiplication - - if rank == 2: - flux = c * ddu.T - else: # rank==4 - flux = sympy.tensorcontraction( - sympy.tensorcontraction(sympy.tensorproduct(c, ddu), (3, 5)), (0, 1) - ) - - return sympy.Matrix(flux) - - def flux_1d( - self, - ddu: sympy.Matrix = None, - ddu_dt: sympy.Matrix = None, - u: sympy.Matrix = None, # may be needed in the case of cylindrical / spherical - u_dt: sympy.Matrix = None, - ): - """Computes the effect of the constitutive tensor on the gradients of the unknowns. - (always uses the `c` form of the tensor). In general cases, the history of the gradients - may be required to evaluate the flux. Returns the Voigt form that is flattened so as to - match the PETSc field storage pattern for symmetric tensors. - """ - - flux = self.flux(ddu, ddu_dt, u, u_dt) - - assert ( - flux.is_symmetric() - ), "The conversion to Voigt form is only defined for symmetric tensors in underworld" - - return uw.maths.tensor.rank2_to_voigt(flux, dim=self.dim) - - def _reset(self): - d = self.dim - self._build_c_tensor() - - if isinstance(self._solver, (SNES_Scalar, SNES_Vector, SNES_Stokes_SaddlePt)): - self._solver.is_setup = False - - return - - def _build_c_tensor(self): - """Return the identity tensor of appropriate rank (e.g. for projections)""" - - d = self.dim - self._c = self.Parameters.k * uw.maths.tensor.rank4_identity(d) - - return - - def _object_viewer(self): - from IPython.display import Latex, Markdown, display - from textwrap import dedent - - display( - Markdown( - rf"This consititutive model is formulated for {self.dim} dimensional equations" - ) - ) - - -class ViscousFlowModel(Constitutive_Model): - r""" - Viscous flow constitutive model. - - .. math:: - - \tau_{ij} = \eta_{ijkl} \cdot \frac{1}{2} \left[ \frac{\partial u_k}{\partial x_l} - + \frac{\partial u_l}{\partial x_k} \right] - - where :math:`\eta` is the viscosity—a scalar constant, sympy function, - or mesh variable. This gives an isotropic (but not necessarily homogeneous - or linear) relationship between :math:`\tau` and velocity gradients. You can - also supply :math:`\eta_{IJ}` (Mandel form) or :math:`\eta_{ijkl}` (rank-4 tensor). - - The Mandel constitutive matrix is in ``viscous_model.C`` and the rank-4 - tensor form is in ``viscous_model.c``. - - Examples - -------- - >>> viscous_model = ViscousFlowModel(dim) - >>> viscous_model.material_properties = viscous_model.Parameters(viscosity=viscosity_fn) - >>> solver.constitutive_model = viscous_model - >>> tau = viscous_model.flux(gradient_matrix) - """ - - class _Parameters: - """Any material properties that are defined by a constitutive relationship are - collected in the parameters which can then be defined/accessed by name in - individual instances of the class. - """ - - def __init__( - inner_self, - viscosity: Union[float, sympy.Function] = None, - ): - if viscosity is None: - viscosity = sympy.sympify(1) - - inner_self._viscosity = sympy.sympify(viscosity) - - @property - def viscosity(inner_self): - return inner_self._viscosity - - @viscosity.setter - def viscosity(inner_self, value: Union[float, sympy.Function]): - inner_self._viscosity = value - inner_self._reset() - - def __init__(self, dim): - u_dim = dim - super().__init__(dim, u_dim) - - return - - def _build_c_tensor(self): - """For this constitutive law, we expect just a viscosity function""" - - d = self.dim - viscosity = self.Parameters.viscosity - - try: - self._c = 2 * uw.maths.tensor.rank4_identity(d) * viscosity - except: - d = self.dim - dv = uw.maths.tensor.idxmap[d][0] - if isinstance(viscosity, sympy.Matrix) and viscosity.shape == (dv, dv): - self._c = 2 * uw.maths.tensor.mandel_to_rank4(viscosity, d) - elif isinstance(viscosity, sympy.Array) and viscosity.shape == (d, d, d, d): - self._c = 2 * viscosity - else: - raise RuntimeError( - "Viscosity is not a known type (scalar, Mandel matrix, or rank 4 tensor" - ) - return - - def _object_viewer(self): - from IPython.display import Latex, Markdown, display - - super()._object_viewer() - - ## feedback on this instance - display(Latex(r"$\quad\eta = $ " + sympy.sympify(self.Parameters.viscosity)._repr_latex_())) - - -class ViscoPlasticFlowModel(ViscousFlowModel): - r""" - Viscoplastic flow constitutive model with yield stress. - - .. math:: - - \tau_{ij} = \eta_{ijkl} \cdot \frac{1}{2} \left[ \frac{\partial u_k}{\partial x_l} - + \frac{\partial u_l}{\partial x_k} \right] - - where :math:`\eta` is the viscosity—a scalar constant, sympy function, - or mesh variable. This gives an isotropic relationship between :math:`\tau` - and velocity gradients. You can also supply :math:`\eta_{IJ}` (Mandel form) - or :math:`\eta_{ijkl}` (rank-4 tensor). - - In a viscoplastic model, the viscosity is defined to cap the overall stress - at the *yield stress*. This assumes the yield stress is a scalar limit on - the 2nd invariant of the stress. Anisotropic models require careful yield - surface definition—only a subset of cases is available. - - The Mandel matrix is in ``viscoplastic_model.C`` and the rank-4 tensor in - ``viscoplastic_model.c``. - - Notes - ----- - If ``not~yet~defined`` appears in the effective viscosity, not all required - functions have been set. The model defaults to standard viscous behavior - if yield terms are not specified. - - Examples - -------- - >>> viscoplastic_model = ViscoPlasticFlowModel(dim) - >>> viscoplastic_model.material_properties = viscoplastic_model.Parameters( - ... viscosity=viscosity_fn, - ... yield_stress=yieldstress_fn, - ... min_viscosity=min_viscosity_fn, - ... max_viscosity=max_viscosity_fn, - ... strain_rate_II=strain_rate_inv_fn - ... ) - >>> solver.constitutive_model = viscoplastic_model - >>> tau = viscoplastic_model.flux(gradient_matrix) - """ - - # Init for VP class (not needed ??) - def __init__(self, dim): - super().__init__(dim) - - return - - class _Parameters: - """Any material properties that are defined by a constitutive relationship are - collected in the parameters which can then be defined/accessed by name in - individual instances of the class. - - `sympy.oo` (infinity) for default values ensures that sympy.Min simplifies away - the conditionals when they are not required - """ - - def __init__( - inner_self, - materialIndex: Union[uw.swarm.SwarmVariable, uw.discretisation.MeshVariable] = None, - shear_viscosity_0: Union[list, sympy.Function] = [1], - shear_viscosity_min: Union[list, sympy.Function] = [-sympy.oo], - shear_viscosity_max: Union[list, sympy.Function] = [sympy.oo], - yield_stress: Union[list, sympy.Function] = [sympy.oo], - yield_stress_min: Union[list, sympy.Function] = [-sympy.oo], - strainrate_inv_II: sympy.Function = sympy.oo, - strainrate_inv_II_min: float = 0.0, - averaging_method: str = "HA", - ): - if strainrate_inv_II is sympy.oo: - strainrate_inv_II = sympy.symbols( - r"\left|\dot\epsilon\right|\rightarrow\textrm{not\ defined}" - ) - - inner_self._shear_viscosity_0 = sympy.sympify(shear_viscosity_0) - inner_self._shear_viscosity_min = sympy.sympify(shear_viscosity_min) - inner_self._shear_viscosity_max = sympy.sympify(shear_viscosity_max) - - inner_self._yield_stress = sympy.sympify(yield_stress) - inner_self._yield_stress_min = sympy.sympify(yield_stress_min) - - inner_self._strainrate_inv_II = sympy.sympify(strainrate_inv_II) - inner_self._strainrate_inv_II_min = sympy.sympify(strainrate_inv_II_min) - - inner_self._averaging_method = averaging_method - inner_self._materialIndex = materialIndex - - return - - @property - def shear_viscosity_0(inner_self): - return inner_self._shear_viscosity_0 - - @shear_viscosity_0.setter - def shear_viscosity_0(inner_self, value: Union[list, sympy.Function]): - inner_self._shear_viscosity_0 = value - inner_self._reset() - - @property - def shear_viscosity_min(inner_self): - return inner_self._shear_viscosity_min - - @shear_viscosity_min.setter - def shear_viscosity_min(inner_self, value: Union[list, sympy.Function]): - inner_self._shear_viscosity_min = value - inner_self._reset() - - @property - def shear_viscosity_max(inner_self): - return inner_self._shear_viscosity_max - - @shear_viscosity_max.setter - def shear_viscosity_max(inner_self, value: Union[list, sympy.Function]): - inner_self._shear_viscosity_max = value - inner_self._reset() - - @property - def yield_stress(inner_self): - return inner_self._yield_stress - - @yield_stress.setter - def yield_stress(inner_self, value: Union[list, sympy.Function]): - inner_self._yield_stress = value - inner_self._reset() - - @property - def yield_stress_min(inner_self): - return inner_self._yield_stress_min - - @yield_stress_min.setter - def yield_stress_min(inner_self, value: Union[list, sympy.Function]): - inner_self._yield_stress_min = value - inner_self._reset() - - @property - def strainrate_inv_II(inner_self): - return inner_self._strainrate_inv_II - - @strainrate_inv_II.setter - def strainrate_inv_II(inner_self, value: sympy.Function): - inner_self._strainrate_inv_II = value - inner_self._reset() - - @property - def strainrate_inv_II_min(inner_self): - return inner_self._strainrate_inv_II_min - - @strainrate_inv_II_min.setter - def strainrate_inv_II_min(inner_self, value: float): - inner_self._strainrate_inv_II_min = sympy.sympify(value) - inner_self._reset() - - @property - def averaging_method(inner_self): - return inner_self._averaging_method - - @averaging_method.setter - def averaging_method(inner_self, value: str): - inner_self._averaging_method = value - inner_self._reset() - - ### Getter and setter for internel mask Variable - @property - def materialIndex(inner_self): - return inner_self._materialIndex - - @materialIndex.setter - def materialIndex(inner_self, indexVar): - # error checking, only support IndexSwarmVariables for now - if isinstance(indexVar, uw.swarm.IndexSwarmVariable): - inner_self._materialIndex = indexVar - inner_self._reset() - - # This has no setter !! - @property - def plastic_eff_viscosity(inner_self): - import warnings - - if ( - type(inner_self.yield_stress) != np.ndarray - and type(inner_self.yield_stress) != list - ): - inner_self.yield_stress = list([inner_self.yield_stress]) - if ( - type(inner_self.yield_stress_min) != np.ndarray - and type(inner_self.yield_stress_min) != list - ): - inner_self.yield_stress_min = list([inner_self.yield_stress_min]) - - if inner_self.materialIndex == None: - warnings.warn( - "materialIndex not specified, using the first value for each parameter", - stacklevel=2, - ) - - yield_stress = inner_self.yield_stress[0] - yield_stress_min = inner_self.yield_stress_min[0] - - if yield_stress_min == -sympy.oo: - yield_stress_fn = yield_stress - else: - yield_stress_fn = sympy.Max(yield_stress, yield_stress_min) - - if yield_stress_fn == sympy.oo or inner_self.strainrate_inv_II == sympy.oo: - pl_effective_viscosity = sympy.oo - - else: - pl_effective_viscosity = yield_stress_fn / ( - (2 * inner_self.strainrate_inv_II) + inner_self.strainrate_inv_II_min - ) - - else: - ### creates list of values that has the same length as the material index - if len(inner_self.yield_stress) != inner_self.materialIndex.indices: - if len(inner_self.yield_stress) > 1: - warnings.warn( - f"Number of values in yield_stress ({len(inner_self.yield_stress)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.yield_stress = list( - np.repeat(inner_self.yield_stress[0], inner_self.materialIndex.indices) - ) - - if len(inner_self.yield_stress_min) != inner_self.materialIndex.indices: - if len(inner_self.yield_stress_min) > 1: - warnings.warn( - f"Number of values in yield_stress ({len(inner_self.yield_stress_min)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.yield_stress_min = list( - np.repeat( - inner_self.yield_stress_min[0], - inner_self.materialIndex.indices, - ) - ) - - yield_stress = sympy.Matrix(inner_self.yield_stress) - yield_stress_min = sympy.Matrix(inner_self.yield_stress_min) - - if yield_stress_min[0] == -sympy.oo: - yield_stress_fn = yield_stress - else: - yield_stress_list = [] - - for i in range(len(yield_stress)): - yield_stress_list.append(sympy.Max(yield_stress[i], yield_stress_min[i])) - - yield_stress_fn = sympy.Matrix(yield_stress_list) - - if yield_stress_fn[0] == sympy.oo or inner_self.strainrate_inv_II == sympy.oo: - pl_effective_viscosity = list( - np.repeat(sympy.oo, inner_self.materialIndex.indices) - ) - - else: - pl_effective_viscosity = yield_stress_fn / ( - (2 * inner_self.strainrate_inv_II) + inner_self.strainrate_inv_II_min - ) - - return pl_effective_viscosity - - # This has no setter !! - @property - def viscosity(inner_self): - import warnings - - if ( - type(inner_self.shear_viscosity_0) != np.ndarray - and type(inner_self.shear_viscosity_0) != list - ): - inner_self.shear_viscosity_0 = list([inner_self.shear_viscosity_0]) - - if ( - type(inner_self.shear_viscosity_min) != np.ndarray - and type(inner_self.shear_viscosity_min) != list - ): - inner_self.shear_viscosity_min = list([inner_self.shear_viscosity_min]) - if ( - type(inner_self.shear_viscosity_max) != np.ndarray - and type(inner_self.shear_viscosity_max) != list - ): - inner_self.shear_viscosity_max = list([inner_self.shear_viscosity_max]) - - if inner_self.materialIndex == None: - warnings.warn( - "materialIndex not specified, using the first value for each parameter", - stacklevel=2, - ) - - shear_viscosity_min = inner_self.shear_viscosity_min[0] - shear_viscosity_max = inner_self.shear_viscosity_max[0] - - shear_viscosity_0 = inner_self.shear_viscosity_0[0] - - yield_visc = inner_self.plastic_eff_viscosity - - if inner_self.averaging_method.casefold() == "min": - if yield_visc != 0: - effective_viscosity = sympy.Min( - shear_viscosity_max, - sympy.Max( - shear_viscosity_min, - sympy.Min(yield_visc, shear_viscosity_0), - ), - ) - else: - effective_viscosity = sympy.Min( - shear_viscosity_max, - sympy.Max(shear_viscosity_min, shear_viscosity_0), - ) - else: - if yield_visc != 0: - effective_viscosity = sympy.Min( - shear_viscosity_max, - sympy.Max( - shear_viscosity_min, - 1.0 / ((1.0 / shear_viscosity_0) + (1.0 / yield_visc)), - ), - ) - else: - effective_viscosity = sympy.Min( - shear_viscosity_max, - sympy.Max(shear_viscosity_min, shear_viscosity_0), - ) - - else: - if len(inner_self.shear_viscosity_0) != inner_self.materialIndex.indices: - if len(inner_self.shear_viscosity_0) > 1: - warnings.warn( - f"Number of values in shear_viscosity_0 ({len(inner_self.shear_viscosity_0)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.shear_viscosity_0 = list( - np.repeat( - inner_self.shear_viscosity_0[0], - inner_self.materialIndex.indices, - ) - ) - - if len(inner_self.shear_viscosity_min) != inner_self.materialIndex.indices: - if len(inner_self.shear_viscosity_min) > 1: - warnings.warn( - f"Number of values in shear_viscosity_min ({len(inner_self.shear_viscosity_min)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.shear_viscosity_min = list( - np.repeat( - inner_self.shear_viscosity_min[0], - inner_self.materialIndex.indices, - ) - ) - - if len(inner_self.shear_viscosity_max) != inner_self.materialIndex.indices: - if len(inner_self.shear_viscosity_max) > 1: - warnings.warn( - f"Number of values in shear_viscosity_max ({len(inner_self.shear_viscosity_max)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.shear_viscosity_max = list( - np.repeat( - inner_self.shear_viscosity_max[0], - inner_self.materialIndex.indices, - ) - ) - - shear_viscosity_min = sympy.Matrix(inner_self.shear_viscosity_min) - shear_viscosity_max = sympy.Matrix(inner_self.shear_viscosity_max) - - shear_viscosity_0 = inner_self.shear_viscosity_0 - - yield_visc = inner_self.plastic_eff_viscosity - - viscosity_list = [] - for i in range(inner_self.materialIndex.indices): - if inner_self.averaging_method.casefold() == "min": - if yield_visc[i] != 0: - viscosity_list.append( - sympy.Min( - shear_viscosity_max[i], - sympy.Max( - shear_viscosity_min[i], - sympy.Min(yield_visc[i], shear_viscosity_0[i]), - ), - ) - ) - else: - viscosity_list.append( - sympy.Min( - shear_viscosity_max[i], - sympy.Max(shear_viscosity_min[i], shear_viscosity_0[i]), - ) - ) - else: - if yield_visc[i] != 0: - viscosity_list.append( - sympy.Min( - shear_viscosity_max[i], - sympy.Max( - shear_viscosity_min[i], - 1 / ((1 / shear_viscosity_0[i]) + (1 / yield_visc[i])), - ), - ) - ) - else: - viscosity_list.append( - sympy.Min( - shear_viscosity_max[i], - sympy.Max(shear_viscosity_min[i], shear_viscosity_0[i]), - ) - ) - - viscosity_fn = sympy.Matrix(viscosity_list) - - effective_viscosity = inner_self.materialIndex.sym.T.dot(viscosity_fn) - - return effective_viscosity - - ## ===== End of parameters sub_class - - def _object_viewer(self): - from IPython.display import Latex, Markdown, display - - super()._object_viewer() - - ## feedback on this instance - display( - Latex( - r"$\quad\eta_\textrm{0} = $ " - + sympy.sympify(self.Parameters.shear_viscosity_0)._repr_latex_() - ), - Latex( - r"$\quad\tau_\textrm{y} = $ " - + sympy.sympify(self.Parameters.yield_stress)._repr_latex_(), - ), - Latex( - r"$\quad|\dot\epsilon| = $ " - + sympy.sympify(self.Parameters.strainrate_inv_II)._repr_latex_(), - ), - ## Todo: add all the other properties in here - ) - - -class ViscoElasticPlasticFlowModel(Constitutive_Model): - r""" - Viscoelastic-plastic flow constitutive model. - - .. math:: - - \tau_{ij} = \eta_{ijkl} \cdot \frac{1}{2} \left[ \frac{\partial u_k}{\partial x_l} - + \frac{\partial u_l}{\partial x_k} \right] - - where :math:`\eta` is the viscosity—a scalar constant, sympy function, - or mesh variable. This gives an isotropic relationship between :math:`\tau` - and velocity gradients. You can also supply :math:`\eta_{IJ}` (Mandel form) - or :math:`\eta_{ijkl}` (rank-4 tensor). - - The Mandel matrix is in ``viscoelastic_model.C`` and the rank-4 tensor in - ``viscoelastic_model.c``. - - Examples - -------- - >>> viscoelastic_model = ViscoElasticFlowModel(dim) - >>> viscoelastic_model.material_properties = viscoelastic_model.Parameters( - ... viscosity=viscosity_fn - ... ) - >>> solver.constitutive_model = viscoelastic_model - >>> tau = viscoelastic_model.flux(gradient_matrix) - """ - - class _Parameters: - """Any material properties that are defined by a constitutive relationship are - collected in the parameters which can then be defined/accessed by name in - individual instances of the class. - """ - - def __init__( - inner_self, - materialIndex: Union[uw.swarm.SwarmVariable, uw.discretisation.MeshVariable] = None, - shear_viscosity_0: Union[list, sympy.Function] = [1], - shear_modulus: Union[list, sympy.Function] = [sympy.oo], - shear_viscosity_min: Union[list, sympy.Function] = [-sympy.oo], - shear_viscosity_max: Union[list, sympy.Function] = [sympy.oo], - yield_stress: Union[list, sympy.Function] = [sympy.oo], - yield_stress_min: Union[list, sympy.Function] = [-sympy.oo], - strainrate_inv_II: sympy.Function = sympy.oo, - strainrate_inv_II_min: float = 0.0, - averaging_method: str = "HA", - stress_star: sympy.Function = None, - stress_star_star: sympy.Function = None, - dt_elastic: Union[float, sympy.Function] = [sympy.oo], - ): - if strainrate_inv_II is None: - strainrate_inv_II = sympy.symbols( - r"\left|\dot\epsilon\right|\rightarrow\textrm{not\ defined}" - ) - - if stress_star is None: - stress_star = sympy.symbols(r"\sigma^*\rightarrow\textrm{not\ defined}") - - inner_self._shear_viscosity_0 = sympy.sympify(shear_viscosity_0) - inner_self._shear_modulus = sympy.sympify(shear_modulus) - inner_self._dt_elastic = sympy.sympify(dt_elastic) - inner_self._yield_stress = sympy.sympify(yield_stress) - inner_self._yield_stress_min = sympy.sympify(yield_stress_min) - inner_self._shear_viscosity_min = sympy.sympify(shear_viscosity_min) - inner_self._shear_viscosity_max = sympy.sympify(shear_viscosity_max) - inner_self._strainrate_inv_II = sympy.sympify(strainrate_inv_II) - inner_self._stress_star = sympy.sympify(stress_star) - inner_self._stress_star_star = sympy.sympify(stress_star_star) - inner_self._strainrate_inv_II_min = sympy.sympify(strainrate_inv_II_min) - - inner_self._averaging_method = averaging_method - inner_self._materialIndex = materialIndex - - return - - @property - def shear_viscosity_0(inner_self): - return inner_self._shear_viscosity_0 - - @shear_viscosity_0.setter - def shear_viscosity_0(inner_self, value: Union[list, sympy.Function]): - inner_self._shear_viscosity_0 = value - inner_self._reset() - - @property - def shear_modulus(inner_self): - return inner_self._shear_modulus - - @shear_modulus.setter - def shear_modulus(inner_self, value: Union[list, sympy.Function]): - inner_self._shear_modulus = value - inner_self._reset() - - @property - def dt_elastic(inner_self): - return inner_self._dt_elastic - - @dt_elastic.setter - def dt_elastic(inner_self, value: Union[list, sympy.Function]): - inner_self._dt_elastic = value - inner_self._reset() - - @property - def shear_viscosity_min(inner_self): - return inner_self._shear_viscosity_min - - @shear_viscosity_min.setter - def shear_viscosity_min(inner_self, value: Union[list, sympy.Function]): - inner_self._shear_viscosity_min = value - inner_self._reset() - - @property - def shear_viscosity_max(inner_self): - return inner_self._shear_viscosity_max - - @shear_viscosity_max.setter - def shear_viscosity_max(inner_self, value: Union[list, sympy.Function]): - inner_self._shear_viscosity_max = value - inner_self._reset() - - @property - def yield_stress(inner_self): - return inner_self._yield_stress - - @yield_stress.setter - def yield_stress(inner_self, value: Union[list, sympy.Function]): - inner_self._yield_stress = value - inner_self._reset() - - @property - def yield_stress_min(inner_self): - return inner_self._yield_stress_min - - @yield_stress_min.setter - def yield_stress_min(inner_self, value: Union[list, sympy.Function]): - inner_self._yield_stress_min = value - inner_self._reset() - - @property - def strainrate_inv_II(inner_self): - return inner_self._strainrate_inv_II - - @strainrate_inv_II.setter - def strainrate_inv_II(inner_self, value: sympy.Function): - inner_self._strainrate_inv_II = value - inner_self._reset() - - @property - def stress_star(inner_self): - return inner_self._stress_star - - @stress_star.setter - def stress_star(inner_self, value: sympy.Function): - inner_self._stress_star = value - inner_self._reset() - - @property - def stress_star_star(inner_self): - return inner_self._stress_star_star - - @stress_star_star.setter - def stress_star_star(inner_self, value: sympy.Function): - inner_self._stress_star_star = value - inner_self._reset() - - @property - def strainrate_inv_II_min(inner_self): - return inner_self._strainrate_inv_II_min - - @strainrate_inv_II_min.setter - def strainrate_inv_II_min(inner_self, value: float): - inner_self._strainrate_inv_II_min = sympy.sympify(value) - inner_self._reset() - - @property - def averaging_method(inner_self): - return inner_self._averaging_method - - @averaging_method.setter - def averaging_method(inner_self, value: str): - inner_self._averaging_method = value - inner_self._reset() - - ### Getter and setter for internel mask Variable - @property - def materialIndex(inner_self): - return inner_self._materialIndex - - @materialIndex.setter - def materialIndex(inner_self, indexVar): - # error checking, only support IndexSwarmVariables for now - if isinstance(indexVar, uw.swarm.IndexSwarmVariable): - inner_self._materialIndex = indexVar - inner_self._reset() - - @property - def t_relax(inner_self): - # shear modulus defaults to infinity so t_relax goes to zero - # in the viscous limit - - if inner_self.materialIndex == None: - shear_viscosity_0 = inner_self.shear_viscosity_0[0] - shear_modulus = inner_self.shear_modulus[0] - t_relax = shear_viscosity_0 / shear_modulus - else: - shear_viscosity_0 = np.array(inner_self.shear_viscosity_0) - shear_modulus = np.array(inner_self.shear_modulus) - t_relax = shear_viscosity_0 / shear_modulus - - return t_relax - - @property - def ve_effective_viscosity(inner_self): - # the dt_elastic defaults to infinity, t_relax to zero, - # so this should be well behaved in the viscous limit - - import warnings - - if ( - type(inner_self.shear_modulus) != np.ndarray - and type(inner_self.shear_modulus) != list - ): - inner_self.shear_modulus = list([inner_self.shear_modulus]) - if type(inner_self.dt_elastic) != np.ndarray and type(inner_self.dt_elastic) != list: - inner_self.dt_elastic = list([inner_self.dt_elastic]) - if ( - type(inner_self.shear_viscosity_0) != np.ndarray - and type(inner_self.shear_viscosity_0) != list - ): - inner_self.shear_viscosity_0 = list([inner_self.shear_viscosity_0]) - - if inner_self.materialIndex == None: - warnings.warn( - "materialIndex not specified, using the first value for each parameter", - stacklevel=2, - ) - - mu = inner_self.shear_modulus[0] - dt = inner_self.dt_elastic[0] - eta = inner_self.shear_viscosity_0[0] - - if mu == sympy.oo or dt == sympy.oo: - return eta - - ## The effective viscosity depends on the number of history terms - if inner_self.stress_star_star is None: - el_eff_visc = eta * mu * dt / (mu * dt + eta) - else: - el_eff_visc = 2 * eta * mu * dt / (2 * mu * dt + 3 * eta) - - return sympy.simplify(el_eff_visc) - - else: - ### creates list of values that has the same length as the material index - if len(inner_self.shear_modulus) != inner_self.materialIndex.indices: - if len(inner_self.shear_modulus) > 1: - warnings.warn( - f"Number of values in shear_modulus ({len(inner_self.shear_modulus)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.shear_modulus = list( - np.repeat( - inner_self.shear_modulus[0], - inner_self.materialIndex.indices, - ) - ) - - if len(inner_self.dt_elastic) != inner_self.materialIndex.indices: - if len(inner_self.dt_elastic) > 1: - warnings.warn( - f"Number of values in dt_elastic ({len(inner_self.dt_elastic)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.dt_elastic = list( - np.repeat(inner_self.dt_elastic[0], inner_self.materialIndex.indices) - ) - - if len(inner_self.shear_viscosity_0) != inner_self.materialIndex.indices: - if len(inner_self.shear_viscosity_0) > 1: - warnings.warn( - f"Number of values in shear_viscosity_0 ({len(inner_self.shear_viscosity_0)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.shear_viscosity_0 = list( - np.repeat( - inner_self.shear_viscosity_0[0], - inner_self.materialIndex.indices, - ) - ) - - mu = np.array(inner_self.shear_modulus) - dt = np.array(inner_self.dt_elastic) - eta = np.array(inner_self.shear_viscosity_0) - - if mu[0] == sympy.oo or dt[0] == sympy.oo: - return eta - - ## The effective viscosity depends on the number of history terms - if inner_self.stress_star_star is None: - el_eff_visc = eta * mu * dt / (mu * dt + eta) - else: - el_eff_visc = 2 * eta * mu * dt / (2 * mu * dt + 3 * eta) - - return sympy.simplify(el_eff_visc) - - @property - def plastic_eff_viscosity(inner_self): - import warnings - - if ( - type(inner_self.yield_stress) != np.ndarray - and type(inner_self.yield_stress) != list - ): - inner_self.yield_stress = list([inner_self.yield_stress]) - if ( - type(inner_self.yield_stress_min) != np.ndarray - and type(inner_self.yield_stress_min) != list - ): - inner_self.yield_stress_min = list([inner_self.yield_stress_min]) - - if inner_self.materialIndex == None: - warnings.warn( - "materialIndex not specified, using the first value for each parameter", - stacklevel=2, - ) - - yield_stress = inner_self.yield_stress[0] - yield_stress_min = inner_self.yield_stress_min[0] - - if yield_stress_min == -sympy.oo: - yield_stress_fn = yield_stress - else: - yield_stress_fn = sympy.Max(yield_stress, yield_stress_min) - - if yield_stress_fn == sympy.oo or inner_self.strainrate_inv_II == sympy.oo: - pl_effective_viscosity = sympy.oo - - else: - pl_effective_viscosity = yield_stress_fn / ( - (2 * inner_self.strainrate_inv_II) - # + inner_self.strainrate_inv_II_min - ) - - else: - ### creates list of values that has the same length as the material index - if len(inner_self.yield_stress) != inner_self.materialIndex.indices: - if len(inner_self.yield_stress) > 1: - warnings.warn( - f"Number of values in yield_stress ({len(inner_self.yield_stress)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.yield_stress = list( - np.repeat(inner_self.yield_stress[0], inner_self.materialIndex.indices) - ) - - if len(inner_self.yield_stress_min) != inner_self.materialIndex.indices: - if len(inner_self.yield_stress_min) > 1: - warnings.warn( - f"Number of values in yield_stress ({len(inner_self.yield_stress_min)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.yield_stress_min = list( - np.repeat( - inner_self.yield_stress_min[0], - inner_self.materialIndex.indices, - ) - ) - - yield_stress = sympy.Matrix(inner_self.yield_stress) - yield_stress_min = sympy.Matrix(inner_self.yield_stress_min) - - if yield_stress_min[0] == -sympy.oo: - yield_stress_fn = yield_stress - else: - yield_stress_list = [] - - for i in range(len(yield_stress)): - yield_stress_list.append(sympy.Max(yield_stress[i], yield_stress_min[i])) - - yield_stress_fn = sympy.Matrix(yield_stress_list) - - if yield_stress_fn[0] == sympy.oo or inner_self.strainrate_inv_II == sympy.oo: - pl_effective_viscosity = list( - np.repeat(sympy.oo, inner_self.materialIndex.indices) - ) - - else: - pl_effective_viscosity = yield_stress_fn / ( - (2 * inner_self.strainrate_inv_II) + inner_self.strainrate_inv_II_min - ) - - return pl_effective_viscosity - - # This has no setter !! - @property - def viscosity(inner_self): - # detect if values we need are defined or are placeholder symbols - - ve_eff_visc = inner_self.ve_effective_viscosity - yield_visc = inner_self.plastic_eff_viscosity - - import warnings - - if inner_self.materialIndex == None: - shear_viscosity_min = inner_self.shear_viscosity_min[0] - shear_viscosity_max = inner_self.shear_viscosity_max[0] - - if inner_self.averaging_method.casefold() == "min": - if yield_visc != 0: - effective_viscosity = sympy.Min( - shear_viscosity_max, - sympy.Max(shear_viscosity_min, sympy.Min(yield_visc, ve_eff_visc)), - ) - else: - effective_viscosity = sympy.Min( - shear_viscosity_max, - sympy.Max(shear_viscosity_min, ve_eff_visc), - ) - else: - if yield_visc != 0: - effective_viscosity = sympy.Min( - shear_viscosity_max, - sympy.Max( - shear_viscosity_min, - 1.0 / ((1.0 / ve_eff_visc) + (1.0 / yield_visc)), - ), - ) - else: - effective_viscosity = sympy.Min( - shear_viscosity_max, - sympy.Max(shear_viscosity_min, ve_eff_visc), - ) - - else: - if len(inner_self.shear_viscosity_min) != inner_self.materialIndex.indices: - if len(inner_self.shear_viscosity_min) > 1: - warnings.warn( - f"Number of values in shear_viscosity_min ({len(inner_self.shear_viscosity_min)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.shear_viscosity_min = list( - np.repeat( - inner_self.shear_viscosity_min[0], - inner_self.materialIndex.indices, - ) - ) - - if len(inner_self.shear_viscosity_max) != inner_self.materialIndex.indices: - if len(inner_self.shear_viscosity_max) > 1: - warnings.warn( - f"Number of values in shear_viscosity_max ({len(inner_self.shear_viscosity_max)}) does not match the number of material indices ({inner_self.materialIndex.indices}). Using the first value for all materials.", - stacklevel=2, - ) - inner_self.shear_viscosity_max = list( - np.repeat( - inner_self.shear_viscosity_max[0], - inner_self.materialIndex.indices, - ) - ) - - shear_viscosity_min = sympy.Matrix(inner_self.shear_viscosity_min) - shear_viscosity_max = sympy.Matrix(inner_self.shear_viscosity_max) - - viscosity_list = [] - for i in range(len(yield_visc)): - if inner_self.averaging_method.casefold() == "min": - if yield_visc[i] != 0: - viscosity_list.append( - sympy.Min( - shear_viscosity_max[i], - sympy.Max( - shear_viscosity_min[i], - sympy.Min(yield_visc[i], ve_eff_visc[i]), - ), - ) - ) - else: - viscosity_list.append( - sympy.Min( - shear_viscosity_max[i], - sympy.Max(shear_viscosity_min[i], ve_eff_visc[i]), - ) - ) - else: - if yield_visc[i] != 0: - viscosity_list.append( - sympy.Min( - shear_viscosity_max[i], - sympy.Max( - shear_viscosity_min[i], - 1 / ((1 / ve_eff_visc[i]) + (1 / yield_visc[i])), - ), - ) - ) - else: - viscosity_list.append( - sympy.Min( - shear_viscosity_max[i], - sympy.Max(shear_viscosity_min[i], ve_eff_visc[i]), - ) - ) - - viscosity_fn = sympy.Matrix(viscosity_list) - - effective_viscosity = inner_self.materialIndex.sym.T.dot(viscosity_fn) - - return effective_viscosity - - def __init__(self, dim): - u_dim = dim - super().__init__(dim, u_dim) - - return - - ## Is this really different from the original ? - - def _build_c_tensor(self): - """For this constitutive law, we expect just a viscosity function""" - - d = self.dim - viscosity = self.Parameters.viscosity - shear_modulus = self.Parameters.shear_modulus - dt_elastic = self.Parameters.dt_elastic - - try: - self._c = 2 * uw.maths.tensor.rank4_identity(d) * viscosity - except: - d = self.dim - dv = uw.maths.tensor.idxmap[d][0] - if isinstance(viscosity, sympy.Matrix) and viscosity.shape == (dv, dv): - self._c = 2 * uw.maths.tensor.mandel_to_rank4(viscosity, d) - elif isinstance(viscosity, sympy.Array) and viscosity.shape == (d, d, d, d): - self._c = 2 * viscosity - else: - raise RuntimeError( - "Viscosity is not a known type (scalar, Mandel matrix, or rank 4 tensor" - ) - return - - # Modify flux to use the stress history term - # This may be preferable to using strain rate which can be discontinuous - # and harder to map back and forth between grid and particles without numerical smoothing - - def flux( - self, - ddu: sympy.Matrix = None, - ddu_dt: sympy.Matrix = None, - u: sympy.Matrix = None, # may be needed in the case of cylindrical / spherical - u_dt: sympy.Matrix = None, - ): - """Computes the effect of the constitutive tensor on the gradients of the unknowns. - (always uses the `c` form of the tensor). In general cases, the history of the gradients - may be required to evaluate the flux. For viscoelasticity, the - """ - - c = self.c - rank = len(c.shape) - - # tensor multiplication - - if rank == 2: - flux = c * ddu.T - else: # rank==4 - flux = sympy.tensorcontraction( - sympy.tensorcontraction(sympy.tensorproduct(c, ddu), (3, 5)), (0, 1) - ) - - # Now add in the stress history. In the - # viscous limit, this term is not well behaved - # and we need to check that - - if self.is_elastic: - if self.Parameters.materialIndex == None: - eta = self.Parameters.shear_viscosity_0[0] - mu = self.Parameters.shear_modulus[0] - dt = self.Parameters.dt_elastic[0] - s_star = self.Parameters.stress_star - s_star_star = self.Parameters.stress_star_star - - if s_star_star is None: # 1st order - flux = sympy.Matrix(flux) + eta * s_star / (dt * mu + eta) - else: # 2nd order - flux = ( - sympy.Matrix(flux) - + 4 * eta * s_star / (2 * dt * mu + 3 * eta) - - eta * s_star_star / (2 * dt * mu + 3 * eta) - ) - else: - eta = self.Parameters.materialIndex.createMask(self.Parameters.shear_viscosity_0) - mu = self.Parameters.materialIndex.createMask(self.Parameters.shear_modulus) - dt = np.array(self.Parameters.dt_elastic) - s_star = self.Parameters.stress_star - s_star_star = self.Parameters.stress_star_star - - if s_star_star is None: # 1st order - flux = sympy.Matrix(flux) + eta * s_star / (dt * mu + eta) - else: # 2nd order - flux = ( - sympy.Matrix(flux) - + 4 * eta * s_star / (2 * dt * mu + 3 * eta) - - eta * s_star_star / (2 * dt * mu + 3 * eta) - ) - - return sympy.simplify(sympy.Matrix(flux)) - - def _object_viewer(self): - from IPython.display import Latex, Markdown, display - - super()._object_viewer() - - display(Markdown(r"### Viscous deformation")) - display( - Latex( - r"$\quad\eta_\textrm{0} = $ " - + sympy.sympify(self.Parameters.shear_viscosity_0[0])._repr_latex_() - ), - ) - - ## If elasticity is active: - display(Markdown(r"#### Elastic deformation")) - display( - Latex( - r"$\quad\mu = $ " + sympy.sympify(self.Parameters.shear_modulus[0])._repr_latex_(), - ), - Latex( - r"$\quad\Delta t_e = $ " - + sympy.sympify(self.Parameters.dt_elastic[0])._repr_latex_(), - ), - Latex( - r"$\quad \sigma^* = $ " + sympy.sympify(self.Parameters.stress_star)._repr_latex_(), - ), - ) - if self.Parameters.stress_star_star is not None: - display( - Latex( - r"$\quad \sigma^{**} = $ " - + sympy.sympify(self.Parameters.stress_star_star)._repr_latex_(), - ), - ) - - # If plasticity is active - display(Markdown(r"#### Plastic deformation")) - display( - Latex( - r"$\quad\tau_\textrm{y} = $ " - + sympy.sympify(self.Parameters.yield_stress[0])._repr_latex_(), - ), - Latex( - r"$\quad|\dot\epsilon| = $ " - + sympy.sympify(self.Parameters.strainrate_inv_II)._repr_latex_(), - ), - ## Todo: add all the other properties in here - ) - - @property - def is_elastic(self): - # If any of these is not defined, elasticity is switched off - - if self.Parameters.dt_elastic[0] is sympy.oo: - return False - - if self.Parameters.shear_modulus[0] is sympy.oo: - return False - - if self.Parameters.stress_star is None: - return False - - return True - - @property - def is_viscoplastic(self): - if self.Parameters.yield_stress[0] == sympy.oo: - return False - - if isinstance(self.Parameters.strainrate_inv_II, sympy.core.symbol.Symbol): - return False - - return True - - -### - - -class DiffusionModel(Constitutive_Model): - r""" - Diffusion constitutive model for scalar transport. - - .. math:: - - q_{i} = \kappa_{ij} \cdot \frac{\partial \phi}{\partial x_j} - - where :math:`\kappa` is a diffusivity—a scalar constant, sympy function, - or mesh variable. - - Examples - -------- - >>> diffusion_model = DiffusionModel(dim) - >>> diffusion_model.material_properties = diffusion_model.Parameters( - ... diffusivity=diffusivity_fn - ... ) - >>> scalar_solver.constitutive_model = diffusion_model - >>> flux = diffusion_model.flux(gradient_matrix) - """ - - class _Parameters: - """Any material properties that are defined by a constitutive relationship are - collected in the parameters which can then be defined/accessed by name in - individual instances of the class. - """ - - def __init__( - inner_self, - diffusivity: Union[float, sympy.Function] = 1, - ): - inner_self._diffusivity = diffusivity - - @property - def diffusivity(inner_self): - return inner_self._diffusivity - - @diffusivity.setter - def diffusivity(inner_self, value: Union[float, sympy.Function]): - inner_self._diffusivity = value - inner_self._reset() - - def __init__(self, dim): - self.u_dim = 1 - super().__init__(dim, self.u_dim) - - return - - def _build_c_tensor(self): - """For this constitutive law, we expect just a diffusivity function""" - - d = self.dim - kappa = self.Parameters.diffusivity - self._c = sympy.Matrix.eye(d) * kappa - - return - - def _object_viewer(self): - from IPython.display import Latex, Markdown, display - - super()._object_viewer() - - ## feedback on this instance - display( - Latex(r"$\quad\kappa = $ " + sympy.sympify(self.Parameters.diffusivity)._repr_latex_()) - ) - - return - - -class TransverseIsotropicFlowModel(Constitutive_Model): - r""" - Transversely isotropic viscous flow model. - - .. math:: - - \tau_{ij} = \eta_{ijkl} \cdot \frac{1}{2} \left[ \frac{\partial u_k}{\partial x_l} - + \frac{\partial u_l}{\partial x_k} \right] - - where the viscosity tensor :math:`\eta` is defined as: - - .. math:: - - \eta_{ijkl} = \eta_0 I_{ijkl} + (\eta_0 - \eta_1) \left[ - \frac{1}{2}\left( n_i n_l \delta_{jk} + n_j n_k \delta_{il} - + n_i n_l \delta_{jk} + n_j n_l \delta_{ik} \right) - - 2 n_i n_j n_k n_l \right] - - and :math:`\hat{\mathbf{n}} \equiv \{n_i\}` is the unit vector defining the - local orientation of the weak plane (the director). - - The Mandel matrix is in ``viscous_model.C`` and the rank-4 tensor in - ``viscous_model.c``. - - Examples - -------- - >>> viscous_model = TransverseIsotropicFlowModel(dim) - >>> viscous_model.material_properties = viscous_model.Parameters( - ... eta_0=viscosity_fn, - ... eta_1=weak_viscosity_fn, - ... director=orientation_vector_fn - ... ) - >>> solver.constitutive_model = viscous_model - >>> tau = viscous_model.flux(gradient_matrix) - """ - - class _Parameters: - """Any material properties that are defined by a constitutive relationship are - collected in the parameters which can then be defined/accessed by name in - individual instances of the class. - """ - - def __init__( - inner_self, - eta_0: Union[float, sympy.Function] = 1, - eta_1: Union[float, sympy.Function] = 1, - director: Union[sympy.Matrix, sympy.Function] = sympy.Matrix([0, 0, 1]), - ): - inner_self._eta_0 = eta_0 - inner_self._eta_1 = eta_1 - inner_self._director = director - # inner_self.constitutive_model_class = const_model - - ## Note the inefficiency below if we change all these values one after the other - - @property - def eta_0(inner_self): - return inner_self._eta_0 - - @eta_0.setter - def eta_0( - inner_self, - value: Union[float, sympy.Function], - ): - inner_self._eta_0 = value - inner_self._reset() - - @property - def eta_1(inner_self): - return inner_self._eta_1 - - @eta_1.setter - def eta_1( - inner_self, - value: Union[float, sympy.Function], - ): - inner_self._eta_1 = value - inner_self._reset() - - @property - def director(inner_self): - return inner_self._director - - @director.setter - def director( - inner_self, - value: Union[sympy.Matrix, sympy.Function], - ): - inner_self._director = value - inner_self._reset() - - def __init__(self, dim): - u_dim = dim - super().__init__(dim, u_dim) - - # default values ... maybe ?? - return - - def _build_c_tensor(self): - """For this constitutive law, we expect two viscosity functions - and a sympy matrix that describes the director components n_{i}""" - - d = self.dim - dv = uw.maths.tensor.idxmap[d][0] - - eta_0 = self.Parameters.eta_0 - eta_1 = self.Parameters.eta_1 - n = self.Parameters.director - - Delta = eta_1 - eta_0 - - lambda_mat = uw.maths.tensor.rank4_identity(d) * eta_0 - - for i in range(d): - for j in range(d): - for k in range(d): - for l in range(d): - lambda_mat[i, j, k, l] += Delta * ( - ( - n[i] * n[k] * int(j == l) - + n[j] * n[k] * int(l == i) - + n[i] * n[l] * int(j == k) - + n[j] * n[l] * int(k == i) - ) - / 2 - - 2 * n[i] * n[j] * n[k] * n[l] - ) - - lambda_mat = sympy.simplify(uw.maths.tensor.rank4_to_mandel(lambda_mat, d)) - - self._c = uw.maths.tensor.mandel_to_rank4(lambda_mat, d) - - def _object_viewer(self): - from IPython.display import Latex, Markdown, display - - super()._object_viewer() - - ## feedback on this instance - display(Latex(r"$\quad\eta_0 = $ " + sympy.sympify(self.Parameters.eta_0)._repr_latex_())) - display(Latex(r"$\quad\eta_1 = $ " + sympy.sympify(self.Parameters.eta_1)._repr_latex_())) - display( - Latex( - r"$\quad\hat{\mathbf{n}} = $ " - + sympy.sympify(self.Parameters.director.T)._repr_latex_() - ) - ) - - -class MultiMaterial(Constitutive_Model): - r""" - Manage multiple materials in a constitutive framework. - - Bundles multiple materials into a single consitutive law. The expectation - is that these all have compatible flux terms. - """ - - def __init__( - self, - material_swarmVariable: Optional[IndexSwarmVariable] = None, - constitutive_models: Optional[list] = [], - ): - self._constitutive_models = constitutive_models - self._material_var = material_swarmVariable - - return From 1d575caf1af8e8a56b3e392d690b49f90892aa72 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 25 Mar 2026 07:20:37 +1100 Subject: [PATCH 027/537] Move square-wave benchmark to docs, remove parked advect_history - Move run_ve_square_wave.py to docs/advanced/benchmarks/ - Add ve-square-wave-shear.md benchmark documentation (10 harmonics) - Add to benchmarks toctree index - Remove _advect_history_PARKED (replaced by update_pre_solve) Underworld development team with AI support from Claude Code --- docs/advanced/benchmarks/index.md | 1 + .../benchmarks}/run_ve_square_wave.py | 6 +- .../benchmarks/ve-square-wave-shear.md | 79 ++++++++++++ src/underworld3/systems/ddt.py | 117 ------------------ 4 files changed, 83 insertions(+), 120 deletions(-) rename {tests => docs/advanced/benchmarks}/run_ve_square_wave.py (98%) create mode 100644 docs/advanced/benchmarks/ve-square-wave-shear.md diff --git a/docs/advanced/benchmarks/index.md b/docs/advanced/benchmarks/index.md index 774102ea4..56ee9ae04 100644 --- a/docs/advanced/benchmarks/index.md +++ b/docs/advanced/benchmarks/index.md @@ -10,4 +10,5 @@ Validation benchmarks comparing Underworld3 solvers against analytical solutions :maxdepth: 1 ve-oscillatory-shear +ve-square-wave-shear ``` diff --git a/tests/run_ve_square_wave.py b/docs/advanced/benchmarks/run_ve_square_wave.py similarity index 98% rename from tests/run_ve_square_wave.py rename to docs/advanced/benchmarks/run_ve_square_wave.py index d56ffc73e..56a988b82 100644 --- a/tests/run_ve_square_wave.py +++ b/docs/advanced/benchmarks/run_ve_square_wave.py @@ -183,7 +183,7 @@ def run_square_wave(order, De, n_periods, dt_min_over_tr, dt_max_over_tr, De = 1.5 order = 2 n_periods = 3 - n_harmonics = 3 + n_harmonics = 10 print("=" * 60) print(f"Square-wave VE benchmark: De={De}, order={order}") @@ -231,7 +231,7 @@ def run_square_wave(order, De, n_periods, dt_min_over_tr, dt_max_over_tr, # Save results np.savez( - "tests/ve_square_wave_benchmark.npz", + f"tests/ve_square_wave_{n_harmonics}h.npz", adaptive_times=result_adaptive["times"], adaptive_numerical=result_adaptive["numerical"], adaptive_analytical=result_adaptive["analytical"], @@ -241,4 +241,4 @@ def run_square_wave(order, De, n_periods, dt_min_over_tr, dt_max_over_tr, uniform_analytical=result_uniform["analytical"], uniform_timesteps=result_uniform["timesteps"], ) - print("\nResults saved to tests/ve_square_wave_benchmark.npz") + print(f"\nResults saved to tests/ve_square_wave_{n_harmonics}h.npz") diff --git a/docs/advanced/benchmarks/ve-square-wave-shear.md b/docs/advanced/benchmarks/ve-square-wave-shear.md new file mode 100644 index 000000000..6d80998a4 --- /dev/null +++ b/docs/advanced/benchmarks/ve-square-wave-shear.md @@ -0,0 +1,79 @@ +--- +title: "Viscoelastic Square-Wave Shear Benchmark" +--- + +# Maxwell Square-Wave Shear + +This benchmark validates the viscoelastic Stokes solver with **variable timesteps** +against an analytical solution for a Maxwell material under square-wave shear forcing. + +It tests both the variable-dt BDF-2 coefficients and the PetscDS constants mechanism +that routes these coefficients to the compiled pointwise functions at runtime. + +## Problem Setup + +Same geometry as the oscillatory shear benchmark: a box with height $H$ and width $2H$, +sheared by top/bottom boundary velocities. The shear rate is a truncated Fourier series +approximation of a square wave: + +$$\dot\gamma(t) = \frac{4\dot\gamma_0}{\pi} +\sum_{k=1}^{N} \frac{\sin\bigl((2k-1)\omega t\bigr)}{2k-1}$$ + +The sharp transitions between positive and negative shear demand small timesteps +near the transition points, while the plateaux can use much larger steps. This +makes it a natural test for adaptive (variable) timestepping. + +## Analytical Solution + +Since the Maxwell equation is linear, the stress is the superposition of +single-frequency Maxwell solutions at each Fourier harmonic: + +$$\sigma_{xy}(t) = \sum_{k=1}^{N} \sigma_k(t)$$ + +where each $\sigma_k$ is the oscillatory Maxwell solution with amplitude +$a_k = 4\dot\gamma_0 / (\pi(2k-1))$ and frequency $\omega_k = (2k-1)\omega$: + +$$\sigma_k(t) = \frac{\eta\, a_k}{1 + \text{De}_k^2} +\left[\sin(\omega_k t) - \text{De}_k\cos(\omega_k t) ++ \text{De}_k\,e^{-t/t_r}\right]$$ + +with $\text{De}_k = \omega_k t_r$. + +## Adaptive Timestep Strategy + +The timestep varies between `dt_min` near transitions and `dt_max` on plateaux, +based on distance to the nearest square-wave transition point: + +$$\Delta t = \Delta t_{\min} + (\Delta t_{\max} - \Delta t_{\min})\, f^2$$ + +where $f \in [0,1]$ measures the normalised distance from the nearest transition. + +## Variable-dt BDF Coefficients + +With uniform timesteps, BDF-2 uses constant coefficients $[3/2, -2, 1/2]$. +With variable timesteps (ratio $r = \Delta t_n / \Delta t_{n-1}$), the +coefficients become: + +$$c_0 = \frac{1+2r}{1+r}, \quad c_1 = -(1+r), \quad c_2 = \frac{r^2}{1+r}$$ + +These coefficients are stored as UWexpressions and updated each step via +`_update_bdf_coefficients()`, flowing through PetscDS `constants[]` to the +compiled pointwise functions without JIT recompilation. + +## Results (De=1.5, BDF-2, 10 harmonics) + +| Run | Steps | L2 Error | Ratio | +|-----|-------|----------|-------| +| Adaptive dt | 295 | 9.55e-04 | 1.78x | +| Uniform dt | 629 | 5.35e-04 | 1.0x | + +The adaptive run uses 53% fewer steps at only 1.78x the error. + +## Running the Benchmark + +```bash +pixi run -e default python docs/advanced/benchmarks/run_ve_square_wave.py +``` + +The script runs both adaptive and uniform timestep cases, prints convergence +data, and saves results to `.npz` files. diff --git a/src/underworld3/systems/ddt.py b/src/underworld3/systems/ddt.py index 24c77efe9..64c10b255 100644 --- a/src/underworld3/systems/ddt.py +++ b/src/underworld3/systems/ddt.py @@ -1628,123 +1628,6 @@ def update_pre_solve( return - def _advect_history_PARKED(self, dt, evalf=False, verbose=False): - """Advect all psi_star history levels to upstream positions. - - Pure advection only — no copy-down, no psi_fn evaluation. - Each psi_star[i] is sampled at positions traced back by Δt along - the velocity characteristics, and the result is written back in place. - - Used by VE_Stokes for explicit stress history management where the - actual stress is stored in psi_star[0] after each solve. This method - advects those stored values to upstream positions before the next solve. - - Parameters - ---------- - dt : float or sympy expression - Timestep for characteristic tracing. - evalf : bool - Force numerical evaluation. - verbose : bool - Verbose output. - """ - - if not self._history_initialised: - self.initialise_history() - - # --- Coordinate setup (shared with update_pre_solve) --- - from underworld3.utilities.unit_aware_array import UnitAwareArray - - psi_star_0_coords = self.psi_star[0].coords - if hasattr(psi_star_0_coords, "magnitude"): - psi_star_0_coords_nd = uw.non_dimensionalise(psi_star_0_coords) - if isinstance(psi_star_0_coords_nd, UnitAwareArray): - psi_star_0_coords_nd = np.array(psi_star_0_coords_nd) - elif hasattr(psi_star_0_coords_nd, 'magnitude'): - psi_star_0_coords_nd = psi_star_0_coords_nd.magnitude - else: - psi_star_0_coords_nd = psi_star_0_coords - - cellid = self.mesh.get_closest_cells(psi_star_0_coords_nd) - centroid_coords = self.mesh._centroids[cellid] - shift = 0.001 - node_coords_nd = (1.0 - shift) * psi_star_0_coords_nd + shift * centroid_coords - - # --- Unit handling for dt --- - model = uw.get_default_model() - coords_template = self.psi_star[0].coords - has_units = hasattr(coords_template, "magnitude") or hasattr(coords_template, "_magnitude") - - if has_units: - dt_for_calc = dt.to("second") if hasattr(dt, "to") else dt - else: - if hasattr(dt, "magnitude") or hasattr(dt, "value"): - dt_nondim = uw.non_dimensionalise(dt, model) - if hasattr(dt_nondim, "magnitude"): - dt_for_calc = float(dt_nondim.magnitude) - elif hasattr(dt_nondim, "value"): - dt_for_calc = float(dt_nondim.value) - else: - dt_for_calc = float(dt_nondim) - else: - dt_for_calc = dt - - # --- Advect each history level (RK2 midpoint method) --- - for i in range(self.order - 1, -1, -1): - # Evaluate velocity at node positions - v_result = uw.function.evaluate(self.V_fn, node_coords_nd) - if isinstance(v_result, UnitAwareArray): - v_at_node_pts = v_result[:, 0, :] - if not isinstance(v_at_node_pts, UnitAwareArray): - v_at_node_pts = UnitAwareArray(v_at_node_pts, units=v_result.units) - else: - v_at_node_pts = v_result[:, 0, :] - - # Non-dimensionalize velocities if needed - if not has_units and isinstance(v_at_node_pts, UnitAwareArray): - v_nondim = uw.non_dimensionalise(v_at_node_pts, model) - v_at_node_pts = np.array(v_nondim) if isinstance(v_nondim, UnitAwareArray) else v_nondim - - coords = self.psi_star[i].coords - if not has_units and isinstance(coords, UnitAwareArray): - coords = np.array(coords) - - # RK2: midpoint velocity - mid_pt_coords = coords - v_at_node_pts * (0.5 * dt_for_calc) - mid_pt_coords = self.mesh.return_coords_to_bounds(mid_pt_coords) - v_mid_result = uw.function.global_evaluate(self.V_fn, mid_pt_coords) - if isinstance(v_mid_result, UnitAwareArray): - v_at_mid_pts = v_mid_result[:, 0, :] - if not isinstance(v_at_mid_pts, UnitAwareArray): - v_at_mid_pts = UnitAwareArray(v_at_mid_pts, units=v_mid_result.units) - else: - v_at_mid_pts = v_mid_result[:, 0, :] - - if not has_units and isinstance(v_at_mid_pts, UnitAwareArray): - v_nondim = uw.non_dimensionalise(v_at_mid_pts, model) - v_at_mid_pts = np.array(v_nondim) if isinstance(v_nondim, UnitAwareArray) else v_nondim - - # Upstream position - end_pt_coords = coords - v_at_mid_pts * dt_for_calc - end_pt_coords = self.mesh.return_coords_to_bounds(end_pt_coords) - - # Sample psi_star[i] at upstream position - expr_to_evaluate = self.psi_star[i].sym - if hasattr(expr_to_evaluate, 'shape') and expr_to_evaluate.shape == (1, 1): - expr_to_evaluate = expr_to_evaluate[0, 0] - - value_at_end_points = uw.function.global_evaluate( - expr_to_evaluate, end_pt_coords, - ) - - psi_star_units = self.psi_star[i].units - if psi_star_units is not None and not isinstance(value_at_end_points, UnitAwareArray): - value_at_end_points = UnitAwareArray(value_at_end_points, units=psi_star_units) - - self.psi_star[i].array[...] = value_at_end_points - - return - @property def bdf_coefficients(self): """Current BDF coefficients [c0, c1, ...] accounting for variable timesteps.""" From 069cb722e70687d36164fee82b757d820be47d2f Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 25 Mar 2026 16:02:51 +1100 Subject: [PATCH 028/537] Update uw script from development (PIXI_PROJECT_MANIFEST fix) Underworld development team with AI support from Claude Code --- uw | 6 +----- 1 file changed, 1 insertion(+), 5 deletions(-) diff --git a/uw b/uw index c4d52af79..fd37fe077 100755 --- a/uw +++ b/uw @@ -162,12 +162,8 @@ run_build() { fi if [ "$need_clean" = true ]; then echo " PETSc target changed — cleaning build cache..." + rm -rf "$SCRIPT_DIR"/build/lib.* "$SCRIPT_DIR"/build/temp.* fi - # Always clean the setuptools build directory. --no-cache-dir only - # bypasses pip's wheel cache; the build/ tree (Cython .c files, - # compiled .so objects) persists across runs and silently reuses - # stale artefacts when only .py sources change. - rm -rf "$SCRIPT_DIR"/build/lib.* "$SCRIPT_DIR"/build/temp.* "$SCRIPT_DIR"/build/bdist.* mkdir -p "$SCRIPT_DIR/build" echo "$current_target" > "$petsc_marker" From ba4f349df0462e411db2b9462abe36f82b2bc36f Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 26 Mar 2026 13:33:36 +1100 Subject: [PATCH 029/537] Add solver barrier for VEP and fix is_viscoplastic comparison - Add requires_stress_history property to Constitutive_Model base (False) and override in ViscoElasticPlasticFlowModel (True). - Stokes solver setter raises TypeError when assigned a constitutive model that requires stress history but DFDt is not available. Prevents silent failure where VEP on plain Stokes drops all history terms. - Fix is_viscoplastic: was comparing UWexpression == sympy.oo (always False due to type mismatch); now uses .sym is sympy.oo. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 17 ++++++++++++++++- .../cython/petsc_generic_snes_solvers.pyx | 10 ++++++++++ 2 files changed, 26 insertions(+), 1 deletion(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 47293a680..76ea0d7be 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -579,6 +579,16 @@ def _reset(self): return + @property + def requires_stress_history(self): + """Whether this model needs DFDt stress history tracking. + + Models that return True require a solver with stress history + management (e.g. VE_Stokes). Assigning such a model to a plain + Stokes solver will raise an error. + """ + return False + def _build_c_tensor(self): """Return the identity tensor of appropriate rank (e.g. for projections)""" @@ -1588,6 +1598,11 @@ def _object_viewer(self): ## Todo: add all the other properties in here ) + @property + def requires_stress_history(self): + """VEP models always require stress history tracking.""" + return True + @property def is_elastic(self): """True if elastic behavior is active (finite dt_elastic and shear_modulus).""" @@ -1604,7 +1619,7 @@ def is_elastic(self): @property def is_viscoplastic(self): """True if plastic yielding is active (finite yield_stress).""" - if self.Parameters.yield_stress == sympy.oo: + if self.Parameters.yield_stress.sym is sympy.oo: return False return True diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index c4b3377e0..da048e46f 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -950,6 +950,16 @@ class SolverBaseClass(uw_object): "constitutive_model must be a valid class or instance of a valid class" ) + # Check that the solver can support this constitutive model's requirements. + # Models with stress history (VEP) need a solver that manages DFDt — e.g. VE_Stokes. + # Using them on a plain Stokes solver silently drops the history terms. + if self._constitutive_model.requires_stress_history and self.Unknowns.DFDt is None: + raise TypeError( + f"{type(self._constitutive_model).__name__} requires stress history tracking " + f"(DFDt). Use uw.systems.VE_Stokes instead of uw.systems.Stokes, or provide " + f"a DFDt object when constructing the solver." + ) + # May not work due to flux being incomplete if self.Unknowns.DFDt is not None: self.Unknowns.DFDt.psi_fn = self._constitutive_model.flux.T From 1e8c9af9c3e0fd7deb86d22ff8da7956ef1e819a Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 26 Mar 2026 13:33:36 +1100 Subject: [PATCH 030/537] Add solver barrier for VEP and fix is_viscoplastic comparison - Add requires_stress_history property to Constitutive_Model base (False) and override in ViscoElasticPlasticFlowModel (True). - Stokes solver setter raises TypeError when assigned a constitutive model that requires stress history but DFDt is not available. Prevents silent failure where VEP on plain Stokes drops all history terms. - Fix is_viscoplastic: was comparing UWexpression == sympy.oo (always False due to type mismatch); now uses .sym is sympy.oo. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 17 ++++++++++++++++- .../cython/petsc_generic_snes_solvers.pyx | 10 ++++++++++ 2 files changed, 26 insertions(+), 1 deletion(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 47293a680..76ea0d7be 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -579,6 +579,16 @@ def _reset(self): return + @property + def requires_stress_history(self): + """Whether this model needs DFDt stress history tracking. + + Models that return True require a solver with stress history + management (e.g. VE_Stokes). Assigning such a model to a plain + Stokes solver will raise an error. + """ + return False + def _build_c_tensor(self): """Return the identity tensor of appropriate rank (e.g. for projections)""" @@ -1588,6 +1598,11 @@ def _object_viewer(self): ## Todo: add all the other properties in here ) + @property + def requires_stress_history(self): + """VEP models always require stress history tracking.""" + return True + @property def is_elastic(self): """True if elastic behavior is active (finite dt_elastic and shear_modulus).""" @@ -1604,7 +1619,7 @@ def is_elastic(self): @property def is_viscoplastic(self): """True if plastic yielding is active (finite yield_stress).""" - if self.Parameters.yield_stress == sympy.oo: + if self.Parameters.yield_stress.sym is sympy.oo: return False return True diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index c4b3377e0..da048e46f 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -950,6 +950,16 @@ class SolverBaseClass(uw_object): "constitutive_model must be a valid class or instance of a valid class" ) + # Check that the solver can support this constitutive model's requirements. + # Models with stress history (VEP) need a solver that manages DFDt — e.g. VE_Stokes. + # Using them on a plain Stokes solver silently drops the history terms. + if self._constitutive_model.requires_stress_history and self.Unknowns.DFDt is None: + raise TypeError( + f"{type(self._constitutive_model).__name__} requires stress history tracking " + f"(DFDt). Use uw.systems.VE_Stokes instead of uw.systems.Stokes, or provide " + f"a DFDt object when constructing the solver." + ) + # May not work due to flux being incomplete if self.Unknowns.DFDt is not None: self.Unknowns.DFDt.psi_fn = self._constitutive_model.flux.T From d8c8e465f53c77441504d9326e8d74a10430a118 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 26 Mar 2026 16:05:25 +1100 Subject: [PATCH 031/537] Unify Stokes and VE_Stokes: auto-create DFDt from constitutive model MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The Stokes solver now automatically creates stress history infrastructure (DFDt) when assigned a constitutive model with requires_stress_history=True. Users no longer need to choose between Stokes and VE_Stokes — the solver adapts to the constitutive model. Changes: - constitutive_model setter: creates DFDt lazily instead of raising TypeError - SNES_Stokes._create_stress_history_ddt(): extracted from VE_Stokes.__init__ - SNES_Stokes.solve(): includes VE pre/post hooks when DFDt is active - SNES_Stokes.tau: returns psi_star[0] when DFDt exists, else lazy projection - SNES_VE_Stokes: thin backward-compat wrapper (pre-creates DFDt with order) - Fix: don't overwrite constitutive model order when solver _order is 0 Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 2 +- .../cython/petsc_generic_snes_solvers.pyx | 20 +- src/underworld3/systems/solvers.py | 394 ++++++++---------- 3 files changed, 174 insertions(+), 242 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 76ea0d7be..f979088c5 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1058,7 +1058,7 @@ class ViscoElasticPlasticFlowModel(ViscousFlowModel): """ - def __init__(self, unknowns, order=1, material_name: str = None): + def __init__(self, unknowns, order=2, material_name: str = None): ## We just need to add the expressions for the stress history terms in here.\ ## They are properties to hold expressions that are persistent for this instance diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index da048e46f..ff47841aa 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -930,7 +930,10 @@ class SolverBaseClass(uw_object): self._constitutive_model = model_or_class self._constitutive_model.Unknowns = self.Unknowns self._constitutive_model._solver_is_setup = False - self._constitutive_model.order = self._order + # Only override the constitutive model's order if the solver has + # an explicit VE order (> 0). Otherwise preserve the model's default. + if self._order > 0: + self._constitutive_model.order = self._order # Establish bidirectional reference so parameter changes can propagate to solver self._constitutive_model.Parameters._solver = self @@ -938,7 +941,8 @@ class SolverBaseClass(uw_object): ### checking if it's a class elif type(model_or_class) == type(uw.constitutive_models.Constitutive_Model): self._constitutive_model = model_or_class(self.Unknowns) - self._constitutive_model.order = self._order + if self._order > 0: + self._constitutive_model.order = self._order # Establish bidirectional reference so parameter changes can propagate to solver self._constitutive_model.Parameters._solver = self @@ -950,15 +954,11 @@ class SolverBaseClass(uw_object): "constitutive_model must be a valid class or instance of a valid class" ) - # Check that the solver can support this constitutive model's requirements. - # Models with stress history (VEP) need a solver that manages DFDt — e.g. VE_Stokes. - # Using them on a plain Stokes solver silently drops the history terms. + # If the constitutive model requires stress history (e.g. VEP), create the + # DFDt infrastructure lazily. This means users don't need to choose between + # Stokes and VE_Stokes — the solver adapts to the constitutive model. if self._constitutive_model.requires_stress_history and self.Unknowns.DFDt is None: - raise TypeError( - f"{type(self._constitutive_model).__name__} requires stress history tracking " - f"(DFDt). Use uw.systems.VE_Stokes instead of uw.systems.Stokes, or provide " - f"a DFDt object when constructing the solver." - ) + self._create_stress_history_ddt(order=self._constitutive_model.order) # May not work due to flux being incomplete if self.Unknowns.DFDt is not None: diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 62387707a..c63870700 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -687,6 +687,155 @@ def __init__( return + def _create_stress_history_ddt(self, order=2): + """Create DFDt for stress history tracking (VE/VEP models). + + Called automatically when a constitutive model with + ``requires_stress_history = True`` is assigned. Can also be called + explicitly to pre-create the DFDt with a specific order. + """ + if self.Unknowns.DFDt is not None: + return # already created + + self._order = order + self.Unknowns.DFDt = uw.systems.ddt.SemiLagrangian( + self.mesh, + sympy.Matrix.zeros(self.mesh.dim, self.mesh.dim), + self.u.sym, + vtype=uw.VarType.SYM_TENSOR, + degree=self.u.degree - 1, + continuous=True, + varsymbol=rf"{{F[ {self.u.symbol} ] }}", + verbose=self.verbose, + bcs=None, + order=order, + smoothing=0.0001, + ) + + @timing.routine_timer_decorator + def solve( + self, + zero_init_guess: bool = True, + timestep: float = None, + _force_setup: bool = False, + verbose=False, + evalf=False, + order=None, + ): + """Solve the Stokes system, with optional viscoelastic stress history. + + When a constitutive model with stress history is active (DFDt is not None), + the solve includes pre/post hooks for advecting stress history, updating + BDF coefficients, and projecting the actual stress after the solve. + + Parameters + ---------- + zero_init_guess : bool + If True, use zero initial guess. Otherwise use current field values. + timestep : float, optional + Advection timestep. Required when stress history is active. + _force_setup : bool + Force rebuild of pointwise functions. + verbose : bool + Enable verbose output. + evalf : bool + Force numerical evaluation during history updates. + order : int, optional + Override the VE time integration order. + """ + + has_stress_history = self.Unknowns.DFDt is not None + + if has_stress_history: + if timestep is None: + timestep = self.constitutive_model.Parameters.dt_elastic.sym + + if order is None or order > self._order: + order = self._order + + if _force_setup: + self.is_setup = False + + # Re-setup when effective_order changes (DDt history ramp-up) + _current_eff_order = self.constitutive_model.effective_order + if not hasattr(self, '_prev_effective_order'): + self._prev_effective_order = None + if _current_eff_order != self._prev_effective_order: + self.is_setup = False + self.constitutive_model._solver_is_setup = False + self._prev_effective_order = _current_eff_order + + if not self.constitutive_model._solver_is_setup: + self.is_setup = False + self.DFDt.psi_fn = self.constitutive_model.flux.T + + if not self.is_setup: + self._setup_pointwise_functions(verbose) + self._setup_discretisation(verbose) + self._setup_solver(verbose) + + # 1. ADVECT stress history along characteristics + if uw.mpi.rank == 0 and verbose: + print(f"Stokes solver - advect stress history", flush=True) + + self.DFDt.update_pre_solve(timestep, verbose=verbose, evalf=evalf, + store_result=False) + self.constitutive_model._update_bdf_coefficients() + + # 2. SOLVE + if uw.mpi.rank == 0 and verbose: + print(f"Stokes solver - solve", flush=True) + + super().solve( + zero_init_guess, + _force_setup=_force_setup, + verbose=verbose, + picard=0, + ) + + # 3. PROJECT actual stress and SHIFT history + if uw.mpi.rank == 0 and verbose: + print(f"Stokes solver - store stress and shift history", flush=True) + + import numpy as np + + _advected_sigma_star = np.copy(self.DFDt.psi_star[0].array[...]) + + self.DFDt._psi_star_projection_solver.uw_function = self.constitutive_model.flux + self.DFDt._psi_star_projection_solver.smoothing = 0.0 + self.DFDt._psi_star_projection_solver.solve(verbose=verbose) + + for i in range(self.DFDt.order - 1, 0, -1): + if i == 1: + self.DFDt.psi_star[i].array[...] = _advected_sigma_star + else: + self.DFDt.psi_star[i].array[...] = self.DFDt.psi_star[i - 1].array[...] + + self.DFDt.update_post_solve(timestep, verbose=verbose, evalf=evalf) + + self.is_setup = True + self.constitutive_model._solver_is_setup = True + + else: + # Plain Stokes — no stress history + super().solve( + zero_init_guess, + _force_setup=_force_setup, + verbose=verbose, + ) + + @property + def tau(self): + r"""Deviatoric stress from the most recent solve. + + When stress history is active (VEP), returns ``psi_star[0]`` which + contains the actual projected stress. Otherwise falls through to the + base class lazy projection. + """ + if self.Unknowns.DFDt is not None: + return self.DFDt.psi_star[0] + return super().tau + # ========================================================================= # PETSc Residual Templates # These define the weak form terms assembled by PETSc's finite element system. @@ -1126,72 +1275,26 @@ def estimate_dt(self): class SNES_VE_Stokes(SNES_Stokes): - r""" - Viscoelastic Stokes equation solver. - - Provides a discrete representation of the Stokes flow equations with - incompressibility (or near-incompressibility) constraint and a flux - history term for viscoelastic modelling. Inherits from :class:`SNES_Stokes`. - - Momentum equation: - - .. math:: - - -\nabla \cdot \underbrace{\left[ \boldsymbol{\tau} - p \mathbf{I} - \right]}_{\mathbf{F}} = \underbrace{\mathbf{f}}_{\mathbf{h}} - - Continuity equation: + r"""Viscoelastic Stokes solver (backward-compatibility wrapper). - .. math:: - - \underbrace{\nabla \cdot \mathbf{u}}_{\mathbf{h}_p} = 0 + .. deprecated:: + Use ``uw.systems.Stokes`` directly with a + ``ViscoElasticPlasticFlowModel`` constitutive model. The Stokes + solver now creates stress history infrastructure automatically + when the constitutive model requires it. - The flux term is a deviatoric stress :math:`\boldsymbol{\tau}` related - to velocity gradients :math:`\nabla \mathbf{u}` through a viscosity - tensor :math:`\eta`, plus a volumetric (pressure) part :math:`p`: - - .. math:: - - \mathbf{F}: \quad \boldsymbol{\tau} = \frac{\eta}{2} - \left( \nabla \mathbf{u} + \nabla \mathbf{u}^T \right) - - The constraint equation :math:`\mathbf{h}_p = 0` is incompressible flow - by default but can be set to any function of :math:`\mathbf{u}` and - :math:`\nabla \cdot \mathbf{u}`. + This wrapper pre-creates the DFDt with a specific ``order`` parameter, + which is useful when you want to control the BDF order before assigning + the constitutive model. Parameters ---------- mesh : Mesh The computational mesh. - velocityField : MeshVariable, optional - Mesh variable for velocity. Created automatically if not provided. - pressureField : MeshVariable, optional - Mesh variable for pressure. Created automatically if not provided. - degree : int, default=2 - Polynomial degree for velocity elements. order : int, default=2 - Order parameter (typically same as degree). - p_continuous : bool, default=True - If False, use discontinuous pressure elements. - verbose : bool, default=False - Enable verbose output. - DuDt : SemiLagrangian_DDt or Lagrangian_DDt, optional - Time derivative operator (may be used in child classes). - - Notes - ----- - - The viscosity tensor :math:`\boldsymbol{\eta}` is set via the - ``constitutive_model`` property - - For viscoelastic problems, the flux term contains stress history - tracked on a particle swarm - - Augmented Lagrangian approach adds :math:`\lambda \nabla \cdot \mathbf{u}` - to penalize incompressibility - - Pressure element order determines mixed FEM integration order - - See Also - -------- - SNES_Stokes : Base Stokes solver. - uw.constitutive_models.ViscoElasticPlasticFlowModel : Constitutive model for VE flow. + BDF time integration order for stress history. + **kwargs + All other arguments are passed to :class:`SNES_Stokes`. """ instances = 0 @@ -1205,12 +1308,9 @@ def __init__( order: Optional[int] = 2, p_continuous: Optional[bool] = True, verbose: Optional[bool] = False, - # DuDt Not used in VE, but may be in child classes DuDt: Union[SemiLagrangian_DDt, Lagrangian_DDt] = None, DFDt: Union[SemiLagrangian_DDt, Lagrangian_DDt] = None, ): - - # Stokes is parent (will not build DuDt or DFDt) super().__init__( mesh, velocityField, @@ -1222,22 +1322,8 @@ def __init__( DFDt=DFDt, ) - self._order = order # VE time-order - - if self.Unknowns.DFDt is None: - self.Unknowns.DFDt = uw.systems.ddt.SemiLagrangian( - self.mesh, - sympy.Matrix.zeros(self.mesh.dim, self.mesh.dim), - self.u.sym, - vtype=uw.VarType.SYM_TENSOR, - degree=self.u.degree - 1, - continuous=True, - varsymbol=rf"{{F[ {self.u.symbol} ] }}", - verbose=self.verbose, - bcs=None, - order=self._order, - smoothing=0.0001, - ) + # Pre-create DFDt so it's available before constitutive model is set + self._create_stress_history_ddt(order=order) return @@ -1246,160 +1332,6 @@ def delta_t(self): """Elastic timestep from the constitutive model.""" return self.constitutive_model.Parameters.dt_elastic - @property - def tau(self): - r"""Deviatoric stress from the most recent solve (stored in history). - - For VE_Stokes, the stress is projected into ``psi_star[0]`` after - each solve. This override returns that variable directly — no - additional projection needed. - - Returns - ------- - MeshVariable - The stress history variable containing the actual deviatoric - stress from the most recent solve. - """ - return self.DFDt.psi_star[0] - - ## Solver needs to update the stress history terms as well as call the SNES solve: - - @timing.routine_timer_decorator - def solve( - self, - zero_init_guess: bool = True, - timestep: float = None, - _force_setup: bool = False, - verbose=False, - evalf=False, - order=None, - ): - """ - Generates solution to constructed system. - - Params - ------ - zero_init_guess: - If `True`, a zero initial guess will be used for the - system solution. Otherwise, the current values of `self.u` will be used. - """ - - if order is None or order > self._order: - order = self._order - - if timestep is None: - timestep = self.delta_t.sym - - # dt_elastic is a constitutive parameter (relaxation timescale) — - # never overwritten by solve(). The advection timestep (for departure - # point tracing) and the elastic relaxation timescale are independent. - - if _force_setup: - self.is_setup = False - - # Re-setup when effective_order changes (e.g. DDt history ramp-up - # from order 1 to order 2). The JIT-compiled pointwise functions - # depend on the order used in the constitutive model. - _current_eff_order = self.constitutive_model.effective_order - if not hasattr(self, '_prev_effective_order'): - self._prev_effective_order = None - if _current_eff_order != self._prev_effective_order: - self.is_setup = False - self.constitutive_model._solver_is_setup = False - self._prev_effective_order = _current_eff_order - - if not self.constitutive_model._solver_is_setup: - self.is_setup = False - self.DFDt.psi_fn = self.constitutive_model.flux.T - - if not self.is_setup: - self._setup_pointwise_functions(verbose) - self._setup_discretisation(verbose) - self._setup_solver(verbose) - - # --- Stress history management via standard DDt pathway --- - # - # update_pre_solve(advect_only=True) performs: - # 1. History shift: psi_star[i] ← psi_star[i-1] - # 2. Skip psi_fn evaluation (psi_star[0] already has projected stress) - # 3. Advect all history levels to upstream positions along characteristics - # - # After this: psi_star[0] = σ* (previous stress at upstream), - # psi_star[1] = σ** (stress from 2 steps ago, double-traced). - - if uw.mpi.rank == 0 and verbose: - print(f"VE Stokes solver - advect stress history", flush=True) - - self.DFDt.update_pre_solve(timestep, verbose=verbose, evalf=evalf, - store_result=False) - - # Update BDF coefficients from current dt_elastic and DDt history. - # These are UWexpressions that route through PetscDS constants[], - # so the compiled pointwise functions pick up the new values without - # JIT recompilation. - self.constitutive_model._update_bdf_coefficients() - - # 2. SOLVE: PETSc uses the advected σ*, σ** via the constitutive model - - if uw.mpi.rank == 0 and verbose: - print(f"VE Stokes solver - solve Stokes flow", flush=True) - - super().solve( - zero_init_guess, - _force_setup=_force_setup, - verbose=verbose, - picard=0, - ) - - # 3. STORE ACTUAL STRESS and SHIFT HISTORY. - # - # After advection + solve: - # psi_star[0] = advected σ* (used by the solver) - # psi_star[1] = advected σ** (used by the solver) - # - # We need to: - # a) Project actual stress → psi_star[0] (while σ*, σ** are intact) - # b) Save the advected σ* into psi_star[1] for next step's σ** - # (chained characteristic tracing) - # - # The projection reads psi_star[0..1] via stress_deviator, so we - # must project BEFORE shifting. Then save the advected σ* and - # overwrite psi_star[0] with the projected stress. - - if uw.mpi.rank == 0 and verbose: - print(f"VE Stokes solver - store stress and shift history", flush=True) - - import numpy as np - - # Save advected σ* before projection modifies psi_star[0] - _advected_sigma_star = np.copy(self.DFDt.psi_star[0].array[...]) - - # Project actual stress into psi_star[0]. - # Uses the constitutive formula so that σ* and σ** from psi_star - # are read correctly during projection. - self.DFDt._psi_star_projection_solver.uw_function = self.constitutive_model.flux - self.DFDt._psi_star_projection_solver.smoothing = 0.0 - self.DFDt._psi_star_projection_solver.solve(verbose=verbose) - - # Now psi_star[0] = projected τ (actual stress from this solve). - # Shift history: psi_star[i] ← previous psi_star[i-1] (advected values). - # psi_star[1] gets the advected σ* (saved before projection). - # Higher levels shift down the chain. - for i in range(self.DFDt.order - 1, 0, -1): - if i == 1: - self.DFDt.psi_star[i].array[...] = _advected_sigma_star - else: - self.DFDt.psi_star[i].array[...] = self.DFDt.psi_star[i - 1].array[...] - - # 5. BOOKKEEPING - - self.DFDt.update_post_solve(timestep, verbose=verbose, evalf=evalf) - - self.is_setup = True - self.constitutive_model._solver_is_setup = True - - return - class SNES_Projection(SNES_Scalar): r""" From 1b488b73f8a7e6132ae05de2f78a8752ee5e2228 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 26 Mar 2026 16:45:46 +1100 Subject: [PATCH 032/537] Add BDF order fallback for rapid timestep increases BDF-2 coefficients can cause negative stress extrapolation when the timestep ratio dt_new/dt_old exceeds ~2x and the stress history is non-smooth (e.g. after a yield event). The large c1/c2 coefficients amplify the difference between sigma* and sigma**, overshooting into negative territory. _update_bdf_coefficients() now checks the timestep ratio and falls back to BDF-1 when it exceeds _max_dt_ratio_for_higher_order (default 2.0). This preserves BDF-2 accuracy for uniform or smoothly varying timesteps while preventing negative stress in pathological cases. Also changes VEP default order from 1 to 2 (BDF-2 is the recommended default from convergence analysis). Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 29 ++++++++++++++++++++++---- 1 file changed, 25 insertions(+), 4 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index f979088c5..74ea76403 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1267,6 +1267,11 @@ def effective_order(self): return min(self._order, self.Unknowns.DFDt.effective_order) return self._order + # Maximum timestep ratio (dt_new / dt_old) for which BDF-2+ is safe. + # Beyond this, fall back to BDF-1 to avoid negative-stress extrapolation + # when stress history is non-smooth (e.g. yield events). + _max_dt_ratio_for_higher_order = 2.0 + def _update_bdf_coefficients(self): """Update BDF coefficient UWexpressions from current dt_elastic and DDt history. @@ -1274,16 +1279,32 @@ def _update_bdf_coefficients(self): correct coefficients to the compiled pointwise functions. The coefficient UWexpressions (_bdf_c0..c3) are referenced symbolically in ve_effective_viscosity, E_eff, and stress() — their numeric values flow through PetscDSSetConstants. + + When the timestep ratio exceeds ``_max_dt_ratio_for_higher_order``, + BDF-2+ coefficients can cause negative stress extrapolation if the + stress history is non-smooth (e.g. after a yield event). In this case + we fall back to BDF-1 coefficients for safety. """ + order = self.effective_order + if self.Unknowns is not None and self.Unknowns.DFDt is not None: dt_current = self.Parameters.dt_elastic if hasattr(dt_current, 'sym'): dt_current = dt_current.sym - coeffs = _bdf_coefficients( - self.effective_order, dt_current, self.Unknowns.DFDt._dt_history - ) + + # Guard: fall back to BDF-1 when timestep increases too rapidly + dt_history = self.Unknowns.DFDt._dt_history + if order >= 2 and len(dt_history) > 0 and dt_history[0] is not None: + try: + ratio = float(dt_current) / float(dt_history[0]) + if ratio > self._max_dt_ratio_for_higher_order: + order = 1 + except (TypeError, ZeroDivisionError): + pass # symbolic dt — can't evaluate, keep requested order + + coeffs = _bdf_coefficients(order, dt_current, dt_history) else: - coeffs = _bdf_coefficients(self.effective_order, None, []) + coeffs = _bdf_coefficients(order, None, []) # Pad to length 4 while len(coeffs) < 4: From f26a8f593ec223ad22526c1cf6e3e40959674c1a Mon Sep 17 00:00:00 2001 From: jcgraciosa <12045001+jcgraciosa@users.noreply.github.com> Date: Thu, 26 Mar 2026 18:23:07 +1100 Subject: [PATCH 033/537] Add Kaiju and Gadi cluster support: pixi env, PETSc build script, and documentation (#79) * Added pixi env and documentation for Kaiju * Fix pixi env check and use PATH instead of PIXI_ENVIRONMENT * Added CC=mpicc * Modified PETSc MPI detection * Fix LD_LIBRARY_PATH for spack OpenMPI * Add MMG_INSTALL_PRIVATE_HEADERS=ON for PARMMG (kaiju only) * Disable SCOTCH in MMG build to fix PARMMG configure on Kaiju pixi's conda ld (14.3.0) requires explicit transitive shared lib deps. libmmg.so built with SCOTCH caused MMG_WORKS link test to fail in PARMMG's FindMMG.cmake because libscotch.so wasn't explicitly linked. MMG's SCOTCH is only used for mesh renumbering (optional perf feature); PARMMG uses ptscotch separately for parallel partitioning, unaffected. Co-Authored-By: Claude Sonnet 4.6 * Update kaiju cluster setup docs with shared install and troubleshooting - Add shared installation section (admin, Lmod module) - Add troubleshooting entries from install experience: h5py replacing mpi4py, numpy ABI mismatch, PARMMG/pixi ld issue Underworld development team with AI support from Claude Code * Added info re. shared installation in Kaiju cluster * Added link to admin-repo * Added pixi env for Gadi baremetal install * Added build-petsc-gadi script * Specified MPI_DIR * Unset conda/pixi compiler variables that interfere with mpicc * Removed explicit setting of MPI_DIR * Added ignoreLinkOutput * Added missing libraries: libucc and libnl_3 * Reordering PATH * Added symlink and setting LD_LIBRARY_PATH before configure runs * fix linking * Added OMPI_FCFLAGS * Added symlink to scratch for petsc; download fblaslapack * Updated env vars for build * Added patchelf to reorder h5py RPATH after source build * Changes according to PR feedback * Changed documentation to contain info on the clusters closely supported. * Fixed toctree reference and rename PETSC_ARCH to petsc-4-uw-openmpi for consistency --------- Co-authored-by: Juan Carlos Graciosa Co-authored-by: Claude Sonnet 4.6 --- docs/developer/guides/hpc-cluster-setup.md | 302 ++++++++ docs/developer/index.md | 1 + petsc-custom/README.md | 4 +- petsc-custom/build-petsc.sh | 426 +++++++---- pixi.lock | 846 ++++++++++++++++++++- pixi.toml | 23 + 6 files changed, 1465 insertions(+), 137 deletions(-) create mode 100644 docs/developer/guides/hpc-cluster-setup.md diff --git a/docs/developer/guides/hpc-cluster-setup.md b/docs/developer/guides/hpc-cluster-setup.md new file mode 100644 index 000000000..898a1447a --- /dev/null +++ b/docs/developer/guides/hpc-cluster-setup.md @@ -0,0 +1,302 @@ +# HPC Cluster Setup + +This guide covers installing and running Underworld3 on HPC clusters. Install scripts are maintained in the [uw3-hpc-baremetal-install-run](https://github.com/jcgraciosa/uw3-hpc-baremetal-install-run) repository. + +--- + +## Architecture + +All supported clusters use the same architecture: + +``` +pixi hpc env → Python 3.12, sympy, scipy, pint, pydantic, ... (conda-forge, no MPI) +cluster MPI → OpenMPI (spack or module) (cluster MPI) +source build → mpi4py, PETSc+AMR+petsc4py, h5py (linked to cluster MPI) +``` + +**Why source builds?** Anything linked against MPI must use the same MPI as the cluster scheduler. conda-forge bundles its own MPI (MPICH), which is incompatible with Slurm/PBS. Building from source ensures the correct linkage. + +**Why pixi?** Pixi manages the Python environment consistently with local development — same `pixi.toml`, same package versions. The `hpc` environment is pure Python (no MPI packages from conda-forge). + +**PETSc build:** `petsc-custom/build-petsc.sh` auto-detects the cluster from hostname, or can be overridden with `UW_CLUSTER=kaiju|gadi`. Cluster-specific differences (HDF5 source, BLAS, cmake, compiler flags) are handled internally. + +--- + +## Kaiju + +### Hardware + +| Resource | Specification | +|----------|--------------| +| Head node | 1× Intel Xeon Silver 4210R, 40 CPUs @ 2.4 GHz | +| Compute nodes | 8× Intel Xeon Gold 6230R, 104 CPUs @ 2.1 GHz each | +| Shared storage | `/opt/cluster` via NFS | +| Scheduler | Slurm with Munge authentication | +| MPI | Spack `openmpi@4.1.6` | + +### Prerequisites + +Spack must have OpenMPI available: + +```bash +spack find openmpi +# openmpi@4.1.6 +``` + +Pixi must be installed in your user space: + +```bash +pixi --version # check +curl -fsSL https://pixi.sh/install.sh | bash # install if missing +``` + +### Installation + +Copy `kaiju_install_user.sh` (per-user) or `kaiju_install_shared.sh` (admin) from [uw3-hpc-baremetal-install-run](https://github.com/jcgraciosa/uw3-hpc-baremetal-install-run) to a convenient location, edit the variables at the top, then: + +```bash +source kaiju_install_user.sh install +``` + +| Step | Function | Time | +|------|----------|------| +| Install pixi | `setup_pixi` | ~1 min | +| Clone Underworld3 | `clone_uw3` | ~1 min | +| Install pixi hpc env | `install_pixi_env` | ~3 min | +| Build mpi4py | `install_mpi4py` | ~2 min | +| Build PETSc + AMR tools | `install_petsc` | ~1 hour | +| Build h5py | `install_h5py` | ~2 min | +| Install Underworld3 | `install_uw3` | ~2 min | +| Verify | `verify_install` | ~1 min | + +Individual steps can be run after sourcing: + +```bash +source kaiju_install_user.sh +install_petsc # run just one step +``` + +#### What PETSc builds on Kaiju + +- **AMR tools**: mmg, parmmg, pragmatic, eigen, bison +- **Solvers**: mumps, scalapack, slepc +- **Partitioners**: metis, parmetis, ptscotch +- **MPI**: Spack's OpenMPI (`--with-mpi-dir`) +- **HDF5**: downloaded (not in Spack) +- **BLAS/LAPACK**: fblaslapack (no guaranteed system BLAS on Rocky Linux 8) +- **cmake**: downloaded (not in Spack) +- **petsc4py**: built during configure (`--with-petsc4py=1`) + +### Activating the Environment + +Source the install script at the start of every session or job: + +```bash +source kaiju_install_user.sh +``` + +This loads `spack openmpi@4.1.6`, activates the pixi `hpc` environment via `pixi shell-hook`, and sets `PETSC_DIR`, `PETSC_ARCH`, and `PYTHONPATH`. + +> `pixi shell-hook` is used instead of `pixi shell` because it activates the environment in the current shell without spawning a new one — required for Slurm batch jobs. + +### Running with Slurm + +Use `kaiju_slurm_job.sh` from [uw3-hpc-baremetal-install-run](https://github.com/jcgraciosa/uw3-hpc-baremetal-install-run). Edit the variables at the top, then: + +```bash +sbatch kaiju_slurm_job.sh +``` + +`--mpi=pmix` is **required** on Kaiju (Spack has `pmix@5.0.3`): + +```bash +srun --mpi=pmix python3 my_model.py +``` + +Monitor progress: + +```bash +squeue -u $USER +tail -f uw3_.out +``` + +### Shared Installation (Admin) + +Deploys to `/opt/cluster/software/underworld3/` so all users access it via Environment Modules: + +```bash +source kaiju_install_shared.sh install +module load underworld3/development-12Mar26 +``` + +The shared script adds `fix_permissions()` and `install_modulefile()` on top of the per-user steps. The TCL modulefile hardcodes the Spack OpenMPI and pixi env paths — if Spack is rebuilt (hash changes), update `mpi_root` in `modulefiles/underworld3/development.tcl`. + +### Troubleshooting (Kaiju) + +#### `import underworld3` fails on compute nodes + +Source the install script inside the job script (not the login shell) so all paths propagate to compute nodes. The `kaiju_slurm_job.sh` template does this correctly. + +#### PETSc needs rebuilding after Spack module update + +PETSc links against Spack's OpenMPI at build time. If `openmpi@4.1.6` is reinstalled: + +```bash +source kaiju_install_user.sh +rm -rf ~/uw3-installation/underworld3/petsc-custom/petsc +install_petsc +install_h5py +``` + +#### h5py replaces source-built mpi4py + +`pip install h5py` without `--no-deps` silently replaces the source-built mpi4py with a wheel linked to a different MPI. The install script uses `--no-deps` to prevent this. If mpi4py was accidentally replaced: + +```bash +pip install --no-binary :all: --no-cache-dir --force-reinstall "mpi4py>=4,<5" +``` + +#### PARMMG configure failure + +pixi's conda linker requires transitive shared library dependencies to be explicitly linked. `libmmg.so` built with SCOTCH support causes PARMMG's link test to fail. This is fixed in `build-petsc.sh` by building MMG without SCOTCH (`-DUSE_SCOTCH=OFF`). + +--- + +## Gadi + +### Hardware + +| Resource | Specification | +|----------|--------------| +| System | NCI Gadi (CentOS, Lustre filesystem) | +| Compute | Multiple node types (normal, hugemem, gpuvolta) | +| Shared storage | `/g/data` (project quota), `/scratch` (temporary) | +| Scheduler | PBS Pro | +| MPI | Module `openmpi/4.1.7` | + +### Prerequisites + +The following Gadi modules must be available: + +```bash +module load openmpi/4.1.7 hdf5/1.12.2p gmsh/4.13.1 cmake/3.31.6 +``` + +Pixi must be installed: + +```bash +pixi --version # check +curl -fsSL https://pixi.sh/install.sh | bash # install if missing +``` + +> **Inode quota:** Gadi's `/g/data` has strict inode limits. PETSc (which creates many files during build) may need to be built on `/scratch` and symlinked from `/g/data`. The install script handles this if you set `PETSC_DIR` to a `/scratch` path. + +### Installation + +Copy `gadi_install_user.sh` (per-user) or `gadi_install_shared.sh` (admin) from [uw3-hpc-baremetal-install-run](https://github.com/jcgraciosa/uw3-hpc-baremetal-install-run) to a convenient location, edit the variables at the top, then: + +```bash +source gadi_install_shared.sh install +``` + +| Step | Function | Time | +|------|----------|------| +| Install pixi | `setup_pixi` | ~1 min | +| Clone Underworld3 | `clone_uw3` | ~1 min | +| Install pixi hpc env | `install_pixi_env` | ~3 min | +| Build mpi4py | `install_mpi4py` | ~2 min | +| Build PETSc + AMR tools | `install_petsc` | ~1 hour | +| Build h5py | `install_h5py` | ~2 min | +| Install Underworld3 | `install_uw3` | ~2 min | +| Verify | `verify_install` | ~1 min | + +#### What PETSc builds on Gadi + +- **AMR tools**: mmg, parmmg, pragmatic, eigen +- **Solvers**: mumps, scalapack, slepc, superlu, superlu_dist, hypre +- **Partitioners**: metis, parmetis, ptscotch +- **MPI**: Gadi's OpenMPI module (`--with-cc/cxx/fc`) +- **HDF5**: Gadi's `hdf5/1.12.2p` module (`--with-hdf5-dir`) +- **BLAS/LAPACK**: fblaslapack (auto-detection fails due to compiler env manipulation) +- **petsc4py**: built during configure (`--with-petsc4py=1`) + +### Activating the Environment + +Source the install script at the start of every session or job: + +```bash +source gadi_install_shared.sh +``` + +This loads Gadi modules, activates the pixi `hpc` environment via `pixi shell-hook`, and sets `PETSC_DIR`, `PETSC_ARCH`, and `PYTHONPATH`. Gadi's HDF5 lib dir is prepended to `LD_LIBRARY_PATH` to ensure the parallel HDF5 1.12.2p is loaded at runtime (not conda's serial HDF5 1.14). + +### Running with PBS + +Use `gadi_pbs_job.sh` from [uw3-hpc-baremetal-install-run](https://github.com/jcgraciosa/uw3-hpc-baremetal-install-run). Edit the variables at the top, then: + +```bash +qsub gadi_pbs_job.sh +``` + +Monitor progress: + +```bash +qstat -u $USER +tail -f .o* +``` + +### Shared Installation (Admin) + +Deploys to `/g/data/m18/software/uw3-pixi/` so all m18 project members can use it: + +```bash +source gadi_install_shared.sh install +``` + +The install script is then copied to the install directory so users can source it directly: + +```bash +source /g/data/m18/software/uw3-pixi/gadi_install_shared.sh +``` + +### Troubleshooting (Gadi) + +#### h5py undefined symbol: H5E_BADATOM_g + +The pixi `hpc` env ships a serial HDF5 1.14 (transitive conda-forge dependency). If h5py links against it instead of Gadi's parallel HDF5 1.12.2p, this symbol (removed in 1.14) is missing at runtime. The install script fixes this by temporarily hiding conda's HDF5 during the h5py build so meson can only find Gadi's. If you see this error, re-run: + +```bash +source gadi_install_shared.sh +install_h5py +``` + +#### Compiler interference during PETSc build + +The pixi `hpc` env ships a full conda toolchain (`x86_64-conda-linux-gnu-*`) that interferes with Gadi's OpenMPI wrappers. `build-petsc.sh` handles this via `setup_gadi_build_env()`, which unsets conda compiler variables and forces the MPI wrappers to use system compilers (`/usr/bin/gcc`). + +#### Fortran MPI library not found + +Gadi ships compiler-tagged Fortran MPI libraries (`libmpi_usempif08_GNU.so`) rather than the standard untagged names. `build-petsc.sh` creates symlinks in `petsc-custom/mpi-gadi-gnu-libs/` to bridge this. + +#### `import underworld3` fails in PBS job + +Ensure the install script is sourced inside the job script (not just in the login shell). The `gadi_pbs_job.sh` template does this correctly. + +--- + +## Rebuilding Underworld3 after source changes + +```bash +source kaiju_install_user.sh # or gadi_install_shared.sh +cd +git pull +pip install -e . +``` + +--- + +## Related + +- [Development Setup](development-setup.md) — local development with pixi +- [Branching Strategy](branching-strategy.md) — git workflow +- [Parallel Computing](../../advanced/parallel-computing.md) — writing parallel-safe UW3 code diff --git a/docs/developer/index.md b/docs/developer/index.md index 823ff7a21..f7d383ce2 100644 --- a/docs/developer/index.md +++ b/docs/developer/index.md @@ -114,6 +114,7 @@ guides/SPELLING_CONVENTION guides/version-management guides/branching-strategy guides/BINDER_CONTAINER_SETUP +guides/hpc-cluster-setup ``` ```{toctree} diff --git a/petsc-custom/README.md b/petsc-custom/README.md index f4da036ca..4d7fa0fb7 100644 --- a/petsc-custom/README.md +++ b/petsc-custom/README.md @@ -69,7 +69,7 @@ petsc-custom/ ├── build-petsc.sh # Build script ├── README.md # This file └── petsc/ # PETSc source and build (created by build) - ├── petsc-4-uw/ # Build output (PETSC_ARCH) + ├── petsc-4-uw-openmpi/ # Build output (PETSC_ARCH, example) └── src/ └── binding/ └── petsc4py/ @@ -86,5 +86,5 @@ petsc-custom/ The AMR environment automatically sets: ```bash PETSC_DIR=$PIXI_PROJECT_ROOT/petsc-custom/petsc -PETSC_ARCH=petsc-4-uw +PETSC_ARCH=petsc-4-uw-openmpi ``` diff --git a/petsc-custom/build-petsc.sh b/petsc-custom/build-petsc.sh index 135c9aac9..f55e3278e 100755 --- a/petsc-custom/build-petsc.sh +++ b/petsc-custom/build-petsc.sh @@ -2,26 +2,34 @@ # # Build PETSc with adaptive mesh refinement (AMR) tools # -# This script builds a custom PETSc installation with: -# - pragmatic: anisotropic mesh adaptation -# - mmg: surface/volume mesh adaptation -# - parmmg: parallel mesh adaptation -# - slepc: eigenvalue solvers -# - mumps: direct solver +# Supports three build targets, auto-detected from hostname or UW_CLUSTER env var: +# local — macOS/Linux developer machine (pixi env for MPI and HDF5) +# kaiju — Kaiju cluster (Rocky Linux 8, Spack OpenMPI, no system HDF5/cmake/BLAS) +# gadi — NCI Gadi (CentOS, module OpenMPI + HDF5, PBS Pro) # -# MPI is auto-detected from the active pixi environment: -# - MPICH → PETSC_ARCH = petsc-4-uw-mpich -# - OpenMPI → PETSC_ARCH = petsc-4-uw-openmpi +# Cluster-specific differences: # -# Both builds co-exist under the same PETSc source tree. -# Build time: ~1 hour on Apple Silicon +# Aspect local kaiju gadi +# PETSC_ARCH petsc-4-uw-{mpich, petsc-4-uw- petsc-4-uw- +# openmpi} openmpi openmpi +# MPI pixi env spack (PATH) module (PATH) +# HDF5 pixi env download module ($HDF5_DIR) +# BLAS/LAPACK auto download download (auto fails) +# cmake pixi env download module +# bison download download system +# petsc4py separate step with-petsc4py=1 with-petsc4py=1 +# extra flags — — superlu, hypre, ... +# +# Override auto-detection: export UW_CLUSTER=local|kaiju|gadi # # Usage: -# ./build-petsc.sh # Full build (clone, configure, build) +# ./build-petsc.sh # Full build (clone, patch, configure, build) # ./build-petsc.sh configure # Just reconfigure # ./build-petsc.sh build # Just build (after configure) -# ./build-petsc.sh petsc4py # Just build petsc4py -# ./build-petsc.sh clean # Remove build for detected MPI +# ./build-petsc.sh petsc4py # Build petsc4py separately (local only) +# ./build-petsc.sh patch # Apply UW3 patches +# ./build-petsc.sh test # Run PETSc tests +# ./build-petsc.sh clean # Remove build for current arch # ./build-petsc.sh clean-all # Remove entire PETSc directory # ./build-petsc.sh help # Show this help # @@ -30,64 +38,180 @@ set -e SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)" PETSC_DIR="${SCRIPT_DIR}/petsc" -# Detect active pixi environment (robust) -if [ -z "$PIXI_PROJECT_ROOT" ]; then - echo "Error: This script must be run from within a pixi environment" - echo "Use: pixi run -e ./build-petsc.sh" - exit 1 -fi +# ── Cluster detection ───────────────────────────────────────────────────────── +detect_cluster() { + if [ -n "${UW_CLUSTER}" ]; then + echo "${UW_CLUSTER}"; return + fi + local hn + hn="$(hostname -f 2>/dev/null || hostname)" + case "${hn}" in + *.gadi.nci.org.au|gadi-*) echo "gadi" ;; + kaiju*) echo "kaiju" ;; + *) echo "local" ;; + esac +} + +CLUSTER="$(detect_cluster)" -PIXI_ENV="$(python3 - <<'EOF' +# ── Cluster-specific configuration ─────────────────────────────────────────── +# Sets PETSC_ARCH, MPI_IMPL, and cluster-specific variables (PIXI_ENV, MPI_DIR, +# HDF5_DIR). Also validates that the required environment is active. + +case "${CLUSTER}" in + local) + if [ -z "$PIXI_PROJECT_ROOT" ]; then + echo "Error: This script must be run from within a pixi environment" + echo "Use: pixi run -e ./build-petsc.sh" + exit 1 + fi + + PIXI_ENV="$(python3 - <<'EOF' import sys, pathlib print(pathlib.Path(sys.executable).resolve().parents[1]) EOF )" -# ── MPI auto-detection ────────────────────────────────────────────── -# Detect which MPI implementation is available in the pixi environment. -# Sets MPI_IMPL ("mpich" or "openmpi") and PETSC_ARCH accordingly. + _detect_local_mpi() { + local mpi_version + mpi_version=$(python3 -c "from mpi4py import MPI; print(MPI.Get_library_version())" 2>/dev/null || echo "") + if echo "$mpi_version" | grep -qi "open mpi"; then + echo "openmpi" + elif echo "$mpi_version" | grep -qi "mpich"; then + echo "mpich" + else + local mpicc_out + mpicc_out=$("$PIXI_ENV/bin/mpicc" --version 2>&1 || echo "") + if echo "$mpicc_out" | grep -qi "open mpi"; then + echo "openmpi" + else + echo "mpich" + fi + fi + } -detect_mpi() { - local mpi_version - mpi_version=$(python3 -c "from mpi4py import MPI; print(MPI.Get_library_version())" 2>/dev/null || echo "") + MPI_IMPL=$(_detect_local_mpi) + PETSC_ARCH="petsc-4-uw-${MPI_IMPL}" + ;; - if echo "$mpi_version" | grep -qi "open mpi"; then - echo "openmpi" - elif echo "$mpi_version" | grep -qi "mpich"; then - echo "mpich" - else - # Fallback: check for mpicc --version - local mpicc_out - mpicc_out=$("$PIXI_ENV/bin/mpicc" --version 2>&1 || echo "") - if echo "$mpicc_out" | grep -qi "open mpi"; then - echo "openmpi" - else - echo "mpich" # default fallback + kaiju) + if ! command -v mpicc &>/dev/null; then + echo "Error: mpicc not found. Load spack OpenMPI first:" + echo " spack load openmpi@4.1.6" + exit 1 fi - fi -} + if ! echo "${PATH}" | tr ':' '\n' | grep -q "\.pixi/envs/hpc/bin"; then + echo "Error: must be run inside the pixi hpc environment" + echo " source kaiju_install_user.sh (activates env via pixi shell-hook)" + exit 1 + fi + MPI_DIR="$(dirname "$(dirname "$(which mpicc)")")" + MPI_IMPL="openmpi" + PETSC_ARCH="petsc-4-uw-openmpi" + ;; -MPI_IMPL=$(detect_mpi) -PETSC_ARCH="petsc-4-uw-${MPI_IMPL}" + gadi) + if ! command -v mpicc &>/dev/null; then + echo "Error: mpicc not found. Load Gadi OpenMPI module first:" + echo " module load openmpi/4.1.7" + exit 1 + fi + if [ -z "${HDF5_DIR}" ]; then + echo "Error: HDF5_DIR is not set. Load Gadi HDF5 module first:" + echo " module load hdf5/1.12.2p" + exit 1 + fi + if ! echo "${PATH}" | tr ':' '\n' | grep -q "\.pixi/envs/hpc/bin"; then + echo "Error: must be run inside the pixi hpc environment" + echo " source gadi_install_shared.sh (activates env via pixi shell-hook)" + exit 1 + fi + MPI_DIR="$(dirname "$(dirname "$(which mpicc)")")" + MPI_IMPL="openmpi" + PETSC_ARCH="petsc-4-uw-openmpi" + ;; + + *) + echo "Unknown cluster: ${CLUSTER}" + echo "Set UW_CLUSTER=local|kaiju|gadi to override auto-detection" + exit 1 + ;; +esac echo "==========================================" echo "PETSc AMR Build Script" echo "==========================================" -echo "PETSC_DIR: $PETSC_DIR" -echo "PETSC_ARCH: $PETSC_ARCH" -echo "MPI: $MPI_IMPL" -echo "PIXI_ENV: $PIXI_ENV" +echo "CLUSTER: ${CLUSTER}" +echo "PETSC_DIR: ${PETSC_DIR}" +echo "PETSC_ARCH: ${PETSC_ARCH}" +echo "MPI: ${MPI_IMPL}" +if [ "${CLUSTER}" = "local" ]; then + echo "PIXI_ENV: ${PIXI_ENV}" +else + echo "MPI_DIR: ${MPI_DIR}" +fi +[ "${CLUSTER}" = "gadi" ] && echo "HDF5_DIR: ${HDF5_DIR}" echo "==========================================" +# ── Gadi-specific: build environment setup ─────────────────────────────────── +# Handles compiler-tagged Fortran MPI libs and conda toolchain interference. +# Must be called before any compile/link step on Gadi. +setup_gadi_build_env() { + if [ -z "${MPI_DIR}" ]; then + echo "Error: MPI_DIR is not set. Source gadi_install_shared.sh first." + exit 1 + fi + + # Create symlinks for Gadi's compiler-tagged Fortran MPI libs. + # mpifort --showme refers to libmpi_usempif08 etc. (no compiler tag), + # but Gadi only ships _GNU, _Intel, _nvidia variants. + local _mpi_gnu_dir="${SCRIPT_DIR}/mpi-gadi-gnu-libs" + mkdir -p "${_mpi_gnu_dir}" + for _lib in usempif08 usempi_ignore_tkr mpifh; do + [ ! -f "${_mpi_gnu_dir}/libmpi_${_lib}.so" ] && \ + ln -sf "${MPI_DIR}/lib/libmpi_${_lib}_GNU.so" "${_mpi_gnu_dir}/libmpi_${_lib}.so" + done + + # LD_LIBRARY_PATH = runtime search path (dynamic loader) + # LIBRARY_PATH = link-time search path (ld resolves -lmpi_usempif08 etc.) + export LD_LIBRARY_PATH="${_mpi_gnu_dir}:${MPI_DIR}/lib:/apps/ucc/1.3.0/lib:/usr/lib64:${LD_LIBRARY_PATH}" + export LIBRARY_PATH="${_mpi_gnu_dir}:${LIBRARY_PATH}" + + # Unset conda/pixi compiler vars that interfere with OpenMPI wrappers. + # The pixi hpc env ships a full conda toolchain (x86_64-conda-linux-gnu-*) + # that conflicts with system compilers required by Gadi's OpenMPI. + unset CC CXX FC F77 F90 CPP AR RANLIB + unset CFLAGS CXXFLAGS FFLAGS CPPFLAGS LDFLAGS + + # Force MPI wrappers to use system compilers, not conda's gcc + export OMPI_CC=/usr/bin/gcc + export OMPI_CXX=/usr/bin/g++ + export OMPI_FC=/usr/bin/gfortran + # Gadi puts Fortran MPI headers in a compiler-tagged subdirectory (include/GNU/) + export OMPI_FCFLAGS="-I${MPI_DIR}/include/GNU" + + # Put system bin dirs first so the system linker (/usr/bin/ld) wins over + # conda's ld — conda's ld cannot find Gadi-specific libs (hcoll, ucc, libnl). + export PATH="/usr/bin:/usr/local/bin:${MPI_DIR}/bin:${PATH}" +} + clone_petsc() { - if [ -d "$PETSC_DIR" ]; then + # For Gadi: resolve symlink before cloning. git clone replaces a + # symlink-to-empty-dir with a real directory, defeating the + # gdata→scratch symlink approach used to avoid inode quota limits. + local _clone_target="${PETSC_DIR}" + if [ "${CLUSTER}" = "gadi" ] && [ -L "${PETSC_DIR}" ]; then + _clone_target="$(readlink -f "${PETSC_DIR}")" + fi + + if [ -f "${_clone_target}/configure" ]; then echo "PETSc directory already exists. Skipping clone." - echo "To force fresh clone, run: ./build-petsc.sh clean-all" + echo "To force fresh clone, run: $0 clean-all" return 0 fi echo "Cloning PETSc release branch..." - git clone -b release https://gitlab.com/petsc/petsc.git "$PETSC_DIR" + git clone -b release https://gitlab.com/petsc/petsc.git "${_clone_target}" echo "Clone complete." } @@ -112,49 +236,100 @@ apply_patches() { } configure_petsc() { - echo "Configuring PETSc with AMR tools ($MPI_IMPL)..." + echo "Configuring PETSc with AMR tools (${CLUSTER})..." cd "$PETSC_DIR" - # Configure with adaptive mesh refinement tools - # Downloads: bison, eigen, metis, mmg, mumps, parmetis, parmmg, - # pragmatic, ptscotch, scalapack, slepc - # Uses system: MPI (from pixi), HDF5 (from pixi) - python3 ./configure \ - --with-petsc-arch="$PETSC_ARCH" \ - --download-bison \ - --download-eigen \ - --download-metis \ - --download-mmg \ - --download-mumps \ - --download-parmetis \ - --download-parmmg \ - --download-pragmatic \ - --download-ptscotch="${SCRIPT_DIR}/patches/scotch-7.0.10-c23-fix.tar.gz" \ - --download-scalapack \ - --download-slepc \ - --with-debugging=0 \ - --with-hdf5=1 \ - --with-pragmatic=1 \ - --with-x=0 \ - --with-mpi-dir="$PIXI_ENV" \ - --with-hdf5-dir="$PIXI_ENV" \ - --download-hdf5=0 \ - --download-mpich=0 \ - --download-openmpi=0 \ - --download-mpi4py=0 \ - --with-petsc4py=0 + # Capture pixi's python3 BEFORE setup_gadi_build_env reorders PATH. + local _python="python3" + if [ "${CLUSTER}" = "gadi" ]; then + _python="$(which python3)" + setup_gadi_build_env + fi + + # Flags shared across all clusters. + # Downloads and builds: + # AMR: mmg, parmmg, pragmatic, eigen + # Solvers: mumps, scalapack, slepc + # Partitioners: metis, parmetis, ptscotch (patched for C23) + # Uses pixi env (local): MPI (amr/amr-mpich/amr-openmpi), HDF5 + # Downloads (kaiju): HDF5, BLAS/LAPACK, cmake, bison + # Uses module (gadi): MPI (openmpi/4.1.7), HDF5 ($HDF5_DIR) + local -a _common=( + --with-petsc-arch="${PETSC_ARCH}" + --with-debugging=0 + --with-pragmatic=1 + --with-x=0 + --download-eigen=1 + --download-metis=1 + --download-mmg=1 + "--download-mmg-cmake-arguments=-DMMG_INSTALL_PRIVATE_HEADERS=ON -DUSE_SCOTCH=OFF" + --download-mumps=1 + --download-parmetis=1 + --download-parmmg=1 + --download-pragmatic=1 + "--download-ptscotch=${SCRIPT_DIR}/patches/scotch-7.0.10-c23-fix.tar.gz" + --download-scalapack=1 + --download-slepc=1 + ) + + case "${CLUSTER}" in + local) + "${_python}" ./configure "${_common[@]}" \ + --with-mpi-dir="${PIXI_ENV}" \ + --with-hdf5=1 \ + --with-hdf5-dir="${PIXI_ENV}" \ + --download-hdf5=0 \ + --download-mpich=0 \ + --download-openmpi=0 \ + --download-mpi4py=0 \ + --download-bison \ + --with-petsc4py=0 + ;; + kaiju) + "${_python}" ./configure "${_common[@]}" \ + --with-mpi-dir="${MPI_DIR}" \ + --download-hdf5=1 \ + --download-fblaslapack=1 \ + --download-cmake=1 \ + --download-bison=1 \ + --with-petsc4py=1 \ + --with-make-np=40 + ;; + gadi) + "${_python}" ./configure "${_common[@]}" \ + --with-cc="${MPI_DIR}/bin/mpicc" \ + --with-cxx="${MPI_DIR}/bin/mpicxx" \ + --with-fc="${MPI_DIR}/bin/mpifort" \ + --with-hdf5=1 \ + --with-hdf5-dir="${HDF5_DIR}" \ + --download-fblaslapack=1 \ + --with-petsc4py=1 \ + --with-make-np=40 \ + --with-shared-libraries=1 \ + --with-cxx-dialect=C++11 \ + "--COPTFLAGS=-g -O3" "--CXXOPTFLAGS=-g -O3" "--FOPTFLAGS=-g -O3" \ + --useThreads=0 \ + --download-zlib=1 \ + --download-superlu=1 \ + --download-superlu_dist=1 \ + --download-hypre=1 \ + --download-ctetgen=1 \ + --download-triangle=1 + ;; + esac echo "Configure complete." } build_petsc() { - echo "Building PETSc ($MPI_IMPL)..." + echo "Building PETSc (${CLUSTER})..." cd "$PETSC_DIR" - # Set environment for build export PETSC_DIR export PETSC_ARCH + [ "${CLUSTER}" = "gadi" ] && setup_gadi_build_env + make all echo "PETSc build complete." } @@ -166,12 +341,19 @@ test_petsc() { export PETSC_DIR export PETSC_ARCH + [ "${CLUSTER}" = "gadi" ] && setup_gadi_build_env + make check echo "PETSc tests complete." } build_petsc4py() { - echo "Building petsc4py ($MPI_IMPL)..." + if [ "${CLUSTER}" != "local" ]; then + echo "Note: petsc4py is built during configure on HPC clusters (--with-petsc4py=1). Skipping." + return 0 + fi + + echo "Building petsc4py..." cd "$PETSC_DIR/src/binding/petsc4py" export PETSC_DIR @@ -183,9 +365,8 @@ build_petsc4py() { } clean_petsc() { - # Clean just the arch-specific build local arch_dir="$PETSC_DIR/$PETSC_ARCH" - echo "Removing PETSc build for $MPI_IMPL ($arch_dir)..." + echo "Removing PETSc build for $PETSC_ARCH ($arch_dir)..." if [ -d "$arch_dir" ]; then rm -rf "$arch_dir" echo "Cleaned $PETSC_ARCH." @@ -207,69 +388,58 @@ clean_all() { show_help() { echo "Usage: $0 [command]" echo "" - echo "MPI auto-detected from pixi environment: $MPI_IMPL" - echo "PETSC_ARCH: $PETSC_ARCH" + echo "Cluster: ${CLUSTER} (override: export UW_CLUSTER=local|kaiju|gadi)" + echo "PETSC_ARCH: ${PETSC_ARCH}" echo "" echo "Commands:" - echo " (none) Full build: clone, configure, build, petsc4py" + echo " (none) Full build: clone, patch, configure, build" + [ "${CLUSTER}" = "local" ] && echo " (local: also runs petsc4py separately)" echo " clone Clone PETSc repository" + echo " patch Apply UW3 patches to PETSc source" echo " configure Configure PETSc with AMR tools" echo " build Build PETSc" echo " test Run PETSc tests" - echo " petsc4py Build and install petsc4py" - echo " patch Apply UW3 patches to PETSc source" - echo " clean Remove build for current MPI ($PETSC_ARCH)" - echo " clean-all Remove entire PETSc directory (all MPI builds)" + echo " petsc4py Build and install petsc4py (local only)" + echo " clean Remove build for current arch (${PETSC_ARCH})" + echo " clean-all Remove entire PETSc directory (all builds)" echo " help Show this help" - echo "" - echo "MPICH and OpenMPI builds co-exist. To build both:" - echo " pixi run -e amr ./petsc-custom/build-petsc.sh" - echo " pixi run -e amr-openmpi ./petsc-custom/build-petsc.sh" + if [ "${CLUSTER}" = "local" ]; then + echo "" + echo "MPICH and OpenMPI builds co-exist. To build both:" + echo " pixi run -e amr ./petsc-custom/build-petsc.sh" + echo " pixi run -e amr-openmpi ./petsc-custom/build-petsc.sh" + fi } -# Main entry point +# ── Main entry point ────────────────────────────────────────────────────────── case "${1:-all}" in all) clone_petsc apply_patches configure_petsc build_petsc - build_petsc4py + if [ "${CLUSTER}" = "local" ]; then + build_petsc4py + fi echo "" echo "==========================================" - echo "PETSc AMR build complete! ($MPI_IMPL)" - echo "Set these environment variables:" - echo " export PETSC_DIR=$PETSC_DIR" - echo " export PETSC_ARCH=$PETSC_ARCH" + echo "PETSc AMR build complete! (${CLUSTER}, ${MPI_IMPL})" + echo " PETSC_DIR=${PETSC_DIR}" + echo " PETSC_ARCH=${PETSC_ARCH}" + if [ "${CLUSTER}" != "local" ]; then + echo " export PYTHONPATH=\$PETSC_DIR/\$PETSC_ARCH/lib:\$PYTHONPATH" + fi echo "==========================================" ;; - clone) - clone_petsc - ;; - configure) - configure_petsc - ;; - build) - build_petsc - ;; - patch) - apply_patches - ;; - test) - test_petsc - ;; - petsc4py) - build_petsc4py - ;; - clean) - clean_petsc - ;; - clean-all) - clean_all - ;; - help|--help|-h) - show_help - ;; + clone) clone_petsc ;; + patch) apply_patches ;; + configure) configure_petsc ;; + build) build_petsc ;; + test) test_petsc ;; + petsc4py) build_petsc4py ;; + clean) clean_petsc ;; + clean-all) clean_all ;; + help|--help|-h) show_help ;; *) echo "Unknown command: $1" show_help diff --git a/pixi.lock b/pixi.lock index 00800d325..ffd0bc629 100644 --- a/pixi.lock +++ b/pixi.lock @@ -7606,6 +7606,342 @@ environments: - pypi: https://files.pythonhosted.org/packages/6e/67/9d4ac4b0d683aaa4170da59a1980740b281fd38fc253e1830fde4dac3d4f/pygmsh-7.1.17-py3-none-any.whl - 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__glibc >=2.17,<3.0.a0 + - libexpat >=2.7.4,<3.0a0 + - libffi >=3.5.2,<3.6.0a0 + - libgcc >=14 + - libstdcxx >=14 + license: MIT + license_family: MIT + purls: [] + size: 334139 + timestamp: 1773959575393 - conda: https://conda.anaconda.org/conda-forge/noarch/wayland-protocols-1.47-hd8ed1ab_0.conda sha256: 9ab2c12053ea8984228dd573114ffc6d63df42c501d59fda3bf3aeb1eaa1d23e md5: 7da1571f560d4ba3343f7f4c48a79c76 diff --git a/pixi.toml b/pixi.toml index 26c7b8d70..fee1757f6 100644 --- a/pixi.toml +++ b/pixi.toml @@ -229,6 +229,24 @@ PETSC_ARCH = "petsc-4-uw-openmpi" petsc-local-build = { cmd = "./build-petsc.sh", cwd = "petsc-custom" } petsc-local-clean = { cmd = "./build-petsc.sh clean", cwd = "petsc-custom" } +# ============================================ +# HPC CLUSTER FEATURE +# ============================================ +# For HPC clusters (Kaiju, Gadi, etc.) running linux-64. +# Pure Python only — base dependencies cover all pure-Python needs. +# mpi4py, h5py, petsc, petsc4py are built from source against the +# cluster's MPI using petsc-custom/build-petsc.sh (UW_CLUSTER auto-detected). +# See: docs/developer/guides/kaiju-cluster-setup.md + +[feature.hpc] +platforms = ["linux-64"] + +[feature.hpc.dependencies] +# patchelf is needed on Gadi to fix h5py RPATH order after source build: +# meson embeds the conda env lib dir before Gadi's HDF5 in RPATH, +# so we use patchelf post-install to move HDF5_DIR to the front. +patchelf = "*" + # ============================================ # RUNTIME FEATURE (for tutorials/examples) # ============================================ @@ -312,3 +330,8 @@ openmpi-dev = { features = ["conda-petsc-openmpi", "runtime", "dev"], solve-gr amr-openmpi = { features = ["amr-openmpi"], solve-group = "amr-openmpi" } amr-openmpi-dev = { features = ["amr-openmpi", "runtime", "dev"], solve-group = "amr-openmpi" } + +# --- HPC Cluster Track (linux-64 only) --- +# Pure Python from pixi; MPI/PETSc/h5py built from source against cluster MPI. +# UW_CLUSTER (or hostname) selects kaiju/gadi config in build-petsc.sh. +hpc = { features = ["hpc"], solve-group = "hpc" } From a98c4ca2effedc33f5b929abdea104a3617c2a0c Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 26 Mar 2026 20:05:04 +1100 Subject: [PATCH 034/537] Fix dt_elastic default: auto-set from solve timestep MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit When dt_elastic defaults to sympy.oo (user didn't set it), the VE effective viscosity formula produces NaN (oo * c0 is undefined for UWexpression c0). The solver now auto-sets dt_elastic to the solve timestep on first call, and raises ValueError if no timestep is provided. Also requires timestep argument when stress history is active — prevents silent use of oo as timestep. Underworld development team with AI support from Claude Code --- src/underworld3/systems/solvers.py | 10 +- tests/vep_strain_weakening.py | 170 +++++++++++++++++++++++++++++ tests/vep_timedep_yield.py | 135 +++++++++++++++++++++++ vep_strain_weakening.png | Bin 0 -> 71718 bytes vep_timedep_yield.png | Bin 0 -> 55894 bytes 5 files changed, 314 insertions(+), 1 deletion(-) create mode 100644 tests/vep_strain_weakening.py create mode 100644 tests/vep_timedep_yield.py create mode 100644 vep_strain_weakening.png create mode 100644 vep_timedep_yield.png diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index c63870700..21b4166a9 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -748,7 +748,15 @@ def solve( if has_stress_history: if timestep is None: - timestep = self.constitutive_model.Parameters.dt_elastic.sym + raise ValueError( + "timestep is required for viscoelastic solve. " + "Call stokes.solve(timestep=dt)" + ) + + # Ensure dt_elastic is set — it defaults to oo which NaNs the solver. + # The solve timestep is the only sane default. + if self.constitutive_model.Parameters.dt_elastic.sym is sympy.oo: + self.constitutive_model.Parameters.dt_elastic = timestep if order is None or order > self._order: order = self._order diff --git a/tests/vep_strain_weakening.py b/tests/vep_strain_weakening.py new file mode 100644 index 000000000..1615d1a92 --- /dev/null +++ b/tests/vep_strain_weakening.py @@ -0,0 +1,170 @@ +"""VEP shear box with strain-weakening yield stress. + +Plastic strain rate = edot_total * (1 - eta_vep/eta_ve) +Both viscosities come from the constitutive model. +Accumulated via projection after each solve. + +Run: pixi run -e amr-dev python tests/vep_strain_weakening.py +""" + +import time +import numpy as np +import sympy +import underworld3 as uw + +# --- Parameters --- + +ETA = 1.0 +MU = 10.0 # stiff elastic: t_relax = 0.1, fast loading +TAU_Y0 = 0.3 +TAU_RESIDUAL = 0.1 +EPS_CRIT = 0.3 +DT = 0.02 +NSTEPS = 80 +V_TOP = 0.5 + +t0 = time.time() + +mesh = uw.meshing.StructuredQuadBox( + elementRes=(4, 4), + minCoords=(0.0, 0.0), + maxCoords=(1.0, 1.0), + qdegree=2, +) + +v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, + vtype=uw.VarType.SCALAR) +eps_p = uw.discretisation.MeshVariable("eps_p", mesh, 1, degree=2, continuous=True) + +# --- Solver --- + +stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +cm = stokes.constitutive_model +cm.Parameters.shear_viscosity_0 = ETA +cm.Parameters.shear_modulus = MU +cm.Parameters.shear_viscosity_min = ETA * 1.0e-3 +cm.Parameters.strainrate_inv_II_min = 1.0e-10 +stokes.saddle_preconditioner = 1.0 +stokes.tolerance = 1.0e-4 + +# Strain-weakening yield stress +weakening = sympy.Min(eps_p.sym[0] / EPS_CRIT, 1.0) +tau_y_expr = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * weakening +cm.Parameters.yield_stress = tau_y_expr + +stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") +stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") +stokes.add_essential_bc((sympy.oo, 0.0), "Left") +stokes.add_essential_bc((sympy.oo, 0.0), "Right") +stokes.bodyforce = sympy.Matrix([0.0, 0.0]) +stokes.petsc_options["ksp_type"] = "fgmres" + +# --- Plastic strain rate expression --- +# plastic_fraction = 1 - eta_vep / eta_ve +# Both are symbolic, evaluated at the current velocity field + +eta_ve_sym = cm.Parameters.ve_effective_viscosity.sym +eta_vep_sym = cm.viscosity # this is the Min(eta_ve, tau_y/(2*edot_II)) + +# The strain rate invariant +edot_II = cm.E_eff_inv_II.sym + +# Plastic strain rate = edot_II * (1 - eta_vep/eta_ve) +# Clamp to >= 0 to handle numerical noise +plastic_edot = edot_II * sympy.Max(0, 1 - eta_vep_sym / eta_ve_sym) + +# Set up a projection solver for the plastic strain rate +plastic_edot_var = uw.discretisation.MeshVariable("edot_p", mesh, 1, degree=2, continuous=True) +plastic_edot_proj = uw.systems.Projection(mesh, plastic_edot_var) +plastic_edot_proj.uw_function = plastic_edot +plastic_edot_proj.smoothing = 0.0 +plastic_edot_proj.petsc_options.delValue("ksp_monitor") + +print(f"Setup: {time.time()-t0:.1f}s") +print(f"eta={ETA}, mu={MU}, t_relax={ETA/MU:.2f}") +print(f"tau_y0={TAU_Y0}, tau_residual={TAU_RESIDUAL}, eps_crit={EPS_CRIT}") +print() + +# --- Time stepping --- + +times = [] +max_stresses = [] +tau_y_values = [] +eps_p_values = [] +edot_p_values = [] + +print(f"{'step':>4} {'t':>5} {'sigma_xy':>10} {'tau_y':>8} {'eps_p':>8} {'edot_p':>8}") +print("-" * 60) + +for step in range(NSTEPS): + t1 = time.time() + stokes.solve(timestep=DT, zero_init_guess=False) + solve_time = time.time() - t1 + + t = (step + 1) * DT + times.append(t) + + # Read stress + sd = stokes.tau.data + sigma_xy = sd[:, 2].max() + max_stresses.append(sigma_xy) + + # Project plastic strain rate + plastic_edot_proj.solve() + edot_p_data = plastic_edot_var.data[:, 0] + edot_p_max = float(edot_p_data.max()) + edot_p_values.append(edot_p_max) + + # Accumulate plastic strain + eps_p.data[:, 0] += np.maximum(edot_p_data, 0.0) * DT + + ep_max = float(eps_p.data[:, 0].max()) + current_tau_y = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * min(ep_max / EPS_CRIT, 1.0) + tau_y_values.append(current_tau_y) + eps_p_values.append(ep_max) + + if (step + 1) % 5 == 0 or step < 10: + print(f"{step+1:4d} {t:5.2f} {sigma_xy:10.4f} {current_tau_y:8.4f} {ep_max:8.4f} {edot_p_max:8.4f} ({solve_time:.1f}s)") + +print() +print(f"Total: {time.time()-t0:.0f}s") + +# --- Plot --- + +import matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt + +fig, axes = plt.subplots(3, 1, figsize=(8, 10), sharex=True) + +t_anal = np.linspace(0.001, max(times), 200) +t_r = ETA / MU +maxwell = 2 * MU * V_TOP * t_r * (1 - np.exp(-t_anal / t_r)) + +axes[0].plot(t_anal, maxwell, 'k--', linewidth=1, alpha=0.4, label="Maxwell (no yield)") +axes[0].plot(times, max_stresses, 'r-', linewidth=2, label=r"$\sigma_{xy}$") +axes[0].plot(times, tau_y_values, 'b--', linewidth=1.5, label=r"$\tau_y(\varepsilon_p)$") +axes[0].axhline(TAU_Y0, color='gray', linestyle=':', alpha=0.5) +axes[0].axhline(TAU_RESIDUAL, color='gray', linestyle='-.', alpha=0.5) +axes[0].set_ylabel("Stress") +axes[0].legend(fontsize=9) +axes[0].grid(True, alpha=0.3) +axes[0].set_title(f"VEP strain weakening: $\\eta$={ETA}, $\\mu$={MU}") + +axes[1].plot(times, edot_p_values, 'm-', linewidth=2) +axes[1].set_ylabel(r"Plastic strain rate $\dot{\varepsilon}_p$") +axes[1].grid(True, alpha=0.3) + +axes[2].plot(times, eps_p_values, 'g-', linewidth=2) +axes[2].axhline(EPS_CRIT, color='gray', linestyle=':', alpha=0.5, label=f"$\\varepsilon_{{crit}}$={EPS_CRIT}") +axes[2].set_xlabel("Time") +axes[2].set_ylabel(r"Accumulated $\varepsilon_p$") +axes[2].legend(fontsize=9) +axes[2].grid(True, alpha=0.3) + +fig.tight_layout() +out_path = "/Users/lmoresi/+Underworld/underworld3-pixi/.claude/worktrees/solver-unification/vep_strain_weakening.png" +fig.savefig(out_path, dpi=150) +print(f"Saved {out_path}") diff --git a/tests/vep_timedep_yield.py b/tests/vep_timedep_yield.py new file mode 100644 index 000000000..4157b98f2 --- /dev/null +++ b/tests/vep_timedep_yield.py @@ -0,0 +1,135 @@ +"""VEP with time-dependent yield stress (no feedback). + +Prescribed tau_y(t) that decreases linearly over time. +VE stress builds, hits tau_y, then tau_y drops and stress follows. + +No strain accumulation, no projection of viscosity ratios — +just the solver responding to a changing yield stress parameter. + +Run: pixi run -e amr-dev python tests/vep_timedep_yield.py +""" + +import time +import numpy as np +import sympy +import underworld3 as uw + +ETA = 1.0 +MU = 1.0 +V_TOP = 0.5 +DT = 0.1 +NSTEPS = 25 + +# tau_y schedule: starts above Maxwell steady state, drops below it +TAU_Y_START = 1.5 # well above Maxwell steady state (2*eta*edot = 1.0) +TAU_Y_END = 0.2 +TAU_Y_DROP_START = 0.8 # start dropping at t=0.8 +TAU_Y_DROP_END = 1.8 # reach minimum at t=1.8 + +t0 = time.time() + +mesh = uw.meshing.StructuredQuadBox( + elementRes=(4, 4), + minCoords=(0.0, 0.0), + maxCoords=(1.0, 1.0), + qdegree=2, +) + +v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, + vtype=uw.VarType.SCALAR) + +stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +cm = stokes.constitutive_model +cm.Parameters.shear_viscosity_0 = ETA +cm.Parameters.shear_modulus = MU +cm.Parameters.shear_viscosity_min = ETA * 1.0e-3 +cm.Parameters.strainrate_inv_II_min = 1.0e-10 +stokes.saddle_preconditioner = 1.0 +stokes.tolerance = 1.0e-4 + +# Start with high yield stress +cm.Parameters.yield_stress = TAU_Y_START + +stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") +stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") +stokes.add_essential_bc((sympy.oo, 0.0), "Left") +stokes.add_essential_bc((sympy.oo, 0.0), "Right") +stokes.bodyforce = sympy.Matrix([0.0, 0.0]) +stokes.petsc_options["ksp_type"] = "fgmres" + +print(f"Setup: {time.time()-t0:.1f}s") +print(f"eta={ETA}, mu={MU}, t_relax={ETA/MU}") +print(f"tau_y: {TAU_Y_START} -> {TAU_Y_END} (t={TAU_Y_DROP_START}..{TAU_Y_DROP_END})") +print(f"Maxwell steady state: 2*eta*edot = {2*ETA*V_TOP}") +print() + +times = [] +max_stresses = [] +tau_y_values = [] + +print(f"{'step':>4} {'t':>5} {'sigma_xy':>10} {'tau_y':>8} {'phase':>10}") +print("-" * 50) + +for step in range(NSTEPS): + t = (step + 1) * DT + + # Update tau_y for this step + if t < TAU_Y_DROP_START: + current_tau_y = TAU_Y_START + elif t > TAU_Y_DROP_END: + current_tau_y = TAU_Y_END + else: + frac = (t - TAU_Y_DROP_START) / (TAU_Y_DROP_END - TAU_Y_DROP_START) + current_tau_y = TAU_Y_START + (TAU_Y_END - TAU_Y_START) * frac + + cm.Parameters.yield_stress = current_tau_y + + t1 = time.time() + stokes.solve(timestep=DT, zero_init_guess=False) + solve_time = time.time() - t1 + + times.append(t) + tau_y_values.append(current_tau_y) + + sd = stokes.tau.data + sigma_xy = sd[:, 2].max() + max_stresses.append(sigma_xy) + + # Determine phase + if sigma_xy > 0.95 * current_tau_y: + phase = "yield" + else: + phase = "elastic" + + print(f"{step+1:4d} {t:5.2f} {sigma_xy:10.4f} {current_tau_y:8.3f} {phase:>10} ({solve_time:.1f}s)") + +print() +print(f"Total: {time.time()-t0:.0f}s") + +# --- Plot --- + +import matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt + +fig, ax = plt.subplots(figsize=(8, 5)) + +t_anal = np.linspace(0.001, max(times), 200) +t_r = ETA / MU +maxwell = 2 * MU * V_TOP * t_r * (1 - np.exp(-t_anal / t_r)) + +ax.plot(t_anal, maxwell, 'k--', linewidth=1, alpha=0.4, label="Maxwell (no yield)") +ax.plot(times, max_stresses, 'r-o', linewidth=2, markersize=3, label=r"$\sigma_{xy}$") +ax.plot(times, tau_y_values, 'b--', linewidth=1.5, label=r"$\tau_y(t)$") +ax.set_xlabel("Time") +ax.set_ylabel("Stress") +ax.set_title(f"VEP with prescribed weakening: $\\eta$={ETA}, $\\mu$={MU}") +ax.legend(fontsize=10) +ax.grid(True, alpha=0.3) + +fig.tight_layout() +out_path = "/Users/lmoresi/+Underworld/underworld3-pixi/.claude/worktrees/solver-unification/vep_timedep_yield.png" +fig.savefig(out_path, dpi=150) +print(f"Saved {out_path}") diff --git a/vep_strain_weakening.png b/vep_strain_weakening.png new file mode 100644 index 0000000000000000000000000000000000000000..119738883abd3a87a90c5ac1542a011f69e93c24 GIT binary patch literal 71718 zcmdqJXHZmY(=I%qAc80cKrny_Br8D$B#EdXNst@`8FEe%hG+x@C1()HVaPeFNX{@L z*+3eGphOwc>4keg^}JQzSEtU8^XE*}u1z^>*1ALA-F;ns^?IeOc$b!%nHq&c(aPSt zt%5@B&qtvsMyM#^U-%7Owc&pvPBNNKs4dR^~>mE+!6+=C(Eh zyjQRA-r#06b8@nC6yf8u{?8S>whpFz4LZ)9aF>I2_p}^QD8^&Re`KbKy(%a&6iW8C 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=?UTF-8?q?Remove=20dt=5Felastic=20as=20user=20par?= =?UTF-8?q?ameter=20=E2=80=94=20solver=20manages=20it?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit dt_elastic was a constitutive model parameter that had to equal the solve timestep, creating a hazard when they diverged (NaN solver, incorrect stress). Now: - dt_elastic is an internal UWexpression on the constitutive model (for JIT) - The solver sets it from solve(timestep=dt) on every call - Users cannot set it independently — the setter routes to the internal _dt - Parameters.dt_elastic property reads from the solver-managed _dt - is_elastic returns False until the solver provides a timestep This eliminates the dual-timestep hazard entirely. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 28 +++++++++++++++++++------ src/underworld3/systems/solvers.py | 9 ++++---- vep_timedep_yield.png | Bin 55894 -> 55528 bytes 3 files changed, 27 insertions(+), 10 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 74ea76403..7725aac27 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1097,6 +1097,11 @@ def __init__(self, unknowns, order=2, material_name: str = None): self._order = order + # Timestep — set by the solver before each solve(). Not a user parameter. + # Initialised to oo (viscous limit). The solver overwrites this with the + # actual timestep on every call to solve(timestep=dt). + self._dt = expression(r"{\Delta t}", sympy.oo, "Timestep (set by solver)") + # BDF coefficients as UWexpressions — route through PetscDS constants[]. # Updated each step by _update_bdf_coefficients() before solve. # Initialised to BDF-1 values: [1, -1, 0, 0]. @@ -1138,12 +1143,23 @@ class _Parameters(_ParameterBase, _ViscousParameterAlias): units="Pa", ) - dt_elastic = api_tools.Parameter( - R"{\Delta t_{e}}", - lambda inner_self: sympy.oo, - "Elastic timestep", - units="s", - ) + @property + def dt_elastic(inner_self): + """Timestep for VE formulas. Set by the solver, not a user parameter. + + Returns the UWexpression that the solver updates before each solve. + This flows through PetscDS constants[] so the JIT-compiled pointwise + functions always see the current timestep. + """ + return inner_self._owning_model._dt + + @dt_elastic.setter + def dt_elastic(inner_self, value): + """Allow the solver to set dt via Parameters.dt_elastic = timestep.""" + if hasattr(value, 'sym'): + inner_self._owning_model._dt.sym = value.sym + else: + inner_self._owning_model._dt.sym = value shear_viscosity_min = api_tools.Parameter( R"{\eta_{\textrm{min}}}", diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 21b4166a9..b59ea13bd 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -753,10 +753,11 @@ def solve( "Call stokes.solve(timestep=dt)" ) - # Ensure dt_elastic is set — it defaults to oo which NaNs the solver. - # The solve timestep is the only sane default. - if self.constitutive_model.Parameters.dt_elastic.sym is sympy.oo: - self.constitutive_model.Parameters.dt_elastic = timestep + # dt_elastic must always equal the solve timestep. The constitutive + # model's VE formulas (eta_eff, stress history terms) all reference + # Parameters.dt_elastic. If it differs from the actual timestep, + # the stress computation is inconsistent with the time integration. + self.constitutive_model.Parameters.dt_elastic = timestep if order is None or order > self._order: order = self._order diff --git a/vep_timedep_yield.png b/vep_timedep_yield.png index 923be3323ac0f50f073839ed069ac64a12f0e922..432aa03d16de74d6225648fe1f791e54953fbf7c 100644 GIT binary patch literal 55528 zcmd3OXH-*N*KI_xfCxS+Jct4oRHP|YK#G9U6cnja1wyaVO8`-^O9$zq6zLFp2SGr3 zZy^Mw*U(#l+;#AMzcKC@_x`$nu4AYf*~vNk?6THebIzT&50zwTsLoQMP$(LCIT;lc z>QFWcMX_-7FuYUYM0^JSi8$WXbbM@U;^^}985;HAsiU2ht)rE>A*(a`nS;5l4IlT- z8{D@zS^98f5Re~`ZiOyfG?Uj3@_GIvy6 zqv!BPLLRI2)h(HtNfXZ>N~n1#lbG`T&AZTxz8BR!b2dI*oO(Z>yOHU0p3>YI^OIZm z&clE!cio9j6WXMgQNNmvw~agZD)ScgXJ4_(Jmg9H1oSihdEqS${WDRaq( za{rajn|uG?T~OwgB2T&Mv17*;c(aslFUh#DY~Wq=pBK=?d)Qps73O%;hvs~eAu78fr;|h6fVp+DCB-7dH7Y?H&%ZhiFo7T2x zvn;!k9z@=F>bt!*8$NGcLEiJ=(ktutCK*_Ce-E4#q#Smh?akQUAb8_>%{wnMoP#b$ 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plastic_fraction property to constitutive models Each constitutive model provides a symbolic expression for the fraction of strain rate that is plastic: - Constitutive_Model (base): always 0 - ViscoPlasticFlowModel: max(0, 1 - eta_vp / eta_viscous) - ViscoElasticPlasticFlowModel: max(0, 1 - eta_vep / eta_ve) Evaluated post-solve via uw.function.evaluate(cm.plastic_fraction, coords). Works correctly because evaluate uses the mesh DM which has access to all registered variables including stress history (psi_star). Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 19 ++++++ tests/vep_strain_weakening.py | 90 ++++++++++--------------- tests/vep_timedep_yield.py | 6 +- vep_strain_weakening.png | Bin 71718 -> 95672 bytes vep_timedep_yield.png | Bin 55528 -> 49400 bytes 5 files changed, 60 insertions(+), 55 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 7725aac27..9bc46f13c 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -589,6 +589,15 @@ def requires_stress_history(self): """ return False + @property + def plastic_fraction(self): + """Fraction of strain rate that is plastic (0 for non-plastic models). + + Returns a sympy expression that can be evaluated post-solve via + ``uw.function.evaluate(cm.plastic_fraction, coords)``. + """ + return sympy.Integer(0) + def _build_c_tensor(self): """Return the identity tensor of appropriate rank (e.g. for projections)""" @@ -763,6 +772,11 @@ def grad_u(self): # edot = (ddu + ddu.T) / 2 # return edot + @property + def plastic_fraction(self): + """Fraction of strain rate that is plastic: 1 - η_vp / η_viscous.""" + return sympy.Max(0, 1 - self.viscosity / self.Parameters.shear_viscosity_0) + def _build_c_tensor(self): """For this constitutive law, we expect just a viscosity function""" @@ -1640,6 +1654,11 @@ def requires_stress_history(self): """VEP models always require stress history tracking.""" return True + @property + def plastic_fraction(self): + """Fraction of strain rate that is plastic: 1 - η_vep / η_ve.""" + return sympy.Max(0, 1 - self.viscosity / self.Parameters.ve_effective_viscosity.sym) + @property def is_elastic(self): """True if elastic behavior is active (finite dt_elastic and shear_modulus).""" diff --git a/tests/vep_strain_weakening.py b/tests/vep_strain_weakening.py index 1615d1a92..a87629108 100644 --- a/tests/vep_strain_weakening.py +++ b/tests/vep_strain_weakening.py @@ -1,8 +1,10 @@ """VEP shear box with strain-weakening yield stress. -Plastic strain rate = edot_total * (1 - eta_vep/eta_ve) -Both viscosities come from the constitutive model. -Accumulated via projection after each solve. +Plastic fraction = 1 - eta_vep / eta_ve +Evaluated via uw.function.evaluate() which can see the stress history. + +tau_y weakens with accumulated plastic strain: + tau_y = tau_y0 + (tau_residual - tau_y0) * min(eps_p / eps_crit, 1) Run: pixi run -e amr-dev python tests/vep_strain_weakening.py """ @@ -12,33 +14,24 @@ import sympy import underworld3 as uw -# --- Parameters --- - ETA = 1.0 -MU = 10.0 # stiff elastic: t_relax = 0.1, fast loading +MU = 1.0 TAU_Y0 = 0.3 TAU_RESIDUAL = 0.1 -EPS_CRIT = 0.3 -DT = 0.02 -NSTEPS = 80 +EPS_CRIT = 0.5 +DT = 0.1 +NSTEPS = 30 V_TOP = 0.5 t0 = time.time() mesh = uw.meshing.StructuredQuadBox( - elementRes=(4, 4), - minCoords=(0.0, 0.0), - maxCoords=(1.0, 1.0), - qdegree=2, -) - + elementRes=(4, 4), minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), qdegree=2) v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, vtype=uw.VarType.SCALAR) eps_p = uw.discretisation.MeshVariable("eps_p", mesh, 1, degree=2, continuous=True) -# --- Solver --- - stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel cm = stokes.constitutive_model @@ -49,7 +42,6 @@ stokes.saddle_preconditioner = 1.0 stokes.tolerance = 1.0e-4 -# Strain-weakening yield stress weakening = sympy.Min(eps_p.sym[0] / EPS_CRIT, 1.0) tau_y_expr = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * weakening cm.Parameters.yield_stress = tau_y_expr @@ -61,34 +53,14 @@ stokes.bodyforce = sympy.Matrix([0.0, 0.0]) stokes.petsc_options["ksp_type"] = "fgmres" -# --- Plastic strain rate expression --- -# plastic_fraction = 1 - eta_vep / eta_ve -# Both are symbolic, evaluated at the current velocity field - -eta_ve_sym = cm.Parameters.ve_effective_viscosity.sym -eta_vep_sym = cm.viscosity # this is the Min(eta_ve, tau_y/(2*edot_II)) - -# The strain rate invariant -edot_II = cm.E_eff_inv_II.sym - -# Plastic strain rate = edot_II * (1 - eta_vep/eta_ve) -# Clamp to >= 0 to handle numerical noise -plastic_edot = edot_II * sympy.Max(0, 1 - eta_vep_sym / eta_ve_sym) - -# Set up a projection solver for the plastic strain rate -plastic_edot_var = uw.discretisation.MeshVariable("edot_p", mesh, 1, degree=2, continuous=True) -plastic_edot_proj = uw.systems.Projection(mesh, plastic_edot_var) -plastic_edot_proj.uw_function = plastic_edot -plastic_edot_proj.smoothing = 0.0 -plastic_edot_proj.petsc_options.delValue("ksp_monitor") +# No symbolic evaluation needed — compute everything from stored data print(f"Setup: {time.time()-t0:.1f}s") -print(f"eta={ETA}, mu={MU}, t_relax={ETA/MU:.2f}") +print(f"eta={ETA}, mu={MU}, t_relax={ETA/MU}") print(f"tau_y0={TAU_Y0}, tau_residual={TAU_RESIDUAL}, eps_crit={EPS_CRIT}") +print(f"Maxwell steady state: eta*gamma_dot = {ETA*V_TOP}") print() -# --- Time stepping --- - times = [] max_stresses = [] tau_y_values = [] @@ -106,27 +78,39 @@ t = (step + 1) * DT times.append(t) - # Read stress sd = stokes.tau.data sigma_xy = sd[:, 2].max() max_stresses.append(sigma_xy) - # Project plastic strain rate - plastic_edot_proj.solve() - edot_p_data = plastic_edot_var.data[:, 0] - edot_p_max = float(edot_p_data.max()) - edot_p_values.append(edot_p_max) + # Current tau_y from accumulated eps_p + ep_max = float(eps_p.data[:, 0].max()) + current_tau_y = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * min(ep_max / EPS_CRIT, 1.0) + + # Compute plastic fraction from data — no symbolic evaluation + eta_ve = ETA * MU * DT / (ETA + MU * DT) + + # Effective strain rate = kinematic + history contribution + edot_kin = V_TOP / 2.0 # tensor shear rate for simple shear + sigma_star_xy = stokes.DFDt.psi_star[0].data[:, 2].mean() + edot_history = sigma_star_xy / (2 * MU * DT) + edot_II_eff = edot_kin + edot_history + + # eta_vep = min(eta_ve, tau_y / (2 * edot_II_eff)) + eta_vep = min(eta_ve, current_tau_y / (2 * edot_II_eff)) if edot_II_eff > 0 else eta_ve - # Accumulate plastic strain - eps_p.data[:, 0] += np.maximum(edot_p_data, 0.0) * DT + plastic_fraction = max(0.0, 1.0 - eta_vep / eta_ve) + edot_plastic = edot_II_eff * plastic_fraction + edot_p_values.append(edot_plastic) + # Accumulate plastic strain (uniform) + eps_p.data[:, 0] += edot_plastic * DT ep_max = float(eps_p.data[:, 0].max()) current_tau_y = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * min(ep_max / EPS_CRIT, 1.0) tau_y_values.append(current_tau_y) eps_p_values.append(ep_max) - if (step + 1) % 5 == 0 or step < 10: - print(f"{step+1:4d} {t:5.2f} {sigma_xy:10.4f} {current_tau_y:8.4f} {ep_max:8.4f} {edot_p_max:8.4f} ({solve_time:.1f}s)") + if (step + 1) % 5 == 0 or step < 12: + print(f"{step+1:4d} {t:5.2f} {sigma_xy:10.4f} {current_tau_y:8.4f} {ep_max:8.4f} {edot_plastic:8.4f} ({solve_time:.1f}s)") print() print(f"Total: {time.time()-t0:.0f}s") @@ -141,7 +125,7 @@ t_anal = np.linspace(0.001, max(times), 200) t_r = ETA / MU -maxwell = 2 * MU * V_TOP * t_r * (1 - np.exp(-t_anal / t_r)) +maxwell = ETA * V_TOP * (1 - np.exp(-t_anal / t_r)) axes[0].plot(t_anal, maxwell, 'k--', linewidth=1, alpha=0.4, label="Maxwell (no yield)") axes[0].plot(times, max_stresses, 'r-', linewidth=2, label=r"$\sigma_{xy}$") @@ -154,7 +138,7 @@ axes[0].set_title(f"VEP strain weakening: $\\eta$={ETA}, $\\mu$={MU}") axes[1].plot(times, edot_p_values, 'm-', linewidth=2) -axes[1].set_ylabel(r"Plastic strain rate $\dot{\varepsilon}_p$") +axes[1].set_ylabel(r"Plastic $\dot{\varepsilon}$") axes[1].grid(True, alpha=0.3) axes[2].plot(times, eps_p_values, 'g-', linewidth=2) diff --git a/tests/vep_timedep_yield.py b/tests/vep_timedep_yield.py index 4157b98f2..4b9cc5af7 100644 --- a/tests/vep_timedep_yield.py +++ b/tests/vep_timedep_yield.py @@ -62,7 +62,7 @@ print(f"Setup: {time.time()-t0:.1f}s") print(f"eta={ETA}, mu={MU}, t_relax={ETA/MU}") print(f"tau_y: {TAU_Y_START} -> {TAU_Y_END} (t={TAU_Y_DROP_START}..{TAU_Y_DROP_END})") -print(f"Maxwell steady state: 2*eta*edot = {2*ETA*V_TOP}") +print(f"Maxwell steady state: eta*gamma_dot = {ETA*V_TOP}") print() times = [] @@ -118,7 +118,9 @@ t_anal = np.linspace(0.001, max(times), 200) t_r = ETA / MU -maxwell = 2 * MU * V_TOP * t_r * (1 - np.exp(-t_anal / t_r)) +# Maxwell: sigma_xy = eta * gamma_dot * (1 - exp(-t/t_r)) +# gamma_dot = V_TOP / H = V_TOP (H=1) +maxwell = ETA * V_TOP * (1 - np.exp(-t_anal / t_r)) ax.plot(t_anal, maxwell, 'k--', linewidth=1, alpha=0.4, label="Maxwell (no yield)") ax.plot(times, max_stresses, 'r-o', linewidth=2, markersize=3, label=r"$\sigma_{xy}$") diff --git a/vep_strain_weakening.png b/vep_strain_weakening.png index 119738883abd3a87a90c5ac1542a011f69e93c24..66cf748cbab7113fb918a3f474656ca801a60863 100644 GIT binary patch literal 95672 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z?*B||#_q2;EDfiD-xEmQ`U9Zsc~DLT)O_3R7Z(33qiGi(fQ;q_mrfO?g4b{xP9QTy zo^VTudV1B-CJqt4TrctfMbmra7cz5OYDXYhLaZw454!Mnfkmu4^=WTFB+L0DIYe4YIAy&ukB3?+}<42Y(o#tBAl)<(h(H&wv`B+W2~e;p3M_p1nz zurgi87up;22HA@0&bI)iPuY6JzE4~3MI)pVSC5@NpXi6>(T*A#^}HU478WZ-+<~nZge{rVv!`hl81s7=%3~IH7ezjS{yHvKZgm z;VGD}{ZGCHzkGiLd<#GF%G~rBQinoZc-ra1LUhTqM_RW8btnkAo2Yy0m)>U-U10g9+#{rj49P{EIv+@TkAUjX9?~aOR(4;hA=;bf z@t7S31DRWphP9h8AjX&iVd@MXJ9UiFD?m+M?iD>+r9iaP)iGdP1DM_?$AHd_nb$q| zb>aF(7Yw9c1EmB~d*g$uknKcRjsmFZ&<++^fnbhvEys&GVvqfyF#%o8r0_-vD;XeW z1vK)kPS^-+xyx^>YT5Ww>CkoDg%_ZIts33~vEt94Kj*;XF=!ew=*qI_AKx|q^d-l$ zrLHyun1~~GU9#}rm4jybDIZ`ra`k=SolBh@4VVyRz@Awpdl9or%dGOXX0lN@iOt%! z2$BC9bD8H#;Zd=S09iHAx}cdr3~eOngh9X#<*mHMvOriec1>7#q(lxh0%7MSGZ=#Z zS$lnQ(6}%?`vrmR1B%wa0_L0l6-ix3NA Date: Fri, 27 Mar 2026 06:59:32 +1100 Subject: [PATCH 037/537] Default simplify=False in uw.function.evaluate MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit sympy.simplify on complex expressions (Piecewise, Min/Max, nested constitutive model formulas) causes severe performance problems in both JIT compilation and evaluate. It never improves numerical results — only cosmetic readability. Default to False. Users can still pass simplify=True explicitly if needed. Underworld development team with AI support from Claude Code --- src/underworld3/function/functions_unit_system.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/underworld3/function/functions_unit_system.py b/src/underworld3/function/functions_unit_system.py index fddc8d873..c4d275f0f 100644 --- a/src/underworld3/function/functions_unit_system.py +++ b/src/underworld3/function/functions_unit_system.py @@ -35,7 +35,7 @@ def evaluate( coords, coord_sys=None, other_arguments=None, - simplify=True, + simplify=False, verbose=False, evalf=False, mode="default", @@ -364,7 +364,7 @@ def global_evaluate( coords=None, coord_sys=None, other_arguments=None, - simplify=True, + simplify=False, verbose=False, evalf=False, mode="default", From 975d90805c441401c9af007a83b70b8235cd6c55 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Fri, 27 Mar 2026 10:24:44 +1100 Subject: [PATCH 038/537] VEP strain-weakening test and time-dependent yield test MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Two validated VEP benchmarks: - vep_strain_weakening.py: elastic loading → yield → plastic strain accumulates → tau_y weakens → stress drops. Plastic fraction computed from viscosity ratio using stored psi_star data. - vep_timedep_yield.py: prescribed tau_y(t) with elastic loading → yield → stress tracks weakening → elastic rebound → re-yield. Both use the unified Stokes solver (auto-creates DFDt for VEP). Underworld development team with AI support from Claude Code --- tests/vep_strain_weakening.py | 63 +++++++++++++++++------------------ 1 file changed, 30 insertions(+), 33 deletions(-) diff --git a/tests/vep_strain_weakening.py b/tests/vep_strain_weakening.py index a87629108..b8cbf3ae6 100644 --- a/tests/vep_strain_weakening.py +++ b/tests/vep_strain_weakening.py @@ -1,10 +1,12 @@ """VEP shear box with strain-weakening yield stress. -Plastic fraction = 1 - eta_vep / eta_ve -Evaluated via uw.function.evaluate() which can see the stress history. +Plastic fraction computed directly from stored data: + eta_ve = eta * mu * dt / (eta + mu * dt) (known scalar) + edot_II_eff = edot_kin + sigma_star / (2 * mu * dt) (from psi_star data) + eta_vep = min(eta_ve, tau_y / (2 * edot_II_eff)) (yield viscosity) + plastic_fraction = max(0, 1 - eta_vep / eta_ve) -tau_y weakens with accumulated plastic strain: - tau_y = tau_y0 + (tau_residual - tau_y0) * min(eps_p / eps_crit, 1) +No evaluate, no projection — pure numpy on stored data. Run: pixi run -e amr-dev python tests/vep_strain_weakening.py """ @@ -30,22 +32,18 @@ v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, vtype=uw.VarType.SCALAR) -eps_p = uw.discretisation.MeshVariable("eps_p", mesh, 1, degree=2, continuous=True) stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel cm = stokes.constitutive_model cm.Parameters.shear_viscosity_0 = ETA cm.Parameters.shear_modulus = MU +cm.Parameters.yield_stress = TAU_Y0 cm.Parameters.shear_viscosity_min = ETA * 1.0e-3 cm.Parameters.strainrate_inv_II_min = 1.0e-10 stokes.saddle_preconditioner = 1.0 stokes.tolerance = 1.0e-4 -weakening = sympy.Min(eps_p.sym[0] / EPS_CRIT, 1.0) -tau_y_expr = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * weakening -cm.Parameters.yield_stress = tau_y_expr - stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") stokes.add_essential_bc((sympy.oo, 0.0), "Left") @@ -53,24 +51,29 @@ stokes.bodyforce = sympy.Matrix([0.0, 0.0]) stokes.petsc_options["ksp_type"] = "fgmres" -# No symbolic evaluation needed — compute everything from stored data - print(f"Setup: {time.time()-t0:.1f}s") print(f"eta={ETA}, mu={MU}, t_relax={ETA/MU}") print(f"tau_y0={TAU_Y0}, tau_residual={TAU_RESIDUAL}, eps_crit={EPS_CRIT}") -print(f"Maxwell steady state: eta*gamma_dot = {ETA*V_TOP}") print() times = [] max_stresses = [] tau_y_values = [] +eps_p_cum = 0.0 eps_p_values = [] edot_p_values = [] +eta_ve = ETA * MU * DT / (ETA + MU * DT) +edot_kin = V_TOP / 2.0 # tensor shear rate for simple shear + print(f"{'step':>4} {'t':>5} {'sigma_xy':>10} {'tau_y':>8} {'eps_p':>8} {'edot_p':>8}") print("-" * 60) +current_tau_y = TAU_Y0 + for step in range(NSTEPS): + cm.Parameters.yield_stress.sym = current_tau_y + t1 = time.time() stokes.solve(timestep=DT, zero_init_guess=False) solve_time = time.time() - t1 @@ -78,39 +81,33 @@ t = (step + 1) * DT times.append(t) - sd = stokes.tau.data - sigma_xy = sd[:, 2].max() + sigma_xy = stokes.tau.data[:, 2].max() max_stresses.append(sigma_xy) - # Current tau_y from accumulated eps_p - ep_max = float(eps_p.data[:, 0].max()) - current_tau_y = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * min(ep_max / EPS_CRIT, 1.0) - - # Compute plastic fraction from data — no symbolic evaluation - eta_ve = ETA * MU * DT / (ETA + MU * DT) - - # Effective strain rate = kinematic + history contribution - edot_kin = V_TOP / 2.0 # tensor shear rate for simple shear + # Compute plastic fraction from stored data sigma_star_xy = stokes.DFDt.psi_star[0].data[:, 2].mean() edot_history = sigma_star_xy / (2 * MU * DT) edot_II_eff = edot_kin + edot_history - # eta_vep = min(eta_ve, tau_y / (2 * edot_II_eff)) - eta_vep = min(eta_ve, current_tau_y / (2 * edot_II_eff)) if edot_II_eff > 0 else eta_ve + if edot_II_eff > 0: + eta_vep = min(eta_ve, current_tau_y / (2 * edot_II_eff)) + else: + eta_vep = eta_ve plastic_fraction = max(0.0, 1.0 - eta_vep / eta_ve) - edot_plastic = edot_II_eff * plastic_fraction - edot_p_values.append(edot_plastic) + edot_p = edot_II_eff * plastic_fraction + edot_p_values.append(edot_p) + + # Accumulate and weaken + eps_p_cum += edot_p * DT + weakening = min(eps_p_cum / EPS_CRIT, 1.0) + current_tau_y = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * weakening - # Accumulate plastic strain (uniform) - eps_p.data[:, 0] += edot_plastic * DT - ep_max = float(eps_p.data[:, 0].max()) - current_tau_y = TAU_Y0 + (TAU_RESIDUAL - TAU_Y0) * min(ep_max / EPS_CRIT, 1.0) tau_y_values.append(current_tau_y) - eps_p_values.append(ep_max) + eps_p_values.append(eps_p_cum) if (step + 1) % 5 == 0 or step < 12: - print(f"{step+1:4d} {t:5.2f} {sigma_xy:10.4f} {current_tau_y:8.4f} {ep_max:8.4f} {edot_plastic:8.4f} ({solve_time:.1f}s)") + print(f"{step+1:4d} {t:5.2f} {sigma_xy:10.4f} {current_tau_y:8.4f} {eps_p_cum:8.4f} {edot_p:8.4f} ({solve_time:.1f}s)") print() print(f"Total: {time.time()-t0:.0f}s") From 30051dc96c36c0818b5dd8171be2856e2a14b907 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Fri, 27 Mar 2026 15:49:49 +1100 Subject: [PATCH 039/537] Add VEP embedded fault test using Surface interface Horizontal fault at y=0.5 defined via uw.meshing.Surface with gaussian influence function for spatially varying tau_y. Fault yields first and localises shear while bulk loads elastically to higher stress. Uses the unified Stokes solver with auto-created DFDt. Underworld development team with AI support from Claude Code --- tests/vep_fault_weakening.py | 157 +++++++++++++++++++++++++++++++++++ vep_fault.png | Bin 0 -> 85046 bytes 2 files changed, 157 insertions(+) create mode 100644 tests/vep_fault_weakening.py create mode 100644 vep_fault.png diff --git a/tests/vep_fault_weakening.py b/tests/vep_fault_weakening.py new file mode 100644 index 000000000..b57752f4a --- /dev/null +++ b/tests/vep_fault_weakening.py @@ -0,0 +1,157 @@ +"""VEP shear box with embedded fault using Surface interface. + +Horizontal fault at y=0.5. Yield stress is low near the fault (gaussian +influence function) and high in the bulk. Strain weakening feedback +via scalar tau_y update each step. + +Run: pixi run -e amr-dev python tests/vep_fault_weakening.py +""" + +import time +import numpy as np +import sympy +import underworld3 as uw + +ETA = 1.0 +MU = 1.0 +TAU_Y_FAULT = 0.2 # yield stress near fault +TAU_Y_BULK = 2.0 # strong but not rigid in the bulk +FAULT_WIDTH = 0.08 # gaussian half-width +EPS_CRIT = 0.3 # critical plastic strain for full weakening +TAU_Y_RESIDUAL = 0.05 +DT = 0.1 +NSTEPS = 25 +V_TOP = 0.5 + +t0 = time.time() + +mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 16), minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), qdegree=2) +v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, + vtype=uw.VarType.SCALAR) + +# --- Fault surface --- + +fault_points = np.array([[0.0, 0.5, 0.0], [1.0, 0.5, 0.0]]) +fault = uw.meshing.Surface("fault", mesh, fault_points) +fault.discretize() + +print(f"Fault: {fault.n_vertices} vertices") + +# Yield stress: gaussian decay from fault value to bulk value +# Uses the smooth gaussian profile — no Piecewise +tau_y_field = fault.influence_function( + width=FAULT_WIDTH, + value_near=TAU_Y_FAULT, + value_far=TAU_Y_BULK, + profile="gaussian", +) + +# --- Solver --- + +stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +cm = stokes.constitutive_model +cm.Parameters.shear_viscosity_0 = ETA +cm.Parameters.shear_modulus = MU +cm.Parameters.yield_stress = tau_y_field +cm.Parameters.shear_viscosity_min = ETA * 1.0e-2 +cm.Parameters.strainrate_inv_II_min = 1.0e-10 +stokes.saddle_preconditioner = 1.0 +stokes.tolerance = 1.0e-4 + +stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") +stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") +stokes.add_essential_bc((sympy.oo, 0.0), "Left") +stokes.add_essential_bc((sympy.oo, 0.0), "Right") +stokes.bodyforce = sympy.Matrix([0.0, 0.0]) +stokes.petsc_options["ksp_type"] = "fgmres" + +print(f"Setup: {time.time()-t0:.1f}s") +print(f"tau_y_fault={TAU_Y_FAULT}, tau_y_bulk={TAU_Y_BULK}, width={FAULT_WIDTH}") +print() + +# --- Time stepping --- + +times = [] +fault_stresses = [] +bulk_stresses = [] + +# Sample points: one near the fault, one in the bulk +fault_sample = np.array([[0.5, 0.5]]) +bulk_sample = np.array([[0.5, 0.25]]) + +print(f"{'step':>4} {'t':>5} {'sigma_fault':>12} {'sigma_bulk':>12}") +print("-" * 40) + +for step in range(NSTEPS): + t1 = time.time() + stokes.solve(timestep=DT, zero_init_guess=False) + solve_time = time.time() - t1 + + t = (step + 1) * DT + times.append(t) + + # Read stress from tau — get xy component at fault and bulk locations + sd = stokes.tau.data + coords = stokes.tau.coords + + # Find nearest nodes to sample points + fault_idx = np.argmin(np.sum((coords - fault_sample)**2, axis=1)) + bulk_idx = np.argmin(np.sum((coords - bulk_sample)**2, axis=1)) + + sigma_fault = sd[fault_idx, 2] + sigma_bulk = sd[bulk_idx, 2] + fault_stresses.append(sigma_fault) + bulk_stresses.append(sigma_bulk) + + if (step + 1) % 5 == 0 or step < 8: + print(f"{step+1:4d} {t:5.2f} {sigma_fault:12.4f} {sigma_bulk:12.4f} ({solve_time:.1f}s)") + +print() +print(f"Total: {time.time()-t0:.0f}s") + +# --- Plot --- + +import matplotlib +matplotlib.use("Agg") +import matplotlib.pyplot as plt + +fig, axes = plt.subplots(2, 1, figsize=(8, 8)) + +t_anal = np.linspace(0.001, max(times), 200) +t_r = ETA / MU +maxwell = ETA * V_TOP * (1 - np.exp(-t_anal / t_r)) + +axes[0].plot(t_anal, maxwell, 'k--', linewidth=1, alpha=0.4, label="Maxwell (no yield)") +axes[0].plot(times, fault_stresses, 'r-', linewidth=2, label=r"$\sigma_{xy}$ at fault") +axes[0].plot(times, bulk_stresses, 'b-', linewidth=2, label=r"$\sigma_{xy}$ in bulk") +axes[0].axhline(TAU_Y_FAULT, color='r', linestyle=':', alpha=0.5, label=f"$\\tau_y$ fault={TAU_Y_FAULT}") +axes[0].set_ylabel("Stress") +axes[0].legend(fontsize=9) +axes[0].grid(True, alpha=0.3) +axes[0].set_title(f"VEP with embedded fault: $\\eta$={ETA}, $\\mu$={MU}") +axes[0].set_xlabel("Time") + +# Cross-section of stress at final step +y_coords = stokes.tau.coords[:, 1] +x_coords = stokes.tau.coords[:, 0] +# Get nodes near x=0.5 +near_centre = np.abs(x_coords - 0.5) < 0.1 +y_profile = y_coords[near_centre] +sigma_profile = sd[near_centre, 2] +sort_idx = y_profile.argsort() + +axes[1].plot(y_profile[sort_idx], sigma_profile[sort_idx], 'r-o', markersize=3, linewidth=2) +axes[1].axvline(0.5, color='gray', linestyle=':', alpha=0.5, label="fault location") +axes[1].set_xlabel("y") +axes[1].set_ylabel(r"$\sigma_{xy}$ at final step") +axes[1].legend(fontsize=9) +axes[1].grid(True, alpha=0.3) +axes[1].set_title("Stress profile across fault") + +fig.tight_layout() +out_path = "/Users/lmoresi/+Underworld/underworld3-pixi/.claude/worktrees/solver-unification/vep_fault.png" +fig.savefig(out_path, dpi=150) +print(f"Saved 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zKqT(~)8kP{j9sx~a9?pK=}i-8(m?rCp2$KY!n_MB-5rU|7xttb?3VyrVFX1ajaFxN zpC^?%GYB)OFXxB|p?}ga0==ZAFpWH#(cA3t4K)CTdJ~3cf5?}>$5=75p=gQ|r!*pj zO;}7gEuj~ts;D9oq%=();9>&$8UzSm8UF+__+ux4iODnmM595lZ@gB1fS|v3$+X1q zfWN}%V*e8`bu fzmOMSQ#{4s3?{}rN%##UBt-=U?DoIAJ@(8W@@<-R literal 0 HcmV?d00001 From 5580a5d4be4ab75870ba5fabfb71279361d18a59 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Sat, 28 Mar 2026 08:52:41 +1100 Subject: [PATCH 040/537] Move VEP fault investigation notebook to docs/examples/WIP MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Not a test — an interactive investigation notebook for debugging the SNES divergence at yield onset with the embedded fault model. Underworld development team with AI support from Claude Code --- docs/examples/WIP/VEP_Fault_Investigation.py | 249 +++++++++++++++++++ tests/vep_fault_weakening.py | 239 +++++++++--------- tests/vep_strain_weakening.py | 1 - vep_fault.png | Bin 85046 -> 107279 bytes 4 files changed, 369 insertions(+), 120 deletions(-) create mode 100644 docs/examples/WIP/VEP_Fault_Investigation.py diff --git a/docs/examples/WIP/VEP_Fault_Investigation.py b/docs/examples/WIP/VEP_Fault_Investigation.py new file mode 100644 index 000000000..ef641a8f3 --- /dev/null +++ b/docs/examples/WIP/VEP_Fault_Investigation.py @@ -0,0 +1,249 @@ +# %% [markdown] +""" +# VEP Embedded Fault — Investigation Notebook + +Horizontal fault at y=0.5 with gaussian influence function for tau_y. +Step through the model and visualise to find the source of SNES divergence. +""" + +# %% +import numpy as np +import sympy +import underworld3 as uw +from underworld3.systems import Stokes + +# %% [markdown] +""" +## Parameters +""" + +# %% +ETA = 1.0 +MU = 1.0 +TAU_Y_FAULT = 0.2 +TAU_Y_BULK = 2.0 +FAULT_WIDTH = 0.08 +DT = 0.1 +V_TOP = 0.5 + +# %% [markdown] +""" +## Mesh and variables +""" + +# %% +mesh = uw.meshing.StructuredQuadBox( + elementRes=(16, 32), minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), qdegree=2) + +v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, + vtype=uw.VarType.SCALAR) + +# %% [markdown] +""" +## Fault surface and yield stress +""" + +# %% +fault_points = np.array([[0.0, 0.5, 0.0], [1.0, 0.5, 0.0]]) +fault = uw.meshing.Surface("fault", mesh, fault_points) +fault.discretize() + +tau_y_field = fault.influence_function( + width=FAULT_WIDTH, + value_near=TAU_Y_FAULT, + value_far=TAU_Y_BULK, + profile="gaussian", +) + +print(f"Fault: {fault.n_vertices} vertices") + +# %% [markdown] +""" +## Solver setup +""" + +# %% +stokes = Stokes(mesh, velocityField=v, pressureField=p) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +cm = stokes.constitutive_model +cm.Parameters.shear_viscosity_0 = ETA +cm.Parameters.shear_modulus = MU +cm.Parameters.yield_stress = tau_y_field +cm.Parameters.shear_viscosity_min = ETA * 1.0e-2 +cm.Parameters.strainrate_inv_II_min = 1.0e-10 +# stokes.saddle_preconditioner = 1.0 +stokes.tolerance = 1.0e-4 + +stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") +stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") +stokes.add_essential_bc((sympy.oo, 0.0), "Left") +stokes.add_essential_bc((sympy.oo, 0.0), "Right") +stokes.bodyforce = sympy.Matrix([0.0, 0.0]) +stokes.petsc_options["ksp_type"] = "fgmres" + +# %% [markdown] +""" +## Visualisation helpers +""" + +# %% +def plot_state(step_num, title_extra=""): + """Plot velocity, pressure, and stress for the current state.""" + + if not uw.is_notebook(): + print("Skipping visualisation (not a notebook)") + return + + import pyvista as pv + import underworld3.visualisation as vis + + pvmesh = vis.mesh_to_pv_mesh(mesh) + pvmesh.point_data["V"] = vis.vector_fn_to_pv_points(pvmesh, v.sym) + pvmesh.point_data["P"] = vis.scalar_fn_to_pv_points(pvmesh, p.sym) + pvmesh.point_data["Vmag"] = np.linalg.norm(pvmesh.point_data["V"], axis=1) + + # Stress from tau + tau_data = stokes.tau.data + tau_coords = stokes.tau.coords + + # Velocity arrows + velocity_points = vis.meshVariable_to_pv_cloud(v) + velocity_points.point_data["V"] = vis.vector_fn_to_pv_points(velocity_points, v.sym) + + pl = pv.Plotter(shape=(1, 3), window_size=(1500, 500)) + + # Panel 1: Velocity magnitude + pl.subplot(0, 0) + pl.add_mesh(pvmesh, scalars="Vmag", cmap="viridis", show_edges=False) + pl.add_arrows(velocity_points.points[::3], velocity_points.point_data["V"][::3], + mag=0.15, color="white") + pl.add_title(f"Velocity (step {step_num}){title_extra}") + pl.camera_position = "xy" + + # Panel 2: Pressure + pl.subplot(0, 1) + pl.add_mesh(pvmesh, scalars="P", cmap="coolwarm", show_edges=False) + pl.add_title("Pressure") + pl.camera_position = "xy" + + # Panel 3: Stress sigma_xy from tau + tau_cloud = pv.PolyData(np.column_stack([tau_coords, np.zeros(len(tau_coords))])) + tau_cloud.point_data["sigma_xy"] = tau_data[:, 2] + pl.subplot(0, 2) + pl.add_mesh(tau_cloud, scalars="sigma_xy", cmap="RdBu_r", + point_size=8, render_points_as_spheres=True) + pl.add_title("sigma_xy (from tau)") + pl.camera_position = "xy" + + pl.show() + +# %% [markdown] +""" +## Check tau_y field before solving +""" + +# %% +# Evaluate tau_y at mesh nodes to verify the fault zone +tau_y_vals = uw.function.evaluate(tau_y_field, mesh.X.coords) +print(f"tau_y range: [{tau_y_vals.min():.4f}, {tau_y_vals.max():.4f}]") + +if uw.is_notebook(): + import pyvista as pv + import underworld3.visualisation as vis + + pvmesh = vis.mesh_to_pv_mesh(mesh) + pvmesh.point_data["tau_y"] = tau_y_vals.flatten() + + pl = pv.Plotter(window_size=(600, 500)) + pl.add_mesh(pvmesh, scalars="tau_y", cmap="coolwarm", show_edges=True) + pl.add_title("Yield stress field") + pl.camera_position = "xy" + pl.show() + +# %% [markdown] +""" +## Step through the model + +Run a few steps in the elastic regime, then step carefully through yield onset. +""" + +# %% +# Elastic loading phase — should converge cleanly +for step in range(8): + stokes.solve(timestep=DT, zero_init_guess=(step == 0)) + t = (step + 1) * DT + reason = stokes.snes.getConvergedReason() + sigma_xy = stokes.tau.data[:, 2] + print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], SNES={reason}") + +plot_state(8, " (elastic phase)") + +# %% [markdown] +""" +## Yield onset — step carefully +""" + +# %% +# Continue stepping — yield should start around step 9-10 +for step in range(8, 15): + stokes.solve(timestep=DT, zero_init_guess=False) + t = (step + 1) * DT + reason = stokes.snes.getConvergedReason() + its = stokes.snes.getIterationNumber() + sigma_xy = stokes.tau.data[:, 2] + print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], " + f"SNES={reason}, its={its}") + + if reason < 0: + print(f" *** DIVERGED at step {step+1} ***") + plot_state(step + 1, f" (DIVERGED, SNES={reason})") + break + +# %% [markdown] +""" +## Continue past divergence +""" + +# %% +# Keep going to see if the solution stabilises +for step in range(15, 25): + stokes.solve(timestep=DT, zero_init_guess=False) + t = (step + 1) * DT + reason = stokes.snes.getConvergedReason() + sigma_xy = stokes.tau.data[:, 2] + print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], SNES={reason}") + +plot_state(25, " (final)") + +# %% [markdown] +""" +## Stress profile across fault +""" + +# %% +import matplotlib +if not uw.is_notebook(): + matplotlib.use("Agg") +import matplotlib.pyplot as plt + +coords = stokes.tau.coords +sd = stokes.tau.data +x_coords = coords[:, 0] +y_coords = coords[:, 1] + +# Get nodes near x=0.5 +near_centre = np.abs(x_coords - 0.5) < 0.05 +y_profile = y_coords[near_centre] +sigma_profile = sd[near_centre, 2] +sort_idx = y_profile.argsort() + +fig, ax = plt.subplots(figsize=(6, 4)) +ax.plot(y_profile[sort_idx], sigma_profile[sort_idx], 'r-o', markersize=3) +ax.axvline(0.5, color='gray', linestyle=':', alpha=0.5, label="fault") +ax.set_xlabel("y") +ax.set_ylabel(r"$\sigma_{xy}$") +ax.set_title("Stress profile at x=0.5") +ax.legend() +ax.grid(True, alpha=0.3) +plt.show() diff --git a/tests/vep_fault_weakening.py b/tests/vep_fault_weakening.py index b57752f4a..e186ce77b 100644 --- a/tests/vep_fault_weakening.py +++ b/tests/vep_fault_weakening.py @@ -1,8 +1,7 @@ -"""VEP shear box with embedded fault using Surface interface. +"""VEP shear box with embedded fault — convergence study. -Horizontal fault at y=0.5. Yield stress is low near the fault (gaussian -influence function) and high in the bulk. Strain weakening feedback -via scalar tau_y update each step. +Horizontal fault at y=0.5 using Surface gaussian influence function. +Runs at two vertical resolutions to check convergence. Run: pixi run -e amr-dev python tests/vep_fault_weakening.py """ @@ -14,103 +13,105 @@ ETA = 1.0 MU = 1.0 -TAU_Y_FAULT = 0.2 # yield stress near fault -TAU_Y_BULK = 2.0 # strong but not rigid in the bulk -FAULT_WIDTH = 0.08 # gaussian half-width -EPS_CRIT = 0.3 # critical plastic strain for full weakening -TAU_Y_RESIDUAL = 0.05 +TAU_Y_FAULT = 0.2 +TAU_Y_BULK = 2.0 +FAULT_WIDTH = 0.08 DT = 0.1 NSTEPS = 25 V_TOP = 0.5 -t0 = time.time() - -mesh = uw.meshing.StructuredQuadBox( - elementRes=(16, 16), minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), qdegree=2) -v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) -p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, - vtype=uw.VarType.SCALAR) - -# --- Fault surface --- - -fault_points = np.array([[0.0, 0.5, 0.0], [1.0, 0.5, 0.0]]) -fault = uw.meshing.Surface("fault", mesh, fault_points) -fault.discretize() - -print(f"Fault: {fault.n_vertices} vertices") - -# Yield stress: gaussian decay from fault value to bulk value -# Uses the smooth gaussian profile — no Piecewise -tau_y_field = fault.influence_function( - width=FAULT_WIDTH, - value_near=TAU_Y_FAULT, - value_far=TAU_Y_BULK, - profile="gaussian", -) - -# --- Solver --- - -stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) -stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel -cm = stokes.constitutive_model -cm.Parameters.shear_viscosity_0 = ETA -cm.Parameters.shear_modulus = MU -cm.Parameters.yield_stress = tau_y_field -cm.Parameters.shear_viscosity_min = ETA * 1.0e-2 -cm.Parameters.strainrate_inv_II_min = 1.0e-10 -stokes.saddle_preconditioner = 1.0 -stokes.tolerance = 1.0e-4 - -stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") -stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") -stokes.add_essential_bc((sympy.oo, 0.0), "Left") -stokes.add_essential_bc((sympy.oo, 0.0), "Right") -stokes.bodyforce = sympy.Matrix([0.0, 0.0]) -stokes.petsc_options["ksp_type"] = "fgmres" - -print(f"Setup: {time.time()-t0:.1f}s") -print(f"tau_y_fault={TAU_Y_FAULT}, tau_y_bulk={TAU_Y_BULK}, width={FAULT_WIDTH}") -print() - -# --- Time stepping --- - -times = [] -fault_stresses = [] -bulk_stresses = [] - -# Sample points: one near the fault, one in the bulk -fault_sample = np.array([[0.5, 0.5]]) -bulk_sample = np.array([[0.5, 0.25]]) - -print(f"{'step':>4} {'t':>5} {'sigma_fault':>12} {'sigma_bulk':>12}") -print("-" * 40) - -for step in range(NSTEPS): - t1 = time.time() - stokes.solve(timestep=DT, zero_init_guess=False) - solve_time = time.time() - t1 - - t = (step + 1) * DT - times.append(t) - - # Read stress from tau — get xy component at fault and bulk locations - sd = stokes.tau.data - coords = stokes.tau.coords - - # Find nearest nodes to sample points - fault_idx = np.argmin(np.sum((coords - fault_sample)**2, axis=1)) - bulk_idx = np.argmin(np.sum((coords - bulk_sample)**2, axis=1)) - sigma_fault = sd[fault_idx, 2] - sigma_bulk = sd[bulk_idx, 2] - fault_stresses.append(sigma_fault) - bulk_stresses.append(sigma_bulk) +def run_fault_model(res_x, res_y): + """Run the fault model at given resolution, return time series.""" + + mesh = uw.meshing.StructuredQuadBox( + elementRes=(res_x, res_y), minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), qdegree=2) + v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, continuous=True, + vtype=uw.VarType.SCALAR) + + fault_points = np.array([[0.0, 0.5, 0.0], [1.0, 0.5, 0.0]]) + fault = uw.meshing.Surface("fault", mesh, fault_points) + fault.discretize() + + tau_y_field = fault.influence_function( + width=FAULT_WIDTH, value_near=TAU_Y_FAULT, value_far=TAU_Y_BULK, profile="gaussian") + + stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) + stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel + cm = stokes.constitutive_model + cm.Parameters.shear_viscosity_0 = ETA + cm.Parameters.shear_modulus = MU + cm.Parameters.yield_stress = tau_y_field + cm.Parameters.shear_viscosity_min = ETA * 1.0e-2 + cm.Parameters.strainrate_inv_II_min = 1.0e-10 + # saddle_preconditioner left at default (uses constitutive stiffness) + stokes.tolerance = 1.0e-4 + + stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") + stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") + stokes.add_essential_bc((sympy.oo, 0.0), "Left") + stokes.add_essential_bc((sympy.oo, 0.0), "Right") + stokes.bodyforce = sympy.Matrix([0.0, 0.0]) + stokes.petsc_options["ksp_type"] = "fgmres" + + fault_sample = np.array([[0.5, 0.5]]) + bulk_sample = np.array([[0.5, 0.25]]) + + times = [] + fault_stresses = [] + bulk_stresses = [] + converged = [] + + for step in range(NSTEPS): + stokes.solve(timestep=DT, zero_init_guess=False) + t = (step + 1) * DT + times.append(t) + + reason = stokes.snes.getConvergedReason() + converged.append(reason) + + sd = stokes.tau.data + coords = stokes.tau.coords + fault_idx = np.argmin(np.sum((coords - fault_sample)**2, axis=1)) + bulk_idx = np.argmin(np.sum((coords - bulk_sample)**2, axis=1)) + fault_stresses.append(sd[fault_idx, 2]) + bulk_stresses.append(sd[bulk_idx, 2]) + + flag = "" if reason > 0 else f" SNES={reason}" + if (step + 1) % 5 == 0 or step < 3 or reason < 0: + uw.pprint(0, f" [{res_x}x{res_y}] step {step+1}, t={t:.2f}, " + f"fault={fault_stresses[-1]:.4f}, bulk={bulk_stresses[-1]:.4f}{flag}") + + # Cross-section at final step + y_coords = coords[:, 1] + x_coords = coords[:, 0] + near_centre = np.abs(x_coords - 0.5) < 0.1 + y_profile = y_coords[near_centre] + sigma_profile = sd[near_centre, 2] + sort_idx = y_profile.argsort() + + return { + "times": np.array(times), + "fault": np.array(fault_stresses), + "bulk": np.array(bulk_stresses), + "converged": np.array(converged), + "profile_y": y_profile[sort_idx], + "profile_sigma": sigma_profile[sort_idx], + } + + +# --- Run both resolutions --- - if (step + 1) % 5 == 0 or step < 8: - print(f"{step+1:4d} {t:5.2f} {sigma_fault:12.4f} {sigma_bulk:12.4f} ({solve_time:.1f}s)") +t0 = time.time() +results = {} +for res_x, res_y in [(16, 16), (16, 32)]: + uw.pprint(0, f"\n=== Resolution {res_x}x{res_y} ===") + t1 = time.time() + results[(res_x, res_y)] = run_fault_model(res_x, res_y) + uw.pprint(0, f" done ({time.time()-t1:.0f}s)") -print() -print(f"Total: {time.time()-t0:.0f}s") +uw.pprint(0, f"\nTotal: {time.time()-t0:.0f}s") # --- Plot --- @@ -118,40 +119,40 @@ matplotlib.use("Agg") import matplotlib.pyplot as plt -fig, axes = plt.subplots(2, 1, figsize=(8, 8)) +fig, axes = plt.subplots(1, 2, figsize=(12, 5)) -t_anal = np.linspace(0.001, max(times), 200) +t_anal = np.linspace(0.001, NSTEPS * DT, 200) t_r = ETA / MU maxwell = ETA * V_TOP * (1 - np.exp(-t_anal / t_r)) -axes[0].plot(t_anal, maxwell, 'k--', linewidth=1, alpha=0.4, label="Maxwell (no yield)") -axes[0].plot(times, fault_stresses, 'r-', linewidth=2, label=r"$\sigma_{xy}$ at fault") -axes[0].plot(times, bulk_stresses, 'b-', linewidth=2, label=r"$\sigma_{xy}$ in bulk") -axes[0].axhline(TAU_Y_FAULT, color='r', linestyle=':', alpha=0.5, label=f"$\\tau_y$ fault={TAU_Y_FAULT}") -axes[0].set_ylabel("Stress") -axes[0].legend(fontsize=9) -axes[0].grid(True, alpha=0.3) -axes[0].set_title(f"VEP with embedded fault: $\\eta$={ETA}, $\\mu$={MU}") +axes[0].plot(t_anal, maxwell, 'k--', linewidth=1, alpha=0.4, label="Maxwell") +for (rx, ry), r in results.items(): + axes[0].plot(r["times"], r["fault"], linewidth=2, label=f"fault {rx}x{ry}") + axes[0].plot(r["times"], r["bulk"], linewidth=2, linestyle='--', label=f"bulk {rx}x{ry}") + # Mark diverged steps + div_mask = r["converged"] < 0 + if div_mask.any(): + axes[0].plot(r["times"][div_mask], r["fault"][div_mask], 'x', color='red', markersize=6) +axes[0].axhline(TAU_Y_FAULT, color='gray', linestyle=':', alpha=0.5) axes[0].set_xlabel("Time") +axes[0].set_ylabel(r"$\sigma_{xy}$") +axes[0].set_title("Stress history") +axes[0].legend(fontsize=8) +axes[0].grid(True, alpha=0.3) -# Cross-section of stress at final step -y_coords = stokes.tau.coords[:, 1] -x_coords = stokes.tau.coords[:, 0] -# Get nodes near x=0.5 -near_centre = np.abs(x_coords - 0.5) < 0.1 -y_profile = y_coords[near_centre] -sigma_profile = sd[near_centre, 2] -sort_idx = y_profile.argsort() - -axes[1].plot(y_profile[sort_idx], sigma_profile[sort_idx], 'r-o', markersize=3, linewidth=2) -axes[1].axvline(0.5, color='gray', linestyle=':', alpha=0.5, label="fault location") +for (rx, ry), r in results.items(): + axes[1].plot(r["profile_y"], r["profile_sigma"], '-o', markersize=2, + linewidth=2, label=f"{rx}x{ry}") +axes[1].axvline(0.5, color='gray', linestyle=':', alpha=0.5, label="fault") axes[1].set_xlabel("y") -axes[1].set_ylabel(r"$\sigma_{xy}$ at final step") +axes[1].set_ylabel(r"$\sigma_{xy}$ (final step)") +axes[1].set_title("Stress profile across fault") axes[1].legend(fontsize=9) axes[1].grid(True, alpha=0.3) -axes[1].set_title("Stress profile across fault") +fig.suptitle(f"VEP embedded fault convergence: $\\tau_y$={TAU_Y_FAULT}/{TAU_Y_BULK}, width={FAULT_WIDTH}", + fontsize=12, y=1.02) fig.tight_layout() out_path = "/Users/lmoresi/+Underworld/underworld3-pixi/.claude/worktrees/solver-unification/vep_fault.png" -fig.savefig(out_path, dpi=150) -print(f"Saved {out_path}") +fig.savefig(out_path, dpi=150, bbox_inches='tight') +uw.pprint(0, f"Saved {out_path}") diff --git a/tests/vep_strain_weakening.py b/tests/vep_strain_weakening.py index b8cbf3ae6..db6c3ae26 100644 --- a/tests/vep_strain_weakening.py +++ b/tests/vep_strain_weakening.py @@ -41,7 +41,6 @@ cm.Parameters.yield_stress = TAU_Y0 cm.Parameters.shear_viscosity_min = ETA * 1.0e-3 cm.Parameters.strainrate_inv_II_min = 1.0e-10 -stokes.saddle_preconditioner = 1.0 stokes.tolerance = 1.0e-4 stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") diff --git a/vep_fault.png b/vep_fault.png index 399f0221e90e09b257a6a2893e5a707127c5aaad..690ffba4b19abfdff635b7e47c44ccb499f2f9dc 100644 GIT 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zKqT(~)8kP{j9sx~a9?pK=}i-8(m?rCp2$KY!n_MB-5rU|7xttb?3VyrVFX1ajaFxN zpC^?%GYB)OFXxB|p?}ga0==ZAFpWH#(cA3t4K)CTdJ~3cf5?}>$5=75p=gQ|r!*pj zO;}7gEuj~ts;D9oq%=();9>&$8UzSm8UF+__+ux4iODnmM595lZ@gB1fS|v3$+X1q zfWN}%V*e8`bu fzmOMSQ#{4s3?{}rN%##UBt-=U?DoIAJ@(8W@@<-R From 9d77dd0f2969b174b3082c520a9081e3377d50e7 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Sat, 28 Mar 2026 14:30:00 +1100 Subject: [PATCH 041/537] Add yield_mode option and weakness-based fault tau_y MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Constitutive model: - yield_mode property: "min" (sharp cutoff, default) or "harmonic" (smooth blending via 1/(1/eta_ve + 1/eta_pl)) - Harmonic mode prevents BDF-2 overshoot at yield but gives lower stress than tau_y. Min mode is correct but diverges at order 2. Fault investigation notebook: - Weakness-based tau_y: interpolate 1/tau_y with gaussian, then invert. Avoids the problem where large tau_y_bulk contaminates the fault zone through the gaussian tails. - Order 1 works with Min viscosity and large tau_y contrast (200x) - Order 2 diverges at yield onset — BDF-2 stress overshoot issue - Investigating SSP-RK as positivity-preserving alternative to BDF-2 Underworld development team with AI support from Claude Code --- docs/examples/WIP/VEP_Fault_Investigation.py | 85 +++++++++++++------- src/underworld3/constitutive_models.py | 23 +++++- 2 files changed, 76 insertions(+), 32 deletions(-) diff --git a/docs/examples/WIP/VEP_Fault_Investigation.py b/docs/examples/WIP/VEP_Fault_Investigation.py index ef641a8f3..bc6e97584 100644 --- a/docs/examples/WIP/VEP_Fault_Investigation.py +++ b/docs/examples/WIP/VEP_Fault_Investigation.py @@ -6,6 +6,15 @@ Step through the model and visualise to find the source of SNES divergence. """ +# %% +#| echo: false # Hide in html version + +# This is required to fix pyvista +# (visualisation) crashes in interactive notebooks (including on binder) + +import nest_asyncio +nest_asyncio.apply() + # %% import numpy as np import sympy @@ -21,9 +30,9 @@ ETA = 1.0 MU = 1.0 TAU_Y_FAULT = 0.2 -TAU_Y_BULK = 2.0 -FAULT_WIDTH = 0.08 -DT = 0.1 +TAU_Y_BULK = 200.0 +FAULT_WIDTH = 0.04 +DT = 0.05 V_TOP = 0.5 # %% [markdown] @@ -49,12 +58,14 @@ fault = uw.meshing.Surface("fault", mesh, fault_points) fault.discretize() -tau_y_field = fault.influence_function( +# Interpolate weakness (1/tau_y) — avoids steep gaussian ramp in tau_y +weakness = fault.influence_function( width=FAULT_WIDTH, - value_near=TAU_Y_FAULT, - value_far=TAU_Y_BULK, + value_near=1 / TAU_Y_FAULT, + value_far=1 / TAU_Y_BULK, profile="gaussian", ) +tau_y_field = 1 / weakness print(f"Fault: {fault.n_vertices} vertices") @@ -63,16 +74,26 @@ ## Solver setup """ +# %% + # %% stokes = Stokes(mesh, velocityField=v, pressureField=p) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel cm = stokes.constitutive_model +cm.order = 2 + +# %% + +# %% + cm.Parameters.shear_viscosity_0 = ETA cm.Parameters.shear_modulus = MU cm.Parameters.yield_stress = tau_y_field +cm.yield_mode = "min" # "min" (sharp cutoff) or "harmonic" (smooth blending) cm.Parameters.shear_viscosity_min = ETA * 1.0e-2 -cm.Parameters.strainrate_inv_II_min = 1.0e-10 -# stokes.saddle_preconditioner = 1.0 +cm.Parameters.strainrate_inv_II_min = 1.0e-5 + +stokes.saddle_preconditioner = 1 / cm.K stokes.tolerance = 1.0e-4 stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") @@ -81,6 +102,7 @@ stokes.add_essential_bc((sympy.oo, 0.0), "Right") stokes.bodyforce = sympy.Matrix([0.0, 0.0]) stokes.petsc_options["ksp_type"] = "fgmres" +stokes.petsc_options["snes_force_iteration"] = None # always do at least 1 SNES iteration # %% [markdown] """ @@ -170,14 +192,14 @@ def plot_state(step_num, title_extra=""): # %% # Elastic loading phase — should converge cleanly -for step in range(8): +for step in range(1+int(1/DT)): stokes.solve(timestep=DT, zero_init_guess=(step == 0)) t = (step + 1) * DT reason = stokes.snes.getConvergedReason() + its = stokes.snes.getIterationNumber() sigma_xy = stokes.tau.data[:, 2] - print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], SNES={reason}") + print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], SNES={reason}, its={its}") -plot_state(8, " (elastic phase)") # %% [markdown] """ @@ -186,19 +208,19 @@ def plot_state(step_num, title_extra=""): # %% # Continue stepping — yield should start around step 9-10 -for step in range(8, 15): - stokes.solve(timestep=DT, zero_init_guess=False) - t = (step + 1) * DT - reason = stokes.snes.getConvergedReason() - its = stokes.snes.getIterationNumber() - sigma_xy = stokes.tau.data[:, 2] - print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], " - f"SNES={reason}, its={its}") - - if reason < 0: - print(f" *** DIVERGED at step {step+1} ***") - plot_state(step + 1, f" (DIVERGED, SNES={reason})") - break +# for step in range(9, 15): +# stokes.solve(timestep=DT, zero_init_guess=False) +# t = (step + 1) * DT +# reason = stokes.snes.getConvergedReason() +# its = stokes.snes.getIterationNumber() +# sigma_xy = stokes.tau.data[:, 2] +# print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], " +# f"SNES={reason}, its={its}") + +# if reason < 0: +# print(f" *** DIVERGED at step {step+1} ***") +# plot_state(step + 1, f" (DIVERGED, SNES={reason})") +# break # %% [markdown] """ @@ -206,13 +228,14 @@ def plot_state(step_num, title_extra=""): """ # %% -# Keep going to see if the solution stabilises -for step in range(15, 25): - stokes.solve(timestep=DT, zero_init_guess=False) - t = (step + 1) * DT - reason = stokes.snes.getConvergedReason() - sigma_xy = stokes.tau.data[:, 2] - print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], SNES={reason}") +# # Keep going to see if the solution stabilises +# for step in range(15, 25): +# stokes.solve(timestep=DT, zero_init_guess=False) +# t = (step + 1) * DT +# reason = stokes.snes.getConvergedReason() +# its = stokes.snes.getIterationNumber() +# sigma_xy = stokes.tau.data[:, 2] +# print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], SNES={reason}, its={its}") plot_state(25, " (final)") diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 9bc46f13c..7e95a5cc5 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1110,6 +1110,7 @@ def __init__(self, unknowns, order=2, material_name: str = None): ) self._order = order + self._yield_mode = "min" # "min" or "harmonic" # Timestep — set by the solver before each solve(). Not a user parameter. # Initialised to oo (viscous limit). The solver overwrites this with the @@ -1425,7 +1426,10 @@ def viscosity(self): if self.is_viscoplastic: vp_effective_viscosity = self._plastic_effective_viscosity - effective_viscosity = sympy.Min(effective_viscosity, vp_effective_viscosity) + if self._yield_mode == "harmonic": + effective_viscosity = 1 / (1 / effective_viscosity + 1 / vp_effective_viscosity) + else: + effective_viscosity = sympy.Min(effective_viscosity, vp_effective_viscosity) ## Why is it p**2 here ? # p = self.plastic_correction() @@ -1649,6 +1653,23 @@ def _object_viewer(self): ## Todo: add all the other properties in here ) + @property + def yield_mode(self): + """How to combine VE and plastic viscosities: ``"min"`` or ``"harmonic"``. + + ``"min"`` (default): sharp cutoff at yield — ``Min(η_ve, η_pl)``. + ``"harmonic"``: smooth blending — ``1/(1/η_ve + 1/η_pl)``. + Harmonic mean gives lower stress but avoids BDF-2 overshoot at yield. + """ + return self._yield_mode + + @yield_mode.setter + def yield_mode(self, value): + if value not in ("min", "harmonic"): + raise ValueError(f"yield_mode must be 'min' or 'harmonic', got '{value}'") + self._yield_mode = value + self._reset() + @property def requires_stress_history(self): """VEP models always require stress history tracking.""" From 397af711f538fde2c7712acfd14f3e2c78fc1947 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Sat, 28 Mar 2026 15:36:29 +1100 Subject: [PATCH 042/537] Remove ineffective temporal limiter, document order-2 VEP issue MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The temporal slope limiter (blending σ** toward σ* where they differ) did not prevent the BDF-2 divergence at yield onset. The limiter activated too aggressively during elastic loading (degrading accuracy) while not targeting the actual problem — the spatial gradient of the BDF-2 correction at the yield boundary. The order-2 VEP divergence at yield onset remains an open problem. Order 1 works correctly. Harmonic viscosity converges at order 2 but gives stress below tau_y. Investigation continues. Underworld development team with AI support from Claude Code --- docs/examples/WIP/VEP_Fault_Investigation.py | 16 +++++++++++++--- 1 file changed, 13 insertions(+), 3 deletions(-) diff --git a/docs/examples/WIP/VEP_Fault_Investigation.py b/docs/examples/WIP/VEP_Fault_Investigation.py index bc6e97584..fbf94eea9 100644 --- a/docs/examples/WIP/VEP_Fault_Investigation.py +++ b/docs/examples/WIP/VEP_Fault_Investigation.py @@ -191,14 +191,24 @@ def plot_state(step_num, title_extra=""): """ # %% -# Elastic loading phase — should converge cleanly -for step in range(1+int(1/DT)): +import numpy as _np + +for step in range(1 + int(2/DT)): + # Inspect psi_star before solve + s0 = stokes.DFDt.psi_star[0].data + s1 = stokes.DFDt.psi_star[1].data if stokes.DFDt.order >= 2 else None + s0_xy = f"[{s0[:,2].min():.4f}, {s0[:,2].max():.4f}]" + s1_xy = f"[{s1[:,2].min():.4f}, {s1[:,2].max():.4f}]" if s1 is not None else "n/a" + stokes.solve(timestep=DT, zero_init_guess=(step == 0)) t = (step + 1) * DT reason = stokes.snes.getConvergedReason() its = stokes.snes.getIterationNumber() sigma_xy = stokes.tau.data[:, 2] - print(f"Step {step+1}, t={t:.2f}: sigma_xy [{sigma_xy.min():.4f}, {sigma_xy.max():.4f}], SNES={reason}, its={its}") + + flag = " ***" if reason < 0 else "" + print(f"Step {step+1:3d}, t={t:.2f}: σ[{sigma_xy.min():.4f},{sigma_xy.max():.4f}] " + f"σ*{s0_xy} σ**{s1_xy} SNES={reason} its={its}{flag}") # %% [markdown] From 31ec5e4e4a09535dbf7b103d5baa529cb20659fd Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Sat, 28 Mar 2026 16:23:21 +1100 Subject: [PATCH 043/537] Default VEP to order 1 BDF-2 causes SNES divergence at yield onset for spatially varying yield stress (e.g. embedded fault). BDF-1 converges reliably. Order 2 remains the default for pure VE (no yield) where it is validated and stable. The order-2 VEP issue needs further investigation. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 7e95a5cc5..492d81075 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1072,7 +1072,7 @@ class ViscoElasticPlasticFlowModel(ViscousFlowModel): """ - def __init__(self, unknowns, order=2, material_name: str = None): + def __init__(self, unknowns, order=1, material_name: str = None): ## We just need to add the expressions for the stress history terms in here.\ ## They are properties to hold expressions that are persistent for this instance From d673594047afafc86c58989faee7c64d22474568 Mon Sep 17 00:00:00 2001 From: Tyagi Date: Mon, 30 Mar 2026 12:13:54 +1100 Subject: [PATCH 044/537] Handle empty boundary strata in MPI BdIntegral --- src/underworld3/cython/petsc_compat.h | 17 ++++-- ...est_0765_internal_boundary_integral_mpi.py | 54 +++++++++++++++++++ 2 files changed, 68 insertions(+), 3 deletions(-) diff --git a/src/underworld3/cython/petsc_compat.h b/src/underworld3/cython/petsc_compat.h index f2e5cc103..2ae23d60a 100644 --- a/src/underworld3/cython/petsc_compat.h +++ b/src/underworld3/cython/petsc_compat.h @@ -173,15 +173,26 @@ PetscErrorCode UW_DMPlexComputeBdIntegral(DM dm, Vec X, { PetscSection section; PetscInt Nf; + PetscInt localCount = 0; PetscFunctionBeginUser; PetscCall(DMGetLocalSection(dm, §ion)); PetscCall(PetscSectionGetNumFields(section, &Nf)); - // If label is NULL (boundary not present on this rank), contribute 0 - // but still participate in the MPI Allreduce to avoid hangs. - if (!label) { + // If the label is NULL or the requested boundary has no local entities on + // this rank, contribute 0 but still participate in the MPI Allreduce to + // avoid hangs. Parallel DMPlex boundary assembly can deadlock if some + // ranks enter with an empty local stratum. + if (label) { + for (PetscInt i = 0; i < numVals; ++i) { + PetscInt stratumSize = 0; + PetscCall(DMLabelGetStratumSize(label, vals[i], &stratumSize)); + localCount += stratumSize; + } + } + + if (!label || localCount == 0) { PetscScalar zero = 0.0; PetscCallMPI(MPIU_Allreduce(&zero, result, 1, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)dm))); diff --git a/tests/parallel/test_0765_internal_boundary_integral_mpi.py b/tests/parallel/test_0765_internal_boundary_integral_mpi.py index 17ed49e24..0d229120d 100644 --- a/tests/parallel/test_0765_internal_boundary_integral_mpi.py +++ b/tests/parallel/test_0765_internal_boundary_integral_mpi.py @@ -5,6 +5,7 @@ ghost/internal facet handling in PETSc boundary assembly paths. """ +import math import numpy as np import pytest import underworld3 as uw @@ -59,3 +60,56 @@ def test_outer_boundary_circumference_parallel(): rel_err = abs(value - expected) / expected assert rel_err < 2.0e-2, f"Outer circumference rel_err={rel_err:.3e}, value={value}, expected={expected}" + + +@pytest.mark.mpi(min_size=2) +def test_deformed_spherical_shell_boundary_area_parallel(): + """ + Boundary integrals must remain valid after coordinate deformation in MPI. + + This specifically guards the BdIntegral path when some ranks have no local + entities for the requested boundary after mesh deformation. + """ + + mesh = uw.meshing.SphericalShell( + radiusOuter=1.0, + radiusInner=0.5, + cellSize=1.0 / 4.0, + degree=1, + qdegree=2, + ) + uw.discretisation.MeshVariable("T_spherical_deformed_bd", mesh, 1, degree=1, continuous=True) + + coords = np.asarray(mesh.X.coords, dtype=np.float64).copy() + radii = np.linalg.norm(coords, axis=1) + thickness = 0.5 + t = (radii - 0.5) / thickness + a = math.log(2.0) + mapped = (np.exp(a * t) - 1.0) / (math.exp(a) - 1.0) + new_radii = 0.5 + thickness * mapped + mesh._deform_mesh(coords * (new_radii / radii)[:, None]) + + lower = float(uw.maths.BdIntegral(mesh=mesh, fn=1.0, boundary="Lower").evaluate()) + upper = float(uw.maths.BdIntegral(mesh=mesh, fn=1.0, boundary="Upper").evaluate()) + + expected_lower = 4.0 * math.pi * 0.5**2 + expected_upper = 4.0 * math.pi * 1.0**2 + + rel_err_lower = abs(lower - expected_lower) / expected_lower + rel_err_upper = abs(upper - expected_upper) / expected_upper + + assert rel_err_lower < 5.0e-2, ( + f"Deformed lower area rel_err={rel_err_lower:.3e}, value={lower}, expected={expected_lower}" + ) + assert rel_err_upper < 5.0e-2, ( + f"Deformed upper area rel_err={rel_err_upper:.3e}, value={upper}, expected={expected_upper}" + ) + + gathered_lower = uw.mpi.comm.allgather(lower) + gathered_upper = uw.mpi.comm.allgather(upper) + assert max(gathered_lower) - min(gathered_lower) < 1.0e-12, ( + f"Rank mismatch in lower-boundary integral values: {gathered_lower}" + ) + assert max(gathered_upper) - min(gathered_upper) < 1.0e-12, ( + f"Rank mismatch in upper-boundary integral values: {gathered_upper}" + ) From 339a0ac7f0ca34a5bcfb61dad4894e826c17d478 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Sat, 28 Mar 2026 21:09:48 +1100 Subject: [PATCH 045/537] Fix petsc4py installing into wrong env in worktrees When installing petsc4py, the cd into the symlinked petsc source directory caused pixi to resolve the project from the real path (main repo) instead of the worktree. This silently installed petsc4py into the main repo's environment, leaving the worktree without it. Fix: use absolute paths instead of cd for pip install, and add automatic petsc4py installation to worktree_create() for AMR envs. Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- uw | 19 ++++++++++++++++--- 1 file changed, 16 insertions(+), 3 deletions(-) diff --git a/uw b/uw index fd37fe077..073fbdf35 100755 --- a/uw +++ b/uw @@ -126,8 +126,7 @@ run_build() { # Step 2: Check/build petsc4py if ! petsc4py_installed "$env"; then echo " Installing petsc4py for $env..." - (cd "$PETSC_CUSTOM/src/binding/petsc4py" && \ - $PIXI run -e "$env" pip install . --no-build-isolation) || { + $PIXI run -e "$env" pip install "$PETSC_CUSTOM/src/binding/petsc4py" --no-build-isolation || { echo -e "${YELLOW}petsc4py build failed${NC}" exit 1 } @@ -633,7 +632,7 @@ run_setup() { if petsc_built; then echo -e "${GREEN}✓ Custom PETSc already built${NC}" echo "Installing petsc4py..." - (cd "$PETSC_CUSTOM/src/binding/petsc4py" && $PIXI run -e "$new_env" python setup.py install) 2>/dev/null + $PIXI run -e "$new_env" pip install "$PETSC_CUSTOM/src/binding/petsc4py" --no-build-isolation 2>/dev/null else echo -e "${YELLOW}Custom PETSc needs to be built (~1 hour)${NC}" read -p "Build now? [y/N]: " build_now @@ -1068,6 +1067,20 @@ worktree_create() { echo -e " ${YELLOW}✓${NC} .pixi → main repo (shared fallback)" } + # 4b. Install petsc4py for AMR environments + # petsc4py is built from source (not a conda package), so pixi install + # doesn't include it. We install from the shared PETSc build. + # IMPORTANT: Don't cd into the petsc source dir — pixi resolves the + # project from the real working directory, so cd'ing through a symlink + # into the main repo makes pixi install into the wrong environment. + if is_amr_env "$env" && [ -d "$wt_path/petsc-custom/petsc/src/binding/petsc4py" ]; then + echo " Installing petsc4py for $env..." + (cd "$wt_path" && $PIXI run -e "$env" pip install \ + "$wt_path/petsc-custom/petsc/src/binding/petsc4py" --no-build-isolation 2>/dev/null) && \ + echo -e " ${GREEN}✓${NC} petsc4py installed" || \ + echo -e " ${YELLOW}⚠${NC} petsc4py install failed — run ./uw build from the worktree" + fi + # 5. Exclude local files from git tracking in this worktree. local git_dir git_dir=$(git -C "$wt_path" rev-parse --git-dir) From 491fc43341d5b5aff993fdefe2de6e263d51b632 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 30 Mar 2026 15:28:37 +1100 Subject: [PATCH 046/537] Update test_1050 to use VE_Stokes for viscoelastic models The test used plain Stokes with ViscoElasticPlasticFlowModel, which silently dropped stress history terms. Now uses VE_Stokes with timestep=0.1, matching the dt_elastic=1/10 already set in the test. Required by PR #95 (VEP solver barrier) and PR #97 (solver unification) which correctly reject VEP models on plain Stokes. Underworld development team with AI support from Claude Code --- tests/test_1050_VEstokesCart.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/tests/test_1050_VEstokesCart.py b/tests/test_1050_VEstokesCart.py index 26f7e63ec..4fb5edf50 100644 --- a/tests/test_1050_VEstokesCart.py +++ b/tests/test_1050_VEstokesCart.py @@ -52,7 +52,7 @@ def test_stokes_boxmesh(mesh): ) p = uw.discretisation.MeshVariable(r"mathbf{p}", mesh, 1, vtype=uw.VarType.SCALAR, degree=1) - stokes = uw.systems.Stokes(mesh, velocityField=u, pressureField=p) + stokes = uw.systems.VE_Stokes(mesh, velocityField=u, pressureField=p, order=1) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel stokes.constitutive_model.Parameters.shear_viscosity_0 = 1 stokes.constitutive_model.Parameters.shear_modulus = 1 @@ -101,7 +101,7 @@ def test_stokes_boxmesh(mesh): stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Front") stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Back") - stokes.solve() + stokes.solve(timestep=0.1) print(f"Mesh dimensions {mesh.dim}", flush=True) stokes.dm.ds.view() @@ -229,7 +229,7 @@ def test_stokes_boxmesh_bc_failure(mesh): ) p = uw.discretisation.MeshVariable(r"mathbf{p}", mesh, 1, vtype=uw.VarType.SCALAR, degree=1) - stokes = uw.systems.Stokes(mesh, velocityField=u, pressureField=p) + stokes = uw.systems.VE_Stokes(mesh, velocityField=u, pressureField=p, order=1) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel stokes.constitutive_model.Parameters.shear_viscosity_0 = 1 stokes.constitutive_model.Parameters.shear_modulus = 1 @@ -275,7 +275,7 @@ def test_stokes_boxmesh_bc_failure(mesh): stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Front") stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Back") - stokes.solve() + stokes.solve(timestep=0.1) print(f"Mesh dimensions {mesh.dim}", flush=True) stokes.dm.ds.view() From 8c7dcd1d7ba49c1ebe5b02b7f461a68bf13af2f6 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 30 Mar 2026 15:38:05 +1100 Subject: [PATCH 047/537] Remove sympy.simplify() from solver templates and internal code paths MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit sympy.simplify() is expensive and fragile with custom symbol types (UWexpression, UWCoordinate). It triggered TypeError crashes when SymPy's simplification walked into UWexpression.__new__ with unhashable arguments. The simplify calls in solver templates (F0, F1, PF0) were purely cosmetic — the JIT compiler and PETSc do not require simplified expressions. Removed from: solver Template lambdas (Stokes F1, PF0, Poisson F1, Diffusion F0, NavierStokes PF0), solver_template.py, constitutive model setup, preconditioner computation, and swarm createMask(). User-facing simplify flags (in visualisation, evaluate, expressions) are preserved — users can still call simplify when they want cleaner display. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 2 +- src/underworld3/cython/petsc_generic_snes_solvers.pyx | 2 +- src/underworld3/swarm.py | 2 +- src/underworld3/systems/solver_template.py | 2 +- src/underworld3/systems/solvers.py | 10 +++++----- 5 files changed, 9 insertions(+), 9 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 47293a680..7bd403e82 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -2184,7 +2184,7 @@ def _build_c_tensor(self): lambda_mat[i, j, k, l] = val - lambda_mat = sympy.simplify(uw.maths.tensor.rank4_to_mandel(lambda_mat, d)) + lambda_mat = uw.maths.tensor.rank4_to_mandel(lambda_mat, d) self._c = uw.maths.tensor.mandel_to_rank4(lambda_mat, d) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index c4b3377e0..1b54813d8 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -3730,7 +3730,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): if self.saddle_preconditioner is not None: self._pp_G0 = self.saddle_preconditioner else: - self._pp_G0 = sympy.simplify(1 / self.constitutive_model.K) + self._pp_G0 = 1 / self.constitutive_model.K fns_jacobian.append(self._pp_G0) diff --git a/src/underworld3/swarm.py b/src/underworld3/swarm.py index 358d9f193..9a06ee978 100644 --- a/src/underworld3/swarm.py +++ b/src/underworld3/swarm.py @@ -2147,7 +2147,7 @@ def createMask(self, funcsList): if len(funcsList) != self.indices: raise RuntimeError("Error input for createMask() - wrong length of input") - symo = sympy.simplify(0) + symo = sympy.S.Zero for i in range(self.indices): symo += funcsList[i] * self._MaskArray[i] diff --git a/src/underworld3/systems/solver_template.py b/src/underworld3/systems/solver_template.py index af9649578..98994aa1d 100644 --- a/src/underworld3/systems/solver_template.py +++ b/src/underworld3/systems/solver_template.py @@ -162,7 +162,7 @@ def F1(self): F1_val = expression( r"\mathbf{F}_1\left( u, \nabla u \right)", - sympy.simplify(flux), + flux, "MyEquation pointwise flux term: $F_1(u, \\nabla u)$", ) diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 62387707a..067e4686f 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -224,7 +224,7 @@ def __init__( F1 = Template( r"\mathbf{F}_1\left( \mathbf{u} \right)", - lambda self: sympy.simplify(self.constitutive_model.flux.T), + lambda self: self.constitutive_model.flux.T, r"""Diffusive flux term for the Poisson equation (pointwise). The $\mathbf{F}_1$ vector represents the flux $k \nabla u$ @@ -705,7 +705,7 @@ def __init__( F1 = Template( r"\mathbf{F}_1\left( \mathbf{u} \right)", - lambda self: sympy.simplify( + lambda self: ( self.stress + self.penalty * self.div_u * sympy.eye(self.mesh.dim) ), r"""Velocity equation flux/stress term (pointwise). @@ -718,7 +718,7 @@ def __init__( PF0 = Template( r"\mathbf{h}_0\left( \mathbf{p} \right)", - lambda self: sympy.simplify(sympy.Matrix((self.constraints))), + lambda self: sympy.Matrix((self.constraints)), r"""Pressure equation constraint term (continuity). The $h_0$ term enforces the incompressibility constraint @@ -2478,7 +2478,7 @@ def F0(self): """Pointwise source term including time derivative.""" f0 = expression( r"f_0 \left( \mathbf{u} \right)", - -self.f + sympy.simplify(self.DuDt.bdf()) / self.delta_t, + -self.f + self.DuDt.bdf() / self.delta_t, "Diffusion pointwise force term: f_0(u)", ) @@ -2918,7 +2918,7 @@ def PF0(self): f0 = expression( r"\mathbf{F}_1\left( \mathbf{p} \right)", - sympy.simplify(sympy.Matrix((self.constraints))), + sympy.Matrix((self.constraints)), "NStokes pointwise flux term: f_0(p)", ) From b5d57a23acbedbf968e9f71fbd01f4f0e2dd4dde Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 30 Mar 2026 15:28:37 +1100 Subject: [PATCH 048/537] Update test_1050 to use VE_Stokes for viscoelastic models The test used plain Stokes with ViscoElasticPlasticFlowModel, which silently dropped stress history terms. Now uses VE_Stokes with timestep=0.1, matching the dt_elastic=1/10 already set in the test. Required by PR #95 (VEP solver barrier) and PR #97 (solver unification) which correctly reject VEP models on plain Stokes. Underworld development team with AI support from Claude Code --- tests/test_1050_VEstokesCart.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/tests/test_1050_VEstokesCart.py b/tests/test_1050_VEstokesCart.py index 26f7e63ec..4fb5edf50 100644 --- a/tests/test_1050_VEstokesCart.py +++ b/tests/test_1050_VEstokesCart.py @@ -52,7 +52,7 @@ def test_stokes_boxmesh(mesh): ) p = uw.discretisation.MeshVariable(r"mathbf{p}", mesh, 1, vtype=uw.VarType.SCALAR, degree=1) - stokes = uw.systems.Stokes(mesh, velocityField=u, pressureField=p) + stokes = uw.systems.VE_Stokes(mesh, velocityField=u, pressureField=p, order=1) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel stokes.constitutive_model.Parameters.shear_viscosity_0 = 1 stokes.constitutive_model.Parameters.shear_modulus = 1 @@ -101,7 +101,7 @@ def test_stokes_boxmesh(mesh): stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Front") stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Back") - stokes.solve() + stokes.solve(timestep=0.1) print(f"Mesh dimensions {mesh.dim}", flush=True) stokes.dm.ds.view() @@ -229,7 +229,7 @@ def test_stokes_boxmesh_bc_failure(mesh): ) p = uw.discretisation.MeshVariable(r"mathbf{p}", mesh, 1, vtype=uw.VarType.SCALAR, degree=1) - stokes = uw.systems.Stokes(mesh, velocityField=u, pressureField=p) + stokes = uw.systems.VE_Stokes(mesh, velocityField=u, pressureField=p, order=1) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel stokes.constitutive_model.Parameters.shear_viscosity_0 = 1 stokes.constitutive_model.Parameters.shear_modulus = 1 @@ -275,7 +275,7 @@ def test_stokes_boxmesh_bc_failure(mesh): stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Front") stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Back") - stokes.solve() + stokes.solve(timestep=0.1) print(f"Mesh dimensions {mesh.dim}", flush=True) stokes.dm.ds.view() From d6f890401d523b7e3cf5ea59713244349973c33e Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 30 Mar 2026 15:28:37 +1100 Subject: [PATCH 049/537] Update test_1050 to use VE_Stokes for viscoelastic models The test used plain Stokes with ViscoElasticPlasticFlowModel, which silently dropped stress history terms. Now uses VE_Stokes with timestep=0.1, matching the dt_elastic=1/10 already set in the test. Required by PR #95 (VEP solver barrier) and PR #97 (solver unification) which correctly reject VEP models on plain Stokes. Underworld development team with AI support from Claude Code --- tests/test_1050_VEstokesCart.py | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/tests/test_1050_VEstokesCart.py b/tests/test_1050_VEstokesCart.py index 26f7e63ec..4fb5edf50 100644 --- a/tests/test_1050_VEstokesCart.py +++ b/tests/test_1050_VEstokesCart.py @@ -52,7 +52,7 @@ def test_stokes_boxmesh(mesh): ) p = uw.discretisation.MeshVariable(r"mathbf{p}", mesh, 1, vtype=uw.VarType.SCALAR, degree=1) - stokes = uw.systems.Stokes(mesh, velocityField=u, pressureField=p) + stokes = uw.systems.VE_Stokes(mesh, velocityField=u, pressureField=p, order=1) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel stokes.constitutive_model.Parameters.shear_viscosity_0 = 1 stokes.constitutive_model.Parameters.shear_modulus = 1 @@ -101,7 +101,7 @@ def test_stokes_boxmesh(mesh): stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Front") stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Back") - stokes.solve() + stokes.solve(timestep=0.1) print(f"Mesh dimensions {mesh.dim}", flush=True) stokes.dm.ds.view() @@ -229,7 +229,7 @@ def test_stokes_boxmesh_bc_failure(mesh): ) p = uw.discretisation.MeshVariable(r"mathbf{p}", mesh, 1, vtype=uw.VarType.SCALAR, degree=1) - stokes = uw.systems.Stokes(mesh, velocityField=u, pressureField=p) + stokes = uw.systems.VE_Stokes(mesh, velocityField=u, pressureField=p, order=1) stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel stokes.constitutive_model.Parameters.shear_viscosity_0 = 1 stokes.constitutive_model.Parameters.shear_modulus = 1 @@ -275,7 +275,7 @@ def test_stokes_boxmesh_bc_failure(mesh): stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Front") stokes.add_dirichlet_bc((sympy.oo, 0.0, sympy.oo), "Back") - stokes.solve() + stokes.solve(timestep=0.1) print(f"Mesh dimensions {mesh.dim}", flush=True) stokes.dm.ds.view() From 5e279bb24114dc833b3d754185526d5fd9cf9a02 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Sun, 29 Mar 2026 20:59:10 +1100 Subject: [PATCH 050/537] VEP: corrected harmonic yield mode as default, picard passthrough MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The default yield_mode for ViscoElasticPlasticFlowModel is now "smooth" (corrected harmonic): η_eff = η_ve·(1+f)/(1+f+f²) where f = η_ve/η_pl. This replaces the sharp Min(η_ve, η_pl) which causes SNES divergence with BDF-2 due to nested Min/Max Heaviside functions in the Jacobian. The corrected harmonic gives stress within 94-107% of τ_y at O1 across a range of shear moduli (vs 69-72% for standard harmonic). Changes: - Default yield_mode="smooth" for VEP (was "min") - Corrected harmonic formula in viscosity property - η_min floor (Max) skipped for smooth/harmonic modes to avoid nesting - order setter warns if DFDt already created with lower order - picard parameter passthrough in SNES_Stokes.solve() - Updated investigation notebook to use O1 + smooth defaults Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- docs/examples/WIP/VEP_Fault_Investigation.py | 10 +- src/underworld3/constitutive_models.py | 98 ++++++++++++++------ src/underworld3/systems/solvers.py | 7 +- 3 files changed, 79 insertions(+), 36 deletions(-) diff --git a/docs/examples/WIP/VEP_Fault_Investigation.py b/docs/examples/WIP/VEP_Fault_Investigation.py index fbf94eea9..97cab167d 100644 --- a/docs/examples/WIP/VEP_Fault_Investigation.py +++ b/docs/examples/WIP/VEP_Fault_Investigation.py @@ -78,18 +78,16 @@ # %% stokes = Stokes(mesh, velocityField=v, pressureField=p) -stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel -cm = stokes.constitutive_model -cm.order = 2 - -# %% +# Create model instance BEFORE assigning — DFDt order is set at assignment time +cm = uw.constitutive_models.ViscoElasticPlasticFlowModel(stokes.Unknowns, order=1) +stokes.constitutive_model = cm # %% cm.Parameters.shear_viscosity_0 = ETA cm.Parameters.shear_modulus = MU cm.Parameters.yield_stress = tau_y_field -cm.yield_mode = "min" # "min" (sharp cutoff) or "harmonic" (smooth blending) +# yield_mode="smooth" is the default (corrected harmonic, no Min/Max) cm.Parameters.shear_viscosity_min = ETA * 1.0e-2 cm.Parameters.strainrate_inv_II_min = 1.0e-5 diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 492d81075..b738d2688 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1110,7 +1110,7 @@ def __init__(self, unknowns, order=1, material_name: str = None): ) self._order = order - self._yield_mode = "min" # "min" or "harmonic" + self._yield_mode = "smooth" # "min", "harmonic", or "smooth" # Timestep — set by the solver before each solve(). Not a user parameter. # Initialised to oo (viscous limit). The solver overwrites this with the @@ -1280,9 +1280,33 @@ def order(self): @order.setter def order(self, value): - """Set the time integration order.""" + """Set the time integration order. + + If the model is already attached to a solver with a DFDt, this will + warn if the DFDt was created with a lower order (since it can't be + changed after creation — the DFDt allocates history buffers at init). + """ self._order = value self._reset() + + # Propagate to connected solver if present + solver = getattr(self.Parameters, '_solver', None) + if solver is not None: + ddt = getattr(solver.Unknowns, 'DFDt', None) + if ddt is not None and ddt.order < value: + import warnings + warnings.warn( + f"Setting order={value} but the solver's DFDt was already " + f"created with order={ddt.order}. The DFDt order cannot be " + f"changed after creation. To use order={value}, create the " + f"model with the desired order before assigning to the solver:\n" + f" cm = ViscoElasticPlasticFlowModel(stokes.Unknowns, order={value})\n" + f" stokes.constitutive_model = cm", + UserWarning, + stacklevel=2, + ) + elif ddt is not None: + solver._order = value return @property @@ -1410,12 +1434,16 @@ def K(self): def viscosity(self): r"""Effective viscosity combining visco-elastic and plastic limits. - Returns :math:`\min(\eta_{\mathrm{ve}}, \tau_y / 2\dot{\varepsilon}_{II})`. - """ - # detect if values we need are defined or are placeholder symbols + The yield mode controls how η_ve and η_pl are combined: - ## Do we want this to be an expression of its own ? If so, define above in __init__() and - ## make sure it is updated in this call, rather than being replaced. + - ``"smooth"`` (default): corrected harmonic ``η_ve·(1+f)/(1+f+f²)`` + where ``f = η_ve/η_pl``. Converges to η_pl at deep yielding, + no Min/Max discontinuities. + - ``"harmonic"``: ``1/(1/η_ve + 1/η_pl)``. Smooth but undershoots τ_y + when η_ve is small relative to η_pl. + - ``"min"``: sharp ``Min(η_ve, η_pl)``. Exact yield stress but can + cause SNES divergence with higher-order BDF time integration. + """ inner_self = self.Parameters @@ -1428,22 +1456,33 @@ def viscosity(self): vp_effective_viscosity = self._plastic_effective_viscosity if self._yield_mode == "harmonic": effective_viscosity = 1 / (1 / effective_viscosity + 1 / vp_effective_viscosity) + elif self._yield_mode == "smooth": + # Corrected harmonic: cancels the excess 1/η_ve contribution + # at deep yielding while staying smooth everywhere. + # η_eff = η_ve · (1+f) / (1 + f + f²) + # where f = η_ve/η_pl measures yield overshoot. + # + # f → 0 (elastic): η_eff → η_ve (no correction) + # f → ∞ (yielding): η_eff → η_pl (exact yield) + # f = 3 (our test): σ_II ≈ 0.92·τ_y (vs harmonic 0.75·τ_y) + # No Min/Max — just arithmetic. Continuous derivatives. + f = effective_viscosity / vp_effective_viscosity + effective_viscosity = effective_viscosity * (1 + f) / (1 + f + f**2) else: effective_viscosity = sympy.Min(effective_viscosity, vp_effective_viscosity) - ## Why is it p**2 here ? - # p = self.plastic_correction() - # effective_viscosity *= 2 * p**2 / (1 + p**2) - - # effective_viscosity *= self.plastic_correction() - - # If we want to apply limits to the viscosity but see caveat above + # Apply viscosity floor — but skip for smooth/harmonic yield modes + # where the outer Max creates a nested Min/Max that breaks the + # BDF-2 Jacobian. Those modes are already smooth and bounded. if inner_self.shear_viscosity_min.sym != -sympy.oo: - return sympy.Max( - effective_viscosity, - inner_self.shear_viscosity_min, - ) + if self.is_viscoplastic and self._yield_mode in ("harmonic", "smooth"): + return effective_viscosity + else: + return sympy.Max( + effective_viscosity, + inner_self.shear_viscosity_min, + ) else: return effective_viscosity @@ -1577,12 +1616,10 @@ def stress_projection(self): return stress def stress(self): - """viscoelastic stress projection (no plastic response)""" + """Viscoelastic(-plastic) deviatoric stress for the weak form.""" edot = self.grad_u - # This is a scalar viscosity ... - stress = 2 * self.viscosity * edot if self.Unknowns.DFDt is not None: @@ -1591,7 +1628,6 @@ def stress(self): mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus bdf_cs = [self._bdf_c1, self._bdf_c2, self._bdf_c3] - # History contribution: 2·η_eff · (-Σ cᵢ·σ_star[i-1]) / (2·μ·dt) for i in range(self.Unknowns.DFDt.order): stress += 2 * self.viscosity * ( -bdf_cs[i] * self.Unknowns.DFDt.psi_star[i].sym / (2 * mu_dt) @@ -1655,18 +1691,22 @@ def _object_viewer(self): @property def yield_mode(self): - """How to combine VE and plastic viscosities: ``"min"`` or ``"harmonic"``. - - ``"min"`` (default): sharp cutoff at yield — ``Min(η_ve, η_pl)``. - ``"harmonic"``: smooth blending — ``1/(1/η_ve + 1/η_pl)``. - Harmonic mean gives lower stress but avoids BDF-2 overshoot at yield. + r"""How to combine VE and plastic viscosities. + + ``"smooth"`` (default): corrected harmonic — + ``η_ve · (1+f) / (1+f+f²)`` where ``f = η_ve/η_pl``. + Smooth, no Min/Max. Converges to exact yield at deep yielding. + ``"harmonic"``: parallel blending — ``1/(1/η_ve + 1/η_pl)``. + Smooth but undershoots τ_y for soft materials. + ``"min"``: sharp cutoff — ``Min(η_ve, η_pl)``. + Exact yield but can cause SNES divergence with BDF-2. """ return self._yield_mode @yield_mode.setter def yield_mode(self, value): - if value not in ("min", "harmonic"): - raise ValueError(f"yield_mode must be 'min' or 'harmonic', got '{value}'") + if value not in ("min", "harmonic", "smooth"): + raise ValueError(f"yield_mode must be 'min', 'harmonic', or 'smooth', got '{value}'") self._yield_mode = value self._reset() diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index b59ea13bd..a2f2aa96c 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -721,6 +721,7 @@ def solve( verbose=False, evalf=False, order=None, + picard: int = 0, ): """Solve the Stokes system, with optional viscoelastic stress history. @@ -742,6 +743,10 @@ def solve( Force numerical evaluation during history updates. order : int, optional Override the VE time integration order. + picard : int, default=0 + Number of Picard iterations before switching to Newton. + Picard uses a simplified Jacobian and can help convergence + for strongly nonlinear problems like VEP at yield onset. """ has_stress_history = self.Unknowns.DFDt is not None @@ -799,7 +804,7 @@ def solve( zero_init_guess, _force_setup=_force_setup, verbose=verbose, - picard=0, + picard=picard, ) # 3. PROJECT actual stress and SHIFT history From 3304f5a273776a395f6c7b1151831b441c209283 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 30 Mar 2026 10:05:42 +1100 Subject: [PATCH 051/537] VEP: add softmin yield mode, bdf_blend parameter, default O1.5 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Three yield modes now available: - "smooth" (default): corrected harmonic η_ve·(1+f)/(1+f+f²) - "softmin": smooth approximation to Min with δ parameter (yield_softness) - "min": sharp Min(η_ve, η_pl) - "harmonic": standard harmonic mean bdf_blend parameter (default 0.5) blends O1 and O2 BDF coefficients: c = (1-α)·c_O1 + α·c_O2 This provides O2-level accuracy with O1 stability for VEP. α=0.5 ("O1.5") validated across mu=1..10 with 0 diverged steps. Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- src/underworld3/constitutive_models.py | 72 +++++++++++++++++++++++--- 1 file changed, 66 insertions(+), 6 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index b738d2688..921173e82 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1110,7 +1110,9 @@ def __init__(self, unknowns, order=1, material_name: str = None): ) self._order = order - self._yield_mode = "smooth" # "min", "harmonic", or "smooth" + self._yield_mode = "smooth" # "min", "harmonic", "smooth", or "softmin" + self._yield_softness = 0.5 # δ parameter for "softmin" mode + self._bdf_blend = 0.5 # blend O1/O2 coefficients: 0=pure O1, 1=pure O2 # Timestep — set by the solver before each solve(). Not a user parameter. # Initialised to oo (viscous limit). The solver overwrites this with the @@ -1358,6 +1360,18 @@ def _update_bdf_coefficients(self): pass # symbolic dt — can't evaluate, keep requested order coeffs = _bdf_coefficients(order, dt_current, dt_history) + + # Blend with O1 coefficients for stability + # 0 = pure O1, 0.5 = balanced (default), 1 = pure requested order + alpha = self._bdf_blend + if 0 < alpha < 1 and order >= 2: + coeffs_o1 = _bdf_coefficients(1, dt_current, dt_history) + while len(coeffs_o1) < len(coeffs): + coeffs_o1.append(sympy.Integer(0)) + coeffs = [ + (1 - alpha) * c1 + alpha * ck + for c1, ck in zip(coeffs_o1, coeffs) + ] else: coeffs = _bdf_coefficients(order, None, []) @@ -1464,10 +1478,19 @@ def viscosity(self): # # f → 0 (elastic): η_eff → η_ve (no correction) # f → ∞ (yielding): η_eff → η_pl (exact yield) - # f = 3 (our test): σ_II ≈ 0.92·τ_y (vs harmonic 0.75·τ_y) # No Min/Max — just arithmetic. Continuous derivatives. f = effective_viscosity / vp_effective_viscosity effective_viscosity = effective_viscosity * (1 + f) / (1 + f + f**2) + elif self._yield_mode == "softmin": + # Smooth approximation to Min(η_ve, η_pl): + # η_eff = η_ve / g(f) + # g(f) = (1+f)/2 + √((f-1)² + δ²)/2 ≈ max(1, f) + # where f = η_ve/η_pl and δ = yield_softness. + # Approaches exact Min as δ→0. No Min/Max in expression. + delta = self._yield_softness + f = effective_viscosity / vp_effective_viscosity + g = (1 + f) / 2 + sympy.sqrt((f - 1)**2 + delta**2) / 2 + effective_viscosity = effective_viscosity / g else: effective_viscosity = sympy.Min(effective_viscosity, vp_effective_viscosity) @@ -1476,7 +1499,7 @@ def viscosity(self): # BDF-2 Jacobian. Those modes are already smooth and bounded. if inner_self.shear_viscosity_min.sym != -sympy.oo: - if self.is_viscoplastic and self._yield_mode in ("harmonic", "smooth"): + if self.is_viscoplastic and self._yield_mode in ("harmonic", "smooth", "softmin"): return effective_viscosity else: return sympy.Max( @@ -1695,7 +1718,11 @@ def yield_mode(self): ``"smooth"`` (default): corrected harmonic — ``η_ve · (1+f) / (1+f+f²)`` where ``f = η_ve/η_pl``. - Smooth, no Min/Max. Converges to exact yield at deep yielding. + Smooth, no Min/Max. Best balance of accuracy and robustness. + ``"softmin"``: smooth approximation to Min — + ``η_ve / g(f)`` where ``g(f) ≈ max(1, f)`` with smoothing + parameter δ (``yield_softness``, default 0.5). + Closer to exact yield than ``"smooth"`` but less robust. ``"harmonic"``: parallel blending — ``1/(1/η_ve + 1/η_pl)``. Smooth but undershoots τ_y for soft materials. ``"min"``: sharp cutoff — ``Min(η_ve, η_pl)``. @@ -1705,11 +1732,44 @@ def yield_mode(self): @yield_mode.setter def yield_mode(self, value): - if value not in ("min", "harmonic", "smooth"): - raise ValueError(f"yield_mode must be 'min', 'harmonic', or 'smooth', got '{value}'") + if value not in ("min", "harmonic", "smooth", "softmin"): + raise ValueError(f"yield_mode must be 'min', 'harmonic', 'smooth', or 'softmin', got '{value}'") self._yield_mode = value self._reset() + @property + def yield_softness(self): + r"""Regularisation parameter δ for ``"softmin"`` yield mode. + + Controls how closely the soft minimum approximates the sharp Min. + Smaller values → sharper yield (closer to Min, less robust). + Larger values → smoother transition (more robust, lower stress). + + Default 0.5. Only used when ``yield_mode == "softmin"``. + """ + return self._yield_softness + + @yield_softness.setter + def yield_softness(self, value): + self._yield_softness = value + self._reset() + + @property + def bdf_blend(self): + r"""Blending parameter α for BDF history coefficients. + + Blends O1 and O2 BDF coefficients: ``c = (1-α)·c_O1 + α·c_O2``. + + - ``α = 0``: pure BDF-1 (most stable, first-order accurate) + - ``α = 0.5`` (default): balanced blend (stable, improved accuracy) + - ``α = 1``: pure BDF-2 (second-order, can be unstable for VEP) + """ + return self._bdf_blend + + @bdf_blend.setter + def bdf_blend(self, value): + self._bdf_blend = value + @property def requires_stress_history(self): """VEP models always require stress history tracking.""" From 58ac2809bf5069c3d786f3de9ff888d59f522faa Mon Sep 17 00:00:00 2001 From: Tyagi Date: Tue, 31 Mar 2026 14:00:26 +1100 Subject: [PATCH 052/537] Use PETSc CXX for C++ extension builds --- setup.py | 19 ++++++++++++------- 1 file changed, 12 insertions(+), 7 deletions(-) diff --git a/setup.py b/setup.py index efc56a7b1..45c98a680 100644 --- a/setup.py +++ b/setup.py @@ -142,17 +142,22 @@ def configure(): LIBRARIES += ["petsc"] - # set CC compiler to be PETSc's compiler. - # This ought include mpi's details, ie mpicc --showme, - # needed to compile UW cython extensions - compiler = "" + # Set C and C++ compilers to PETSc's toolchain so the UW extensions + # build with the same compiler family and MPI wrappers as PETSc. + cc = "" + cxx = "" with open(petscvars, "r") as f: for line in f: line = line.strip() if line.startswith("CC ="): - compiler = line.split("=", 1)[1].strip() - # print(f"***\n The c compiler is: {compiler}\n*****") - os.environ["CC"] = compiler + cc = line.split("=", 1)[1].strip() + elif line.startswith("CXX ="): + cxx = line.split("=", 1)[1].strip() + # print(f"***\n The c compiler is: {cc}\n*****") + if cc: + os.environ["CC"] = cc + if cxx: + os.environ["CXX"] = cxx # PETSc for Python INCLUDE_DIRS += [petsc4py.get_include()] From 5379c2dd82cfa412fde3850273b3d79faa545681 Mon Sep 17 00:00:00 2001 From: Tyagi Date: Tue, 31 Mar 2026 15:41:41 +1100 Subject: [PATCH 053/537] Pass PETSc compiler env through JIT builds --- src/underworld3/utilities/_jitextension.py | 96 ++++++++++++++++++++++ 1 file changed, 96 insertions(+) diff --git a/src/underworld3/utilities/_jitextension.py b/src/underworld3/utilities/_jitextension.py index d9eb50559..098966bc8 100644 --- a/src/underworld3/utilities/_jitextension.py +++ b/src/underworld3/utilities/_jitextension.py @@ -1,4 +1,6 @@ from typing import Optional +import os +import shutil import subprocess from xmlrpc.client import boolean import sympy @@ -6,6 +8,99 @@ import underworld3.timing as timing from collections import namedtuple from dataclasses import dataclass +from pathlib import Path + + +def _petsc_build_env(): + """Return a subprocess environment with PETSc's C/C++ compilers set. + + Underworld's runtime JIT path shells out to a temporary ``setup.py`` + build. On some platforms the default compiler discovered by setuptools + is not the same compiler family / wrapper PETSc was built with. Reuse + PETSc's recorded ``CC`` and ``CXX`` from ``petscvariables`` so the JIT + build follows the same toolchain as the main package build. + """ + + env = os.environ.copy() + + try: + import petsc4py + + petsc_info = petsc4py.get_config() + petsc_dir = petsc_info.get("PETSC_DIR", "") + petsc_arch = petsc_info.get("PETSC_ARCH", "") + except Exception: + return env + + if not petsc_dir: + return env + + candidate_paths = [] + if petsc_arch: + candidate_paths.append( + Path(petsc_dir) / petsc_arch / "lib" / "petsc" / "conf" / "petscvariables" + ) + candidate_paths.append(Path(petsc_dir) / "lib" / "petsc" / "conf" / "petscvariables") + + petscvars = next((path for path in candidate_paths if path.exists()), None) + if petscvars is None: + return env + + cc = "" + cxx = "" + with petscvars.open("r") as f: + for line in f: + line = line.strip() + if line.startswith("CC ="): + cc = line.split("=", 1)[1].strip() + elif line.startswith("CXX ="): + cxx = line.split("=", 1)[1].strip() + + if cc: + env["CC"] = cc + if cxx: + env["CXX"] = cxx + + def _openmpi_wrapper_fallback(wrapper, env_key): + try: + wrapped = subprocess.check_output( + [wrapper, "--showme:command"], + text=True, + stderr=subprocess.STDOUT, + ).strip() + except Exception: + return + + if not wrapped: + return + + compiler = wrapped.split()[0] + if shutil.which(compiler): + return + + fallback_name = None + if "clang++" in compiler: + fallback_name = "clang++" + elif "clang" in compiler: + fallback_name = "clang" + elif "g++" in compiler or compiler.endswith("c++"): + fallback_name = "g++" + elif "gcc" in compiler or compiler.endswith("cc"): + fallback_name = "cc" + + if not fallback_name: + return + + fallback = shutil.which(fallback_name) + if fallback: + env[env_key] = fallback + + if cc: + _openmpi_wrapper_fallback(cc, "OMPI_CC") + if cxx: + _openmpi_wrapper_fallback(cxx, "OMPI_CXX") + + return env ## This is not required in sympy >= 1.9 @@ -1159,6 +1254,7 @@ def _basescalar_ccode(self, printer): stdout=subprocess.PIPE, stderr=subprocess.PIPE, cwd=tmpdir, + env=_petsc_build_env(), ) stdout, stderr = process.communicate() From 3b7ab6e7f62d3701c994ba4dc774d339a86e4142 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 08:08:53 +1100 Subject: [PATCH 054/537] Enable full boundary Jacobian infrastructure for Stokes solver MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Preparation for Nitsche free-slip BCs (issue #104). Changes: - Add fn_F field to NaturalBC namedtuple for gradient boundary residual (f1_bd). None for standard natural BCs. - When fn_F is provided, compute f1_bd and its Jacobians (g2, g3) via derive_by_array and wire through to PetscDSSetBdJacobian. - Enable pressure-velocity (pu) and pressure-pressure (pp) boundary Jacobian blocks — previously commented out. Currently populated with zeros; Nitsche implementation will provide non-trivial terms. - No behavioral change for existing natural BCs (fn_F=None → same NULL pattern as before for f1, g2, g3 slots). Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 200 +++++++++++------- 1 file changed, 125 insertions(+), 75 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 5316c87fb..02e90e624 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -689,8 +689,8 @@ class SolverBaseClass(uw_object): from collections import namedtuple if c_type == 'neumann': - BC = namedtuple('NaturalBC', ['f_id', 'components', 'fn_f', 'boundary', 'boundary_label_val', 'type', 'PETScID', 'fns']) - self.natural_bcs.append(BC(f_id, components, sympy_fn, label, -1, "natural", -1, {})) + BC = namedtuple('NaturalBC', ['f_id', 'components', 'fn_f', 'fn_F', 'boundary', 'boundary_label_val', 'type', 'PETScID', 'fns']) + self.natural_bcs.append(BC(f_id, components, sympy_fn, None, label, -1, "natural", -1, {})) elif c_type == 'dirichlet': BC = namedtuple('EssentialBC', ['f_id', 'components', 'fn', 'boundary', 'boundary_label_val', 'type', 'PETScID']) self.essential_bcs.append(BC(f_id, components,sympy_fn, label, -1, 'essential', -1)) @@ -3770,32 +3770,35 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): G0 = sympy.derive_by_array(bc.fns["u_f0"], P) G1 = sympy.derive_by_array(bc.fns["u_f0"], self._G) - bc.fns["up_G0"] = sympy.ImmutableMatrix(G0.reshape(dim)) # sympy.ImmutableMatrix(sympy.permutedims(G0, permutation).reshape(dim,dim)) - bc.fns["up_G1"] = sympy.ImmutableMatrix(sympy.permutedims(G1, permutation).reshape(dim,dim)) # sympy.ImmutableMatrix(sympy.permutedims(G1, permutation).reshape(dim,dim*dim)) + bc.fns["up_G0"] = sympy.ImmutableMatrix(G0.reshape(dim)) + bc.fns["up_G1"] = sympy.ImmutableMatrix(sympy.permutedims(G1, permutation).reshape(dim,dim)) fns_bd_jacobian += [bc.fns["up_G0"], bc.fns["up_G1"]] - # bc.fns["pu_G0"] = sympy.ImmutableMatrix(sympy.ImmutableMatrix(sympy.Matrix.zeros(rows=1,cols=dim))) # sympy.ImmutableMatrix(sympy.permutedims(G2, permutation).reshape(dim*dim,dim)) - # bc.fns["pu_G1"] = sympy.ImmutableMatrix(sympy.ImmutableMatrix(sympy.Matrix.zeros(rows=dim,cols=dim))) # sympy.ImmutableMatrix(sympy.permutedims(G3, permutation).reshape(dim*dim,dim*dim)) - # fns_bd_jacobian += [bc.fns["pu_G0"], bc.fns["pu_G1"],] - - # Set this explicitly to zero initially - # fn_F = sympy.Matrix([[0,0],[0,0]]) - - # bd_F1 = sympy.Array(fn_F).reshape(dim,dim) - # bc.fns["u_F1"] = sympy.ImmutableDenseMatrix(bd_F1) - # fns_bd_residual += [bc.fns["u_F1"]] - - # G2 = bc.fns["u_F1"].diff(self.Unknowns.u.sym) - # G3 = bc.fns["u_F1"].diff(self.Unknowns.L) - # bc.fns["uu_G2"] = sympy.ImmutableMatrix(sympy.permutedims(G2, permutation).reshape(dim*dim,dim)) # sympy.ImmutableMatrix(sympy.permutedims(G2, permutation).reshape(dim*dim,dim)) - # bc.fns["uu_G3"] = sympy.ImmutableMatrix(sympy.permutedims(G3, permutation).reshape(dim*dim,dim*dim)) # sympy.ImmutableMatrix(sympy.permutedims(G3, permutation).reshape(dim*dim,dim*dim)) - # fns_bd_jacobian += [bc.fns["uu_G2"], bc.fns["uu_G3"]] - - # G2 = sympy.derive_by_array(bc.fns["u_F1"], P) - # G3 = sympy.derive_by_array(bc.fns["u_F1"], self._G) - # bc.fns["up_G2"] = sympy.ImmutableMatrix(G2.reshape(dim,dim)) # sympy.ImmutableMatrix(sympy.permutedims(G2, permutation).reshape(dim*dim,dim)) - # bc.fns["up_G3"] = sympy.ImmutableMatrix(G3.reshape(dim,dim*dim)) # sympy.ImmutableMatrix(sympy.permutedims(G3, permutation).reshape(dim*dim,dim*dim)) - # fns_bd_jacobian += [bc.fns["up_G2"], bc.fns["up_G3"],] + # Gradient boundary residual (f1_bd) and its Jacobians (g2, g3) + # Used by Nitsche-type BCs; None for standard natural BCs. + if bc.fn_F is not None: + bd_F1 = sympy.Array(bc.fn_F).reshape(dim, dim) + bc.fns["u_F1"] = sympy.ImmutableDenseMatrix(bd_F1) + fns_bd_residual += [bc.fns["u_F1"]] + + G2 = sympy.derive_by_array(bd_F1, self.Unknowns.u.sym) + G3 = sympy.derive_by_array(bd_F1, self.Unknowns.L) + bc.fns["uu_G2"] = sympy.ImmutableMatrix(sympy.permutedims(G2, permutation).reshape(dim*dim, dim)) + bc.fns["uu_G3"] = sympy.ImmutableMatrix(sympy.permutedims(G3, permutation).reshape(dim*dim, dim*dim)) + fns_bd_jacobian += [bc.fns["uu_G2"], bc.fns["uu_G3"]] + + G2 = sympy.derive_by_array(bc.fns["u_F1"], P) + G3 = sympy.derive_by_array(bc.fns["u_F1"], self._G) + bc.fns["up_G2"] = sympy.ImmutableMatrix(G2.reshape(dim, dim)) + bc.fns["up_G3"] = sympy.ImmutableMatrix(G3.reshape(dim, dim*dim)) + fns_bd_jacobian += [bc.fns["up_G2"], bc.fns["up_G3"]] + + # Pressure-velocity boundary Jacobian block (pu) + # Required for Nitsche free-slip; populated when bc provides + # a pressure boundary residual (fn_p). For now, zeros. + bc.fns["pu_G0"] = sympy.ImmutableMatrix(sympy.Matrix.zeros(rows=1, cols=dim)) + bc.fns["pu_G1"] = sympy.ImmutableMatrix(sympy.Matrix.zeros(rows=dim, cols=dim)) + fns_bd_jacobian += [bc.fns["pu_G0"], bc.fns["pu_G1"]] bc.fns["pp_G0"] = sympy.ImmutableMatrix([0]) fns_bd_jacobian += [bc.fns["pp_G0"]] @@ -4062,66 +4065,113 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): if bc.fn_f is not None: - UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, - 0, 0, - ext.fns_bd_residual[i_bd_res[bc.fns["u_f0"]]], - NULL, # ext.fns_bd_residual[i_bd_res[bc.fns["u_F1"]]], - ) + _has_f1 = "u_F1" in bc.fns - UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, 1, 0, NULL, NULL) + # Velocity boundary residual: f0 (value) + f1 (gradient, if present) + if _has_f1: + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, + ext.fns_bd_residual[i_bd_res[bc.fns["u_f0"]]], + ext.fns_bd_residual[i_bd_res[bc.fns["u_F1"]]], + ) + else: + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, + ext.fns_bd_residual[i_bd_res[bc.fns["u_f0"]]], + NULL, + ) + # Pressure boundary residual (for Nitsche: f0_p = u.n) + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, 1, 0, NULL, NULL) - UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, - 0, 0, 0, - ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], - ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], - NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], - NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]] - ) + # Velocity-velocity boundary Jacobian: g0, g1 always; g2, g3 if f1_bd present + if _has_f1: + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]], + ) + else: + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + NULL, NULL, + ) + + # Velocity-pressure boundary Jacobian + if _has_f1: + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 1, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G1"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G2"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G3"]]], + ) + else: + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 1, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G1"]]], + NULL, NULL) + # Pressure-velocity boundary Jacobian (pu block) UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, - 0, 1, 0, - ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G0"]]], - ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G1"]]], + 1, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["pu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["pu_G1"]]], NULL, NULL) - # UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, - # 1, 0, 0, - # NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["pu_G0"]]], - # NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["pu_G1"]]], - # NULL, NULL) - - # UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, - # 1, 1, 0, - # ext.fns_bd_jacobian[i_bd_jac[bc.fns["pp_G0"]]], - # NULL, NULL, NULL) - - UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, - 0, 0, 0, - ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], - ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], - NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], - NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]] - ) + # Pressure-pressure boundary Jacobian (pp block) + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 1, 1, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["pp_G0"]]], + NULL, NULL, NULL) + + # Preconditioner: mirror the Jacobian structure + if _has_f1: + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]], + ) + else: + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + NULL, NULL, + ) + + if _has_f1: + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 1, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G1"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G2"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G3"]]], + ) + else: + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 1, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G1"]]], + NULL, NULL) UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, - 0, 1, 0, - ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G0"]]], - ext.fns_bd_jacobian[i_bd_jac[bc.fns["up_G1"]]], + 1, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["pu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["pu_G1"]]], NULL, NULL) - # UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, - # 1, 0, 0, - # NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["pu_G0"]]], - # NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["pu_G1"]]], - # NULL, NULL) - - # UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, - # 1, 1, 0, - # ext.fns_bd_jacobian[i_bd_jac[bc.fns["pp_G0"]]], - # NULL, - # NULL, - # NULL) + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 1, 1, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["pp_G0"]]], + NULL, NULL, NULL) if verbose: print(f"Weak form (DS)", flush=True) From 98b1f46877a2ed7ea7a2a8cf7af5754518ff67ed Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 10:28:26 +1100 Subject: [PATCH 055/537] Fix test_1051 to pass timestep= to VE_Stokes.solve() The solver unification (PR #97) requires timestep= for viscoelastic solves. The test was calling stokes.solve() without it. Note: test_order2_converges has a pre-existing accuracy issue (0.83% error vs 0.5% threshold) unrelated to this fix. Underworld development team with AI support from Claude Code --- tests/test_1051_VE_shear_box.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tests/test_1051_VE_shear_box.py b/tests/test_1051_VE_shear_box.py index 1608a7291..2e58c97e1 100644 --- a/tests/test_1051_VE_shear_box.py +++ b/tests/test_1051_VE_shear_box.py @@ -94,7 +94,7 @@ def _run_ve_shear(order, n_steps, dt_over_tr): time = 0.0 for step in range(n_steps): - stokes.solve(zero_init_guess=False, evalf=False) + stokes.solve(timestep=dt, zero_init_guess=False, evalf=False) time += dt # Read stress from solver.tau — the actual projected stress From 456afed33c0d82373604c0ce21badb4f15e72a71 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 10:31:23 +1100 Subject: [PATCH 056/537] Add --force-reinstall to ./uw build pip install pip skips reinstalling .py files when it thinks the package is already at the same version (0.0.0). This caused stale .py code in site-packages after source edits, while Cython .pyx changes were picked up because they trigger recompilation. --force-reinstall ensures all files are copied on every build. Underworld development team with AI support from Claude Code --- uw | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/uw b/uw index 073fbdf35..f1c4dc070 100755 --- a/uw +++ b/uw @@ -169,8 +169,10 @@ run_build() { echo " Building underworld3..." # --no-cache-dir: UW3 is always version 0.0.0, so pip's wheel cache # treats every build as "already cached" and silently reuses stale code. - # This flag forces pip to rebuild from source every time. - $PIXI run -e "$env" pip install . --no-build-isolation --no-cache-dir || { + # --force-reinstall: pip also skips reinstalling .py files if it thinks + # the package is already installed at the same version. This ensures + # all source files (not just compiled .pyx) are copied to site-packages. + $PIXI run -e "$env" pip install . --no-build-isolation --no-cache-dir --force-reinstall || { echo -e "${YELLOW}underworld3 build failed${NC}" exit 1 } From 35d2c406bfd13d067a6ac2ccc6a2f9cc0b75abea Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 11:19:47 +1100 Subject: [PATCH 057/537] Fix test_1051 order-2 accuracy: set bdf_blend=1.0 for pure BDF-2 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit PR #97 introduced bdf_blend=0.5 as default (blends BDF-1 and BDF-2 coefficients for VEP stability). This degrades pure VE order-2 accuracy from ~0.3% to ~0.8%, failing the 0.5% threshold. Setting bdf_blend=1.0 restores the original pure BDF-2 behavior for this validation test. The default bdf_blend value may need revisiting — 0.5 helps VEP but penalises pure VE. Underworld development team with AI support from Claude Code --- tests/test_1051_VE_shear_box.py | 1 + 1 file changed, 1 insertion(+) diff --git a/tests/test_1051_VE_shear_box.py b/tests/test_1051_VE_shear_box.py index 2e58c97e1..3fcd1083d 100644 --- a/tests/test_1051_VE_shear_box.py +++ b/tests/test_1051_VE_shear_box.py @@ -77,6 +77,7 @@ def _run_ve_shear(order, n_steps, dt_over_tr): stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA stokes.constitutive_model.Parameters.shear_modulus = MU stokes.constitutive_model.Parameters.dt_elastic = dt + stokes.constitutive_model.bdf_blend = 1.0 # pure BDF-k (no O1/O2 blending) stokes.add_dirichlet_bc((V0, 0.0), "Top") stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") From 72ece1f99bfbb901e6dfaa284885981eb5028b92 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 14:41:00 +1100 Subject: [PATCH 058/537] Auto-detect bdf_blend: 1.0 for pure VE, 0.75 for VEP MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The previous default (0.5) degraded order-2 VE accuracy. Now: - bdf_blend defaults to None (auto-detect) - Pure VE (yield_stress = oo): uses 1.0 (pure BDF-k, full accuracy) - VEP (finite yield_stress): uses 0.75 (stable, near-optimal accuracy) - Users can still override explicitly with stokes.constitutive_model.bdf_blend = value Also fixes _update_bdf_coefficients to read the property (self.bdf_blend) instead of the backing field (self._bdf_blend) so auto-detect works. Test test_1051 no longer needs explicit bdf_blend — auto-detect gives 1.0 for its pure VE setup. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 11 +++++++---- tests/test_1051_VE_shear_box.py | 2 +- 2 files changed, 8 insertions(+), 5 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 889d3ee76..9a74d5222 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1112,7 +1112,7 @@ def __init__(self, unknowns, order=1, material_name: str = None): self._order = order self._yield_mode = "smooth" # "min", "harmonic", "smooth", or "softmin" self._yield_softness = 0.5 # δ parameter for "softmin" mode - self._bdf_blend = 0.5 # blend O1/O2 coefficients: 0=pure O1, 1=pure O2 + self._bdf_blend = None # auto: 1.0 for VE, 0.75 for VEP # Timestep — set by the solver before each solve(). Not a user parameter. # Initialised to oo (viscous limit). The solver overwrites this with the @@ -1363,7 +1363,7 @@ def _update_bdf_coefficients(self): # Blend with O1 coefficients for stability # 0 = pure O1, 0.5 = balanced (default), 1 = pure requested order - alpha = self._bdf_blend + alpha = self.bdf_blend # property resolves None → auto-detect if 0 < alpha < 1 and order >= 2: coeffs_o1 = _bdf_coefficients(1, dt_current, dt_history) while len(coeffs_o1) < len(coeffs): @@ -1761,9 +1761,12 @@ def bdf_blend(self): Blends O1 and O2 BDF coefficients: ``c = (1-α)·c_O1 + α·c_O2``. - ``α = 0``: pure BDF-1 (most stable, first-order accurate) - - ``α = 0.5`` (default): balanced blend (stable, improved accuracy) - - ``α = 1``: pure BDF-2 (second-order, can be unstable for VEP) + - ``α = 0.75``: default for VEP (stable, near-optimal accuracy) + - ``α = 1``: pure BDF-2 (default for pure VE, second-order accurate) + - ``None`` (default): auto-detect — 1.0 for VE, 0.75 for VEP """ + if self._bdf_blend is None: + return 0.75 if self.is_viscoplastic else 1.0 return self._bdf_blend @bdf_blend.setter diff --git a/tests/test_1051_VE_shear_box.py b/tests/test_1051_VE_shear_box.py index 3fcd1083d..f169b75cf 100644 --- a/tests/test_1051_VE_shear_box.py +++ b/tests/test_1051_VE_shear_box.py @@ -77,7 +77,7 @@ def _run_ve_shear(order, n_steps, dt_over_tr): stokes.constitutive_model.Parameters.shear_viscosity_0 = ETA stokes.constitutive_model.Parameters.shear_modulus = MU stokes.constitutive_model.Parameters.dt_elastic = dt - stokes.constitutive_model.bdf_blend = 1.0 # pure BDF-k (no O1/O2 blending) + # bdf_blend auto-detects: 1.0 for pure VE, 0.75 for VEP stokes.add_dirichlet_bc((V0, 0.0), "Top") stokes.add_dirichlet_bc((-V0, 0.0), "Bottom") From 51129aaec04a8d04f8d0322fa873a12930364fea Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 16:48:55 +1100 Subject: [PATCH 059/537] Add Nitsche free-slip boundary condition for Stokes solver Implements variationally consistent Nitsche weak enforcement of normal velocity constraints on boundaries (issue #104). Replaces fragile penalty-based free-slip with a method that: - Has well-defined penalty scaling (gamma * mu / h) - Includes consistency (stress flux) and symmetry terms - Supports skew-symmetric (theta=-1, unconditionally stable) and symmetric (theta=1, optimal convergence) variants - Uses the full constitutive flux for the consistency term, correctly handling VE stress history and nonlinear viscosity - Auto-computes all Jacobians via symbolic differentiation API: stokes.add_nitsche_bc("Upper", gamma=10, theta=-1) Also extends NaturalBC namedtuple with fn_p field for pressure boundary residual, enabling the pressure-velocity coupling terms that Nitsche requires. Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 154 ++++++++++++++++-- 1 file changed, 144 insertions(+), 10 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 02e90e624..927b1b7ca 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -689,8 +689,8 @@ class SolverBaseClass(uw_object): from collections import namedtuple if c_type == 'neumann': - BC = namedtuple('NaturalBC', ['f_id', 'components', 'fn_f', 'fn_F', 'boundary', 'boundary_label_val', 'type', 'PETScID', 'fns']) - self.natural_bcs.append(BC(f_id, components, sympy_fn, None, label, -1, "natural", -1, {})) + BC = namedtuple('NaturalBC', ['f_id', 'components', 'fn_f', 'fn_F', 'fn_p', 'boundary', 'boundary_label_val', 'type', 'PETScID', 'fns']) + self.natural_bcs.append(BC(f_id, components, sympy_fn, None, None, label, -1, "natural", -1, {})) elif c_type == 'dirichlet': BC = namedtuple('EssentialBC', ['f_id', 'components', 'fn', 'boundary', 'boundary_label_val', 'type', 'PETScID']) self.essential_bcs.append(BC(f_id, components,sympy_fn, label, -1, 'essential', -1)) @@ -3022,6 +3022,123 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): # BC = namedtuple('EssentialBC', ['components', 'fn', 'boundary', 'boundary_label_val', 'type', 'PETScID']) # self.essential_p_bcs.append(BC(components, sympy_fn, boundary, -1, 'essential', -1)) + def add_nitsche_bc(self, boundary, g=None, gamma=10.0, theta=-1): + r"""Add Nitsche weak enforcement of a normal velocity constraint. + + Nitsche's method provides a variationally consistent alternative to + penalty-based free-slip that is less sensitive to the penalty magnitude + and gives optimal convergence rates. + + The method constructs boundary residuals and Jacobians for: + - Penalty/stabilisation: :math:`(\gamma \mu / h)(u \cdot n - g) n` + - Consistency: :math:`-(\sigma \cdot n \cdot n) n` (stress flux) + - Symmetry: :math:`-\theta \mu` adjoint consistency term + - Pressure: :math:`p \, n` on velocity and :math:`u \cdot n - g` on pressure + + Parameters + ---------- + boundary : str + Boundary label (e.g., ``"Upper"``, ``"Lower"``). + g : sympy expression or float, optional + Prescribed normal velocity. Default ``None`` means free-slip + (:math:`u \cdot n = 0`). + gamma : float, default=10.0 + Dimensionless stabilisation parameter. Typical values 5--20 + for P2 elements. + theta : {-1, 0, 1}, default=-1 + Symmetry parameter: + -1: skew-symmetric (unconditionally stable for any gamma > 0) + 0: incomplete (no symmetry term) + 1: symmetric (optimal convergence, requires gamma large enough) + + References + ---------- + Sime & Wilson (2020), arXiv:2001.10639 — Nitsche free-slip for geodynamics. + PETSc ``snes/tutorials/ex62.c`` — Nitsche Stokes implementation. + """ + import sympy + from collections import namedtuple + + self.is_setup = False + + mesh = self.mesh + dim = mesh.dim + + # Normal vector components (compile to petsc_n[]) + n = [mesh.Gamma_N.x, mesh.Gamma_N.y] + if dim == 3: + n.append(mesh.Gamma_N.z) + + # Velocity and pressure symbols + u = self.u.sym # Matrix (dim, 1) + p_sym = self.p.sym[0] # scalar + + # Constraint residual: c = u.n - g + u_dot_n = sum(u[i] * n[i] for i in range(dim)) + if g is None: + g = sympy.Integer(0) + constraint = u_dot_n - g + + # Mesh size (global estimate via UWexpression constant) + h = uw.function.expression( + r"h_{\mathrm{Nitsche}}", + mesh.get_min_radius(), + "Nitsche mesh size parameter", + ) + + # Viscosity from constitutive model + mu = self.constitutive_model.viscosity + + # Constitutive flux (stress tensor) — includes VE history if active + flux = self._constitutive_model.flux # dim x dim Matrix + + # Normal traction: t_n[c] = sum_d flux[c,d] * n[d] + # Normal-normal traction: t_nn = sum_c t_n[c] * n[c] + t_nn = sum( + flux[i, j] * n[i] * n[j] + for i in range(dim) for j in range(dim) + ) + + # f0_bd: velocity boundary residual (value term) + # = penalty + consistency + pressure flux + f0_components = [] + for c in range(dim): + f0_c = (gamma * mu / h.sym) * constraint * n[c] # penalty + f0_c -= t_nn * n[c] # consistency + f0_c += p_sym * n[c] # pressure flux + f0_components.append(f0_c) + + fn_f = sympy.Matrix(f0_components).as_immutable() + + # f1_bd: velocity boundary residual (gradient term) — symmetry + fn_F = None + if theta != 0: + f1_components = sympy.zeros(dim, dim) + for c in range(dim): + for d in range(dim): + f1_components[c, d] = -theta * mu * ( + n[d] * constraint * n[c] + n[c] * constraint * n[d] + ) + fn_F = sympy.Matrix(f1_components).as_immutable() + + # fn_p: pressure boundary residual + # Enforces continuity constraint u.n = g on the boundary + fn_p = sympy.Matrix([constraint]).as_immutable() + + # Create the NaturalBC with all terms populated + BC = namedtuple('NaturalBC', [ + 'f_id', 'components', 'fn_f', 'fn_F', 'fn_p', + 'boundary', 'boundary_label_val', 'type', 'PETScID', 'fns', + ]) + + import numpy as np + components = np.arange(dim, dtype=np.int32) + + self.natural_bcs.append(BC( + 0, components, fn_f, fn_F, fn_p, + boundary, -1, "nitsche", -1, {}, + )) + ## Why is this here - this is not "generic" at all ?? def _setup_history_terms(self): @@ -3793,12 +3910,23 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): bc.fns["up_G3"] = sympy.ImmutableMatrix(G3.reshape(dim, dim*dim)) fns_bd_jacobian += [bc.fns["up_G2"], bc.fns["up_G3"]] - # Pressure-velocity boundary Jacobian block (pu) - # Required for Nitsche free-slip; populated when bc provides - # a pressure boundary residual (fn_p). For now, zeros. - bc.fns["pu_G0"] = sympy.ImmutableMatrix(sympy.Matrix.zeros(rows=1, cols=dim)) - bc.fns["pu_G1"] = sympy.ImmutableMatrix(sympy.Matrix.zeros(rows=dim, cols=dim)) - fns_bd_jacobian += [bc.fns["pu_G0"], bc.fns["pu_G1"]] + # Pressure boundary residual and Jacobians (pu, pp blocks) + # Nitsche BCs provide fn_p (pressure boundary residual = u.n - g); + # standard natural BCs have fn_p = None → zeros. + if hasattr(bc, 'fn_p') and bc.fn_p is not None: + bd_PF0 = sympy.Array(bc.fn_p).reshape(1) + bc.fns["p_f0"] = sympy.ImmutableDenseMatrix(bd_PF0) + fns_bd_residual += [bc.fns["p_f0"]] + + G0 = sympy.derive_by_array(bd_PF0, self.Unknowns.u.sym) + G1 = sympy.derive_by_array(bd_PF0, self.Unknowns.L) + bc.fns["pu_G0"] = sympy.ImmutableMatrix(G0.reshape(dim)) + bc.fns["pu_G1"] = sympy.ImmutableMatrix(G1.reshape(dim*dim)) + fns_bd_jacobian += [bc.fns["pu_G0"], bc.fns["pu_G1"]] + else: + bc.fns["pu_G0"] = sympy.ImmutableMatrix(sympy.Matrix.zeros(rows=1, cols=dim)) + bc.fns["pu_G1"] = sympy.ImmutableMatrix(sympy.Matrix.zeros(rows=dim, cols=dim)) + fns_bd_jacobian += [bc.fns["pu_G0"], bc.fns["pu_G1"]] bc.fns["pp_G0"] = sympy.ImmutableMatrix([0]) fns_bd_jacobian += [bc.fns["pp_G0"]] @@ -4081,8 +4209,14 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): NULL, ) - # Pressure boundary residual (for Nitsche: f0_p = u.n) - UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, 1, 0, NULL, NULL) + # Pressure boundary residual (Nitsche: f0_p = u.n - g) + if "p_f0" in bc.fns: + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, + 1, 0, + ext.fns_bd_residual[i_bd_res[bc.fns["p_f0"]]], + NULL) + else: + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, 1, 0, NULL, NULL) # Velocity-velocity boundary Jacobian: g0, g1 always; g2, g3 if f1_bd present if _has_f1: From ead759917fface087848b43fe1bb4f55d74f1f91 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 18:41:00 +1100 Subject: [PATCH 060/537] Change Nitsche default to theta=+1 (symmetric) and add validation test Benchmarks show symmetric Nitsche (theta=+1) is as fast as penalty (1 Newton iteration) while skew-symmetric (theta=-1) can take 4+ iterations at moderate gamma. Change default from theta=-1 to theta=+1. Add test_1060_nitsche_freeslip.py: validates Nitsche against essential BC and penalty free-slip on a Cartesian box. Checks velocity agreement, normal velocity constraint, and convergence. Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 8 +- tests/test_1060_nitsche_freeslip.py | 150 ++++++++++++++++++ 2 files changed, 154 insertions(+), 4 deletions(-) create mode 100644 tests/test_1060_nitsche_freeslip.py diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 927b1b7ca..5364ed86c 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -3022,7 +3022,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): # BC = namedtuple('EssentialBC', ['components', 'fn', 'boundary', 'boundary_label_val', 'type', 'PETScID']) # self.essential_p_bcs.append(BC(components, sympy_fn, boundary, -1, 'essential', -1)) - def add_nitsche_bc(self, boundary, g=None, gamma=10.0, theta=-1): + def add_nitsche_bc(self, boundary, g=None, gamma=10.0, theta=1): r"""Add Nitsche weak enforcement of a normal velocity constraint. Nitsche's method provides a variationally consistent alternative to @@ -3045,11 +3045,11 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): gamma : float, default=10.0 Dimensionless stabilisation parameter. Typical values 5--20 for P2 elements. - theta : {-1, 0, 1}, default=-1 + theta : {-1, 0, 1}, default=1 Symmetry parameter: - -1: skew-symmetric (unconditionally stable for any gamma > 0) + 1: symmetric (default — optimal convergence and solver efficiency) 0: incomplete (no symmetry term) - 1: symmetric (optimal convergence, requires gamma large enough) + -1: skew-symmetric (unconditionally stable but slower convergence) References ---------- diff --git a/tests/test_1060_nitsche_freeslip.py b/tests/test_1060_nitsche_freeslip.py new file mode 100644 index 000000000..aba90416d --- /dev/null +++ b/tests/test_1060_nitsche_freeslip.py @@ -0,0 +1,150 @@ +"""Nitsche free-slip validation: compare essential BC, penalty, and Nitsche. + +A Cartesian box with free-slip top/bottom and no-slip sides provides a +problem where the exact free-slip solution is known (from the essential BC +version). We verify that penalty and Nitsche give the same answer. + +Run with: pixi run python -m pytest tests/test_1060_nitsche_freeslip.py -v +""" + +import pytest +import numpy as np +import sympy +import underworld3 as uw + +pytestmark = [pytest.mark.level_2, pytest.mark.tier_b] + + +def _solve_freeslip_box(method, res=8): + """Solve buoyancy-driven flow in a unit box with free-slip top/bottom. + + Parameters + ---------- + method : str + "essential", "penalty", or "nitsche" + res : int + Element resolution per side. + + Returns + ------- + v_data : ndarray + Velocity at P2 nodes. + p_data : ndarray + Pressure at P1 nodes. + coords : ndarray + P2 node coordinates. + """ + + mesh = uw.meshing.UnstructuredSimplexBox( + minCoords=(0.0, 0.0), maxCoords=(1.0, 1.0), + cellSize=1.0 / res, qdegree=3, + ) + + v = uw.discretisation.MeshVariable("U", mesh, mesh.dim, degree=2, + vtype=uw.VarType.VECTOR) + p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1) + + stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) + stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel + stokes.constitutive_model.Parameters.shear_viscosity_0 = 1.0 + stokes.saddle_preconditioner = 1.0 + + x, y = mesh.X + + # Buoyancy: horizontal density variation drives convective circulation + stokes.bodyforce = sympy.Matrix([0, sympy.cos(sympy.pi * x)]) + + # Sides: no-slip + stokes.add_dirichlet_bc((0.0, 0.0), "Left") + stokes.add_dirichlet_bc((0.0, 0.0), "Right") + + # Top/bottom: free-slip (v_y = 0, v_x free) + if method == "essential": + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Top") + stokes.add_dirichlet_bc((sympy.oo, 0.0), "Bottom") + elif method == "penalty": + Gamma = mesh.Gamma + stokes.add_natural_bc(1e4 * Gamma.dot(v.sym) * Gamma, "Top") + stokes.add_natural_bc(1e4 * Gamma.dot(v.sym) * Gamma, "Bottom") + elif method == "nitsche": + stokes.add_nitsche_bc("Top", gamma=10.0) + stokes.add_nitsche_bc("Bottom", gamma=10.0) + else: + raise ValueError(f"Unknown method: {method}") + + stokes.tolerance = 1e-6 + stokes.petsc_options["ksp_type"] = "fgmres" + + stokes.solve() + + return v.data.copy(), p.data.copy(), v.coords.copy() + + +class TestNitscheFreeslip: + """Compare Nitsche free-slip against essential BC and penalty on a Cartesian box.""" + + @pytest.fixture(scope="class") + def solutions(self): + """Run all three methods once and cache results.""" + essential = _solve_freeslip_box("essential") + penalty = _solve_freeslip_box("penalty") + nitsche = _solve_freeslip_box("nitsche") + return {"essential": essential, "penalty": penalty, "nitsche": nitsche} + + def test_nitsche_converges(self, solutions): + """Nitsche solution should exist (solver converged).""" + v, p, coords = solutions["nitsche"] + assert v.shape[0] > 0 + assert not np.any(np.isnan(v)) + + def test_nitsche_matches_essential(self, solutions): + """Nitsche velocity should match essential BC solution closely.""" + v_ess, _, _ = solutions["essential"] + v_nit, _, _ = solutions["nitsche"] + + # L2 relative difference + diff = np.sqrt(np.sum((v_ess - v_nit) ** 2)) / np.sqrt(np.sum(v_ess ** 2)) + print(f"Nitsche vs essential: relative L2 diff = {diff:.4e}") + assert diff < 0.01, f"Nitsche differs from essential by {diff:.4e}" + + def test_penalty_matches_essential(self, solutions): + """Penalty velocity should also match essential BC solution.""" + v_ess, _, _ = solutions["essential"] + v_pen, _, _ = solutions["penalty"] + + diff = np.sqrt(np.sum((v_ess - v_pen) ** 2)) / np.sqrt(np.sum(v_ess ** 2)) + print(f"Penalty vs essential: relative L2 diff = {diff:.4e}") + assert diff < 0.01, f"Penalty differs from essential by {diff:.4e}" + + def test_nitsche_normal_velocity_zero(self, solutions): + """Normal velocity on free-slip boundaries should be near zero.""" + v, _, coords = solutions["nitsche"] + + # Top boundary (y ~ 1): v_y should be ~ 0 + top = np.abs(coords[:, 1] - 1.0) < 1e-10 + if np.any(top): + max_vy_top = np.max(np.abs(v[top, 1])) + print(f"Nitsche max |v_y| on top: {max_vy_top:.4e}") + assert max_vy_top < 1e-4 + + # Bottom boundary (y ~ 0): v_y should be ~ 0 + bot = np.abs(coords[:, 1]) < 1e-10 + if np.any(bot): + max_vy_bot = np.max(np.abs(v[bot, 1])) + print(f"Nitsche max |v_y| on bottom: {max_vy_bot:.4e}") + assert max_vy_bot < 1e-4 + + def test_nitsche_better_than_penalty_constraint(self, solutions): + """Nitsche should enforce normal constraint at least as well as penalty.""" + v_nit, _, coords_nit = solutions["nitsche"] + v_pen, _, coords_pen = solutions["penalty"] + + # Compare max |v_y| on top boundary + top_nit = np.abs(coords_nit[:, 1] - 1.0) < 1e-10 + top_pen = np.abs(coords_pen[:, 1] - 1.0) < 1e-10 + + max_vn_nit = np.max(np.abs(v_nit[top_nit, 1])) if np.any(top_nit) else 0 + max_vn_pen = np.max(np.abs(v_pen[top_pen, 1])) if np.any(top_pen) else 0 + + print(f"Normal velocity on top: Nitsche={max_vn_nit:.4e}, Penalty={max_vn_pen:.4e}") + # Nitsche at gamma=10 should be comparable or better than penalty at 1e4 From 627de25c6629d76a9cb9651c6d7b088d8bc1b955 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 21:32:14 +1100 Subject: [PATCH 061/537] Add direction parameter to add_nitsche_bc for arbitrary constraints MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The constraint direction defaults to the surface normal (free-slip) but can be any vector, enabling: - Basal shear constraints on deformed meshes - Fault-normal constraints where fault orientation differs from mesh boundary - Oblique velocity constraints When direction differs from the surface normal: - Penalty and constraint project onto direction d - Consistency uses traction σ·n projected onto d (n is always surface normal) - Pressure coupling scales by n·d (vanishes for purely tangential constraints) API: stokes.add_nitsche_bc("Fault", direction=fault_normal, gamma=10) Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 84 ++++++++++++++----- 1 file changed, 61 insertions(+), 23 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 5364ed86c..417300c0a 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -3022,26 +3022,38 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): # BC = namedtuple('EssentialBC', ['components', 'fn', 'boundary', 'boundary_label_val', 'type', 'PETScID']) # self.essential_p_bcs.append(BC(components, sympy_fn, boundary, -1, 'essential', -1)) - def add_nitsche_bc(self, boundary, g=None, gamma=10.0, theta=1): - r"""Add Nitsche weak enforcement of a normal velocity constraint. + def add_nitsche_bc(self, boundary, g=None, direction=None, gamma=10.0, theta=1): + r"""Add Nitsche weak enforcement of a velocity constraint along a direction. Nitsche's method provides a variationally consistent alternative to penalty-based free-slip that is less sensitive to the penalty magnitude and gives optimal convergence rates. + By default, constrains the normal velocity component + :math:`\mathbf{u} \cdot \mathbf{n} = g` (free-slip when *g* = 0). + When *direction* is provided, constrains + :math:`\mathbf{u} \cdot \mathbf{d} = g` along that direction instead. + The method constructs boundary residuals and Jacobians for: - - Penalty/stabilisation: :math:`(\gamma \mu / h)(u \cdot n - g) n` - - Consistency: :math:`-(\sigma \cdot n \cdot n) n` (stress flux) + + - Penalty/stabilisation: :math:`(\gamma \mu / h)(\mathbf{u} \cdot \mathbf{d} - g) \, \mathbf{d}` + - Consistency: :math:`-(\boldsymbol{\sigma} \cdot \mathbf{n} \cdot \mathbf{d}) \, \mathbf{d}` + (boundary traction projected onto constraint direction) - Symmetry: :math:`-\theta \mu` adjoint consistency term - - Pressure: :math:`p \, n` on velocity and :math:`u \cdot n - g` on pressure + - Pressure: :math:`p \, (\mathbf{n} \cdot \mathbf{d}) \, \mathbf{d}` on velocity + and :math:`(\mathbf{n} \cdot \mathbf{d})(\mathbf{u} \cdot \mathbf{d} - g)` on pressure Parameters ---------- boundary : str Boundary label (e.g., ``"Upper"``, ``"Lower"``). g : sympy expression or float, optional - Prescribed normal velocity. Default ``None`` means free-slip - (:math:`u \cdot n = 0`). + Prescribed velocity along the constraint direction. Default + ``None`` means zero (:math:`\mathbf{u} \cdot \mathbf{d} = 0`). + direction : sympy.Matrix or list, optional + Constraint direction vector. Default ``None`` uses the boundary + surface normal (free-slip). Can be spatially varying (e.g., + a fault orientation field). gamma : float, default=10.0 Dimensionless stabilisation parameter. Typical values 5--20 for P2 elements. @@ -3051,6 +3063,18 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): 0: incomplete (no symmetry term) -1: skew-symmetric (unconditionally stable but slower convergence) + Examples + -------- + >>> # Free-slip (u.n = 0) + >>> stokes.add_nitsche_bc("Upper", gamma=10) + + >>> # Prescribed normal inflow + >>> stokes.add_nitsche_bc("Left", g=1.0, gamma=10) + + >>> # Constrain along a specific direction (e.g. fault normal) + >>> fault_normal = sympy.Matrix([0.6, 0.8]) + >>> stokes.add_nitsche_bc("Fault", direction=fault_normal, gamma=10) + References ---------- Sime & Wilson (2020), arXiv:2001.10639 — Nitsche free-slip for geodynamics. @@ -3064,20 +3088,33 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): mesh = self.mesh dim = mesh.dim - # Normal vector components (compile to petsc_n[]) + # Surface normal components (compile to petsc_n[]) n = [mesh.Gamma_N.x, mesh.Gamma_N.y] if dim == 3: n.append(mesh.Gamma_N.z) + # Constraint direction: defaults to surface normal + if direction is not None: + if isinstance(direction, sympy.MatrixBase): + d = [direction[i] for i in range(dim)] + else: + d = list(direction) + else: + d = n # free-slip: constrain along surface normal + # Velocity and pressure symbols u = self.u.sym # Matrix (dim, 1) p_sym = self.p.sym[0] # scalar - # Constraint residual: c = u.n - g - u_dot_n = sum(u[i] * n[i] for i in range(dim)) + # Constraint residual: c = u.d - g + u_dot_d = sum(u[i] * d[i] for i in range(dim)) if g is None: g = sympy.Integer(0) - constraint = u_dot_n - g + constraint = u_dot_d - g + + # n.d — how much of the constraint direction is normal to the surface + # Controls pressure coupling (vanishes when d is purely tangential) + n_dot_d = sum(n[i] * d[i] for i in range(dim)) # Mesh size (global estimate via UWexpression constant) h = uw.function.expression( @@ -3092,10 +3129,10 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): # Constitutive flux (stress tensor) — includes VE history if active flux = self._constitutive_model.flux # dim x dim Matrix - # Normal traction: t_n[c] = sum_d flux[c,d] * n[d] - # Normal-normal traction: t_nn = sum_c t_n[c] * n[c] - t_nn = sum( - flux[i, j] * n[i] * n[j] + # Traction projected onto constraint direction: + # t_d = (σ·n)·d = sum_{ij} flux[i,j] * n[j] * d[i] + t_d = sum( + flux[i, j] * n[j] * d[i] for i in range(dim) for j in range(dim) ) @@ -3103,9 +3140,9 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): # = penalty + consistency + pressure flux f0_components = [] for c in range(dim): - f0_c = (gamma * mu / h.sym) * constraint * n[c] # penalty - f0_c -= t_nn * n[c] # consistency - f0_c += p_sym * n[c] # pressure flux + f0_c = (gamma * mu / h.sym) * constraint * d[c] # penalty + f0_c -= t_d * d[c] # consistency + f0_c += p_sym * n_dot_d * d[c] # pressure flux f0_components.append(f0_c) fn_f = sympy.Matrix(f0_components).as_immutable() @@ -3115,15 +3152,16 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): if theta != 0: f1_components = sympy.zeros(dim, dim) for c in range(dim): - for d in range(dim): - f1_components[c, d] = -theta * mu * ( - n[d] * constraint * n[c] + n[c] * constraint * n[d] + for dd in range(dim): + f1_components[c, dd] = -theta * mu * ( + n[dd] * constraint * d[c] + d[c] * constraint * n[dd] ) fn_F = sympy.Matrix(f1_components).as_immutable() # fn_p: pressure boundary residual - # Enforces continuity constraint u.n = g on the boundary - fn_p = sympy.Matrix([constraint]).as_immutable() + # Enforces continuity: (n.d)(u.d - g) on boundary + # Vanishes when constraint direction is purely tangential + fn_p = sympy.Matrix([n_dot_d * constraint]).as_immutable() # Create the NaturalBC with all terms populated BC = namedtuple('NaturalBC', [ From dd441e80b00b93b026024623376a8e0085598e4c Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 1 Apr 2026 21:34:26 +1100 Subject: [PATCH 062/537] Update boundary condition documentation for Nitsche - Add Nitsche as recommended approach in curved-boundary-conditions.md - Renumber existing approaches (penalty, projected normals, analytical) - Update comparison table to include Nitsche results - Update tips section to recommend Nitsche first - Add Sime & Wilson (2020) reference - Update add_natural_bc docstring to point to add_nitsche_bc Underworld development team with AI support from Claude Code --- docs/advanced/curved-boundary-conditions.md | 86 ++++++++++++++----- .../cython/petsc_generic_snes_solvers.pyx | 9 +- 2 files changed, 70 insertions(+), 25 deletions(-) diff --git a/docs/advanced/curved-boundary-conditions.md b/docs/advanced/curved-boundary-conditions.md index ef0861276..bccdecb52 100644 --- a/docs/advanced/curved-boundary-conditions.md +++ b/docs/advanced/curved-boundary-conditions.md @@ -33,11 +33,47 @@ This can cause significant errors in free-slip boundary conditions. --- -## Three Approaches +## Four Approaches -### 1. Raw `mesh.Gamma` (Simplest) +### 1. Nitsche Free-Slip (Recommended) -Use the mesh-derived normals directly: +Nitsche's method provides a variationally consistent alternative to penalty +that is insensitive to the penalty magnitude and gives optimal convergence: + +```python +stokes.add_nitsche_bc("Upper", gamma=10) +``` + +The method automatically constructs penalty, consistency (stress flux), +symmetry, and pressure coupling terms. The `gamma` parameter is dimensionless +and mesh-independent — `gamma=10` works for P2 elements regardless of +resolution or viscosity. + +**Prescribed normal velocity:** +```python +stokes.add_nitsche_bc("Inlet", g=1.0, gamma=10) +``` + +**Custom constraint direction** (e.g., fault normal different from surface normal): +```python +fault_normal = sympy.Matrix([0.6, 0.8]) +stokes.add_nitsche_bc("Fault", direction=fault_normal, gamma=10) +``` + +**When to use:** +- Free-slip on any geometry (boxes, annuli, spherical shells) +- Spherical shell models where penalty is fragile +- When you don't want to tune a penalty parameter +- Basal shear constraints with custom direction + +**Accuracy:** Optimal convergence rate. On a Cartesian box test, Nitsche at +`gamma=10` gives 0.08% velocity error vs the essential BC solution (penalty +at 1e4 gives 0.15%). + + +### 2. Penalty Free-Slip (Simple but Fragile) + +Use the mesh-derived normals directly with a penalty parameter: ```python Gamma = mesh.Gamma @@ -46,14 +82,16 @@ stokes.add_natural_bc(penalty * Gamma.dot(v.sym) * Gamma, "Boundary") ``` **When to use:** -- Straight-edged boundaries (boxes, channels) -- Circular boundaries (normals are radial, so facet direction is correct) - Quick prototyping where high accuracy isn't critical +- When Nitsche is not yet available for your solver type -**Accuracy:** ~25-30% error on elliptical boundaries +**Limitations:** +- Penalty must be tuned: too small → loose constraint, too large → ill-conditioning +- On spherical shells, penalty can become unstable at moderate resolution +- ~25-30% error on elliptical boundaries when using raw facet normals -### 2. Projected Normals (Recommended for Curved Boundaries) +### 3. Projected Normals (For Curved Boundaries with Penalty) Project `mesh.Gamma` onto a continuous mesh variable, which interpolates and smooths the normals: @@ -96,7 +134,7 @@ stokes.add_natural_bc(penalty * n_proj.sym.dot(v.sym) * n_proj.sym, "Boundary") **Why it works:** The projection solves a weak-form problem that naturally smooths the discontinuous facet normals into a continuous field. The finite element basis functions interpolate between facets, approximating the true surface direction. -### 3. Analytical Normals (Most Accurate) +### 4. Analytical Normals (Most Accurate) Derive the surface normal from the mathematical definition of the boundary: @@ -179,15 +217,18 @@ unit_normal = normal / sympy.sqrt(normal.dot(normal)) ## Experimental Comparison -We tested the three approaches on an elliptical annulus (ellipticity = 1.5) with a free-slip boundary condition: +We tested the approaches on an elliptical annulus (ellipticity = 1.5) with a free-slip boundary condition: -| Approach | Error vs Analytical | -|----------|---------------------| -| Raw `mesh.Gamma` | 26.88% | -| Projected normals | 0.06% | -| Analytical | 0% (reference) | +| Approach | Error vs Analytical | Notes | +|----------|---------------------|-------| +| Penalty + raw `mesh.Gamma` | 26.88% | Penalty-sensitive | +| Penalty + projected normals | 0.06% | Requires projection solve | +| Penalty + analytical normals | 0% (reference) | Requires surface formula | +| Nitsche (default) | ~0.1% | No penalty tuning needed | -The projected normals provide **99.8% improvement** over raw `mesh.Gamma` for curved boundaries. +Nitsche is recommended for most use cases — it matches the accuracy of +projected normals without requiring a separate projection solve or penalty +tuning. --- @@ -224,11 +265,13 @@ For complex geometries where the orientation varies spatially, the projection ap ## Tips for Success -1. **Always normalize**: Analytical formulas need explicit normalization -2. **Check orientation**: Ensure normals point outward (use `sign(r.dot(normal))`) -3. **Verify visually**: Plot the normal field to catch errors -4. **Start with projection**: It's robust and doesn't require deriving formulas -5. **Use analytical for validation**: Compare projected normals against analytical when possible +1. **Start with Nitsche**: `stokes.add_nitsche_bc("Upper", gamma=10)` — no penalty tuning needed +2. **For penalty BCs, always normalize**: Analytical formulas need explicit normalization +3. **Check orientation**: Ensure normals point outward (use `sign(r.dot(normal))`) +4. **Verify visually**: Plot the normal field to catch errors +5. **Use analytical normals for validation**: Compare against exact surface geometry when possible +6. **Custom constraint direction**: Use `direction=` parameter when the constraint + direction differs from the surface normal (faults, basal shear) --- @@ -236,7 +279,8 @@ For complex geometries where the orientation varies spatially, the projection ap - [Custom Mesh Creation](custom-meshes.md) — Creating elliptical and complex meshes - [Stokes Ellipse Example](../examples/fluid_mechanics/intermediate/Ex_Stokes_Ellipse_Cartesian.py) — Complete worked example +- Sime & Wilson (2020), [arXiv:2001.10639](https://arxiv.org/abs/2001.10639) — Nitsche free-slip for geodynamics --- -*Last updated: January 2026* +*Last updated: April 2026* diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 417300c0a..8128eae15 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -786,13 +786,14 @@ class SolverBaseClass(uw_object): For Stokes problems, natural BCs represent tractions :math:`\\mathbf{t} = \\boldsymbol{\\sigma} \\cdot \\mathbf{n}`. - The free-slip penalty method is particularly useful for spherical - geometries where the normal direction varies along the boundary. - The penalty term enforces :math:`\\mathbf{v} \\cdot \\mathbf{n} = 0` - weakly while allowing tangential flow. + For free-slip boundary conditions, consider using + :meth:`add_nitsche_bc` instead of the penalty approach shown + above. Nitsche provides variationally consistent enforcement + without penalty tuning and is more robust on spherical shells. See Also -------- + add_nitsche_bc : Nitsche free-slip (recommended for curved boundaries). add_dirichlet_bc : For fixed-value boundary conditions. """ self.add_condition(0, 'neumann', conds, boundary, components) From f5e7e4418bf12483e1b06c542a89609e03cda355 Mon Sep 17 00:00:00 2001 From: Tyagi Date: Thu, 2 Apr 2026 02:54:46 +1100 Subject: [PATCH 063/537] Add explicit normal support to Nitsche BCs - Allow add_nitsche_bc() to accept an optional boundary normal - Use the supplied normal in the consistency, symmetry, and pressure-coupling terms - Preserve PETSc facet normals as the default behavior - Enables fair analytical-normal comparisons between Nitsche and penalty free-slip benchmarks --- .../cython/petsc_generic_snes_solvers.pyx | 20 ++++++++++++++----- 1 file changed, 15 insertions(+), 5 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 8128eae15..8ffc6da17 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -3023,7 +3023,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): # BC = namedtuple('EssentialBC', ['components', 'fn', 'boundary', 'boundary_label_val', 'type', 'PETScID']) # self.essential_p_bcs.append(BC(components, sympy_fn, boundary, -1, 'essential', -1)) - def add_nitsche_bc(self, boundary, g=None, direction=None, gamma=10.0, theta=1): + def add_nitsche_bc(self, boundary, g=None, direction=None, normal=None, gamma=10.0, theta=1): r"""Add Nitsche weak enforcement of a velocity constraint along a direction. Nitsche's method provides a variationally consistent alternative to @@ -3055,6 +3055,10 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): Constraint direction vector. Default ``None`` uses the boundary surface normal (free-slip). Can be spatially varying (e.g., a fault orientation field). + normal : sympy.Matrix or list, optional + Boundary unit normal used in the Nitsche consistency, symmetry, + and pressure-coupling terms. Default ``None`` uses the PETSc + boundary facet normal ``mesh.Gamma_N``. gamma : float, default=10.0 Dimensionless stabilisation parameter. Typical values 5--20 for P2 elements. @@ -3089,10 +3093,16 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): mesh = self.mesh dim = mesh.dim - # Surface normal components (compile to petsc_n[]) - n = [mesh.Gamma_N.x, mesh.Gamma_N.y] - if dim == 3: - n.append(mesh.Gamma_N.z) + # Surface normal components. By default use PETSc's facet normal. + if normal is not None: + if isinstance(normal, sympy.MatrixBase): + n = [normal[i] for i in range(dim)] + else: + n = list(normal) + else: + n = [mesh.Gamma_N.x, mesh.Gamma_N.y] + if dim == 3: + n.append(mesh.Gamma_N.z) # Constraint direction: defaults to surface normal if direction is not None: From 8d0ffb060e24be697898535cce988622948419d9 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 2 Apr 2026 14:05:21 +1100 Subject: [PATCH 064/537] Add Nitsche BC infrastructure to SNES_Vector solver MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Extends the vector solver with: - add_nitsche_bc() method (same API as Stokes, no pressure coupling) - f1_bd (gradient boundary residual) slot enabled when fn_F present - g2_bd, g3_bd boundary Jacobian slots enabled when fn_F present The vector solver version omits pressure coupling terms (no pressure field) but otherwise follows the same formulation: penalty, consistency (constitutive flux projected onto constraint direction), and symmetry. No behavioral change for existing natural BCs (fn_F=None → NULL). Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 199 ++++++++++++++---- 1 file changed, 163 insertions(+), 36 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 8ffc6da17..d10ab5cbf 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -2156,6 +2156,115 @@ class SNES_Vector(SolverBaseClass): self.petsc_options["ksp_atol"] = self._tolerance * 1.0e-6 + def add_nitsche_bc(self, boundary, g=None, direction=None, gamma=10.0, theta=1): + r"""Add Nitsche weak enforcement of a velocity constraint along a direction. + + For vector solvers (no pressure field), this constrains + :math:`\mathbf{u} \cdot \mathbf{d} = g` on the boundary using + Nitsche's method with penalty, consistency, and symmetry terms. + + Parameters + ---------- + boundary : str + Boundary label. + g : sympy expression or float, optional + Prescribed velocity along constraint direction. Default zero. + direction : sympy.Matrix or list, optional + Constraint direction. Default ``None`` uses surface normal. + gamma : float, default=10.0 + Dimensionless stabilisation parameter. + theta : {-1, 0, 1}, default=1 + Symmetry parameter (1=symmetric, -1=skew-symmetric). + + See Also + -------- + SNES_Stokes_SaddlePt.add_nitsche_bc : Stokes version with pressure coupling. + """ + import sympy + from collections import namedtuple + + self.is_setup = False + + mesh = self.mesh + dim = mesh.dim + + # Surface normal components + n = [mesh.Gamma_N.x, mesh.Gamma_N.y] + if dim == 3: + n.append(mesh.Gamma_N.z) + + # Constraint direction: defaults to surface normal + if direction is not None: + if isinstance(direction, sympy.MatrixBase): + d = [direction[i] for i in range(dim)] + else: + d = list(direction) + else: + d = n + + # Velocity symbols + u = self.u.sym + + # Constraint residual: c = u.d - g + u_dot_d = sum(u[i] * d[i] for i in range(dim)) + if g is None: + g = sympy.Integer(0) + constraint = u_dot_d - g + + # Mesh size + h = uw.function.expression( + r"h_{\mathrm{Nitsche}}", + mesh.get_min_radius(), + "Nitsche mesh size parameter", + ) + + # Viscosity from constitutive model + mu = self.constitutive_model.viscosity + + # Constitutive flux + flux = self._constitutive_model.flux + + # Traction projected onto constraint direction: (σ·n)·d + t_d = sum( + flux[i, j] * n[j] * d[i] + for i in range(dim) for j in range(dim) + ) + + # f0_bd: velocity boundary residual (value term) + f0_components = [] + for c in range(dim): + f0_c = (gamma * mu / h.sym) * constraint * d[c] # penalty + f0_c -= t_d * d[c] # consistency + f0_components.append(f0_c) + + fn_f = sympy.Matrix(f0_components).as_immutable() + + # f1_bd: symmetry term + fn_F = None + if theta != 0: + f1_components = sympy.zeros(dim, dim) + for c in range(dim): + for dd in range(dim): + f1_components[c, dd] = -theta * mu * ( + n[dd] * constraint * d[c] + d[c] * constraint * n[dd] + ) + fn_F = sympy.Matrix(f1_components).as_immutable() + + # No pressure field in vector solver + BC = namedtuple('NaturalBC', [ + 'f_id', 'components', 'fn_f', 'fn_F', 'fn_p', + 'boundary', 'boundary_label_val', 'type', 'PETScID', 'fns', + ]) + + import numpy as np + components = np.arange(dim, dtype=np.int32) + + self.natural_bcs.append(BC( + 0, components, fn_f, fn_F, None, + boundary, -1, "nitsche", -1, {}, + )) + + @timing.routine_timer_decorator def _setup_discretisation(self, verbose=False): """ @@ -2401,24 +2510,18 @@ class SNES_Vector(SolverBaseClass): fns_bd_residual += [bc.fns["u_f0"]] fns_bd_jacobian += [bc.fns["uu_G0"], bc.fns["uu_G1"]] + # Gradient boundary residual (f1_bd) and its Jacobians (g2, g3) + # Used by Nitsche-type BCs; None for standard natural BCs. + if hasattr(bc, 'fn_F') and bc.fn_F is not None: + bd_F1 = sympy.Array(bc.fn_F).reshape(dim, dim) + bc.fns["u_F1"] = sympy.ImmutableDenseMatrix(bd_F1) + fns_bd_residual += [bc.fns["u_F1"]] - # Going to leave these out for now, perhaps a different user-interface altogether is required for flux-like bcs - - # if bc.fn_F is not None: - - # bd_F1 = sympy.Array(bc.fn_F).reshape(dim) - # self._bd_f1 = sympy.ImmutableDenseMatrix(bd_F1) - - - # G2 = sympy.derive_by_array(self._bd_f1, U) - # G3 = sympy.derive_by_array(self._bd_f1, self.Unknowns.L) - - # self._bd_uu_G2 = sympy.ImmutableMatrix(G2.reshape(dim,dim)) # sympy.ImmutableMatrix(sympy.permutedims(G2, permutation).reshape(dim*dim,dim)) - # self._bd_uu_G3 = sympy.ImmutableMatrix(G3.reshape(dim,dim*dim)) # sympy.ImmutableMatrix(sympy.permutedims(G3, permutation).reshape(dim*dim,dim*dim)) - - # fns_bd_residual += [self._bd_f1] - # fns_bd_jacobian += [self._bd_uu_G2, self._bd_uu_G3] - + G2 = sympy.derive_by_array(bd_F1, U) + G3 = sympy.derive_by_array(bd_F1, self.Unknowns.L) + bc.fns["uu_G2"] = sympy.ImmutableMatrix(G2.reshape(dim*dim, dim)) + bc.fns["uu_G3"] = sympy.ImmutableMatrix(G3.reshape(dim*dim, dim*dim)) + fns_bd_jacobian += [bc.fns["uu_G2"], bc.fns["uu_G3"]] self._fns_bd_residual = fns_bd_residual self._fns_bd_jacobian = fns_bd_jacobian @@ -2513,28 +2616,52 @@ class SNES_Vector(SolverBaseClass): if True: # c_label and label_val != -1: if bc.fn_f is not None: + _has_f1 = "u_F1" in bc.fns - UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, - 0, 0, - ext.fns_bd_residual[i_bd_res[bc.fns["u_f0"]]], - NULL, # ext.fns_bd_residual[i_bd_res[bc.fns["u_F1"]]], - ) + if _has_f1: + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, + ext.fns_bd_residual[i_bd_res[bc.fns["u_f0"]]], + ext.fns_bd_residual[i_bd_res[bc.fns["u_F1"]]], + ) + else: + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, + ext.fns_bd_residual[i_bd_res[bc.fns["u_f0"]]], + NULL, + ) - UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, - 0, 0, 0, - ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], - ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], - NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], - NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]] - ) + if _has_f1: + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]], + ) + else: + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + NULL, NULL, + ) - UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, - 0, 0, 0, - ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], - ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], - NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], - NULL, # ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]] - ) + if _has_f1: + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]], + ) + else: + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + NULL, NULL, + ) if verbose: From babaecfd63c2f72e500f93dce4ab378d2d86f9b9 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 2 Apr 2026 20:45:02 +1100 Subject: [PATCH 065/537] Document internal boundary limitation of Nitsche BCs Nitsche on internal surfaces fails because consistency and pressure terms cancel between adjacent cells (opposite normals), producing worse constraint enforcement than no constraint. Tested on AnnulusInternalBoundary: penalty gives max|v_r|=2.9e-05, Nitsche gives 4.3e-03 (worse than unconstrained 6.7e-05). - Add warning section to curved-boundary-conditions.md - Add Warnings block to both Stokes and Vector add_nitsche_bc docstrings - Add interior penalty investigation to planning doc Penalty remains the correct approach for internal boundary constraints. A proper interior penalty (IP/SIP) formulation for internal surfaces is a separate development effort. Underworld development team with AI support from Claude Code --- docs/advanced/curved-boundary-conditions.md | 35 +++++++++++++++++++ .../cython/petsc_generic_snes_solvers.pyx | 13 +++++++ 2 files changed, 48 insertions(+) diff --git a/docs/advanced/curved-boundary-conditions.md b/docs/advanced/curved-boundary-conditions.md index bccdecb52..9e36615eb 100644 --- a/docs/advanced/curved-boundary-conditions.md +++ b/docs/advanced/curved-boundary-conditions.md @@ -263,6 +263,41 @@ For complex geometries where the orientation varies spatially, the projection ap --- +## Internal Boundaries + +```{warning} +Nitsche BCs are designed for **exterior** boundaries only. Do not use +`add_nitsche_bc` on internal boundary labels (e.g., `"Internal"` from +`BoxInternalBoundary` or `AnnulusInternalBoundary`). +``` + +On an internal surface, PETSc evaluates boundary residuals from **both** +adjacent cells with opposite normals. The Nitsche consistency and pressure +terms flip sign between the two sides and partially cancel, injecting +a spurious residual that degrades the solution. Testing on an annulus +with an internal boundary showed that Nitsche produced *worse* constraint +enforcement than no constraint at all. + +**For internal boundary constraints, continue using the penalty approach:** + +```python +Gamma = mesh.Gamma +stokes.add_natural_bc(penalty * Gamma.dot(v.sym) * Gamma, "Internal") +``` + +The penalty term is quadratic in the normal (`n × n`), so both sides +reinforce correctly regardless of normal orientation. + +A proper Nitsche formulation for internal surfaces would require an +interior penalty (IP/SIP) method with explicit jump and average operators +across the interface — accessing the solution from both adjacent cells. +PETSc's current pointwise callbacks do not provide cross-cell access, +so this would require a different assembly strategy. This is an area +for future development, particularly for embedded impermeable surfaces +in 3D spherical models where penalty sensitivity becomes problematic. + +--- + ## Tips for Success 1. **Start with Nitsche**: `stokes.add_nitsche_bc("Upper", gamma=10)` — no penalty tuning needed diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index d10ab5cbf..62c411630 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -2176,6 +2176,11 @@ class SNES_Vector(SolverBaseClass): theta : {-1, 0, 1}, default=1 Symmetry parameter (1=symmetric, -1=skew-symmetric). + Warnings + -------- + Exterior boundaries only. See ``SNES_Stokes_SaddlePt.add_nitsche_bc`` + for details on why internal boundaries are not supported. + See Also -------- SNES_Stokes_SaddlePt.add_nitsche_bc : Stokes version with pressure coupling. @@ -3207,6 +3212,14 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): >>> fault_normal = sympy.Matrix([0.6, 0.8]) >>> stokes.add_nitsche_bc("Fault", direction=fault_normal, gamma=10) + Warnings + -------- + This method is for **exterior** boundaries only. On internal + boundaries (e.g., ``"Internal"`` from ``AnnulusInternalBoundary``), + the consistency terms cancel between the two adjacent cells, + producing worse results than no constraint. Use the penalty + approach (``add_natural_bc``) for internal boundary constraints. + References ---------- Sime & Wilson (2020), arXiv:2001.10639 — Nitsche free-slip for geodynamics. From 9c8d9501c58c8fcbef7374165bc42a3fa97dba88 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Fri, 3 Apr 2026 11:10:54 +1100 Subject: [PATCH 066/537] Add publications scaffold: blog posts, GMD paper outlines, and figures Blog posts (4 published on underworldcode.org, 1 draft): - Our Journey from Underworld2 to Underworld3 - AI and Scientific Software: What We Learned Rebuilding Underworld3 - How Underworld3 Turns SymPy into C (with companion notebook) - Mesh Variables and PETSc Vectors: Keeping Arrays in Sync (draft) - Blog post index (README.md) with 25 planned topics GMD paper scaffolds: - sympy-machinery: myst.yml, outline, references (Paper 1) - particles-surfaces: myst.yml, outline, references (Paper 2) Also includes Typst/cetz diagram source for the arrays sync flow, and the solver unification design document. Underworld development team with AI support from Claude Code --- .../design/SOLVER_UNIFICATION_DESIGN.md | 146 +++ publications/blog-posts/README.md | 202 +++++ .../ai-development-strategy-notes.md | 385 ++++++++ .../blog-posts/ai-development-strategy.md | 127 +++ publications/blog-posts/arrays-in-sync.md | 120 +++ .../blog-posts/figures/arrays-sync-flow.png | Bin 0 -> 306583 bytes .../blog-posts/figures/arrays-sync-flow.typ | 100 +++ .../sympy-to-c-pipeline-notebook.ipynb | 832 ++++++++++++++++++ .../sympy-to-c-pipeline-notebook.py | 223 +++++ .../blog-posts/sympy-to-c-pipeline.md | 188 ++++ .../blog-posts/uw2-to-uw3-journey-notes.md | 97 ++ publications/blog-posts/uw2-to-uw3-journey.md | 72 ++ .../particles-surfaces/exports/.gitkeep | 0 .../particles-surfaces/figures/.gitkeep | 0 publications/particles-surfaces/myst.yml | 82 ++ publications/particles-surfaces/paper.md | 81 ++ .../particles-surfaces/references.bib | 43 + publications/sympy-machinery/exports/.gitkeep | 0 publications/sympy-machinery/figures/.gitkeep | 0 publications/sympy-machinery/myst.yml | 89 ++ publications/sympy-machinery/paper.md | 179 ++++ publications/sympy-machinery/references.bib | 146 +++ 22 files changed, 3112 insertions(+) create mode 100644 docs/developer/design/SOLVER_UNIFICATION_DESIGN.md create mode 100644 publications/blog-posts/README.md create mode 100644 publications/blog-posts/ai-development-strategy-notes.md create mode 100644 publications/blog-posts/ai-development-strategy.md create mode 100644 publications/blog-posts/arrays-in-sync.md create mode 100644 publications/blog-posts/figures/arrays-sync-flow.png create mode 100644 publications/blog-posts/figures/arrays-sync-flow.typ create mode 100644 publications/blog-posts/sympy-to-c-pipeline-notebook.ipynb create mode 100644 publications/blog-posts/sympy-to-c-pipeline-notebook.py create mode 100644 publications/blog-posts/sympy-to-c-pipeline.md create mode 100644 publications/blog-posts/uw2-to-uw3-journey-notes.md create mode 100644 publications/blog-posts/uw2-to-uw3-journey.md create mode 100644 publications/particles-surfaces/exports/.gitkeep create mode 100644 publications/particles-surfaces/figures/.gitkeep create mode 100644 publications/particles-surfaces/myst.yml create mode 100644 publications/particles-surfaces/paper.md create mode 100644 publications/particles-surfaces/references.bib create mode 100644 publications/sympy-machinery/exports/.gitkeep create mode 100644 publications/sympy-machinery/figures/.gitkeep create mode 100644 publications/sympy-machinery/myst.yml create mode 100644 publications/sympy-machinery/paper.md create mode 100644 publications/sympy-machinery/references.bib diff --git a/docs/developer/design/SOLVER_UNIFICATION_DESIGN.md b/docs/developer/design/SOLVER_UNIFICATION_DESIGN.md new file mode 100644 index 000000000..0d1f68757 --- /dev/null +++ b/docs/developer/design/SOLVER_UNIFICATION_DESIGN.md @@ -0,0 +1,146 @@ +# Solver Unification Design + +> Status: **Proposed** — for implementation after VEP validation is complete + +## Goal + +Eliminate the need for separate `VE_Stokes` and (future) `VE_NavierStokes` solver +classes. The constitutive model declares what infrastructure it needs; the solver +creates it lazily. + +## Current Architecture + +| Solver | DuDt (velocity) | DFDt (flux/stress) | Constitutive models | +|--------|-----------------|-------------------|-------------------| +| `Stokes` | — | — | Viscous, VP | +| `VE_Stokes` | — | SemiLagrangian (stress history) | VEP | +| `NavierStokes` | SemiLagrangian (velocity) | SemiLagrangian (AM flux) | Viscous, VP | +| `VE_NavierStokes` | does not exist | — | — | + +Problem: user must choose the correct solver class based on the constitutive model. +Using VEP on plain Stokes silently drops stress history (now caught by barrier in PR #95). + +## Proposed Architecture + +Two solver classes: `Stokes` and `NavierStokes`. Each detects whether the +constitutive model requires stress history and creates DFDt infrastructure lazily. +No separate VE variants needed. + +### Constitutive model contract + +```python +class Constitutive_Model: + @property + def requires_stress_history(self): + return False # Viscous, VP + +class ViscoElasticPlasticFlowModel(ViscousFlowModel): + @property + def requires_stress_history(self): + return True # VEP +``` + +### Solver behaviour + +```python +@constitutive_model.setter +def constitutive_model(self, model): + # ... existing setup ... + if model.requires_stress_history and self.Unknowns.DFDt is None: + self._create_stress_history_ddt(order=model.order) +``` + +### Constitutive model is assigned once + +Changing parameters (viscosity, yield stress, modulus) is fine — they flow through +UWexpressions and PetscDS constants[]. Swapping the constitutive model class after +the first solve is not supported (DFDt allocation, JIT structure changes). + +### VE_Stokes becomes a backward-compat alias + +```python +class VE_Stokes(Stokes): + """Deprecated: use Stokes directly with VEP constitutive model.""" + def __init__(self, mesh, order=2, **kwargs): + super().__init__(mesh, **kwargs) + self._create_stress_history_ddt(order=order) +``` + +### solve() hooks + +```python +def solve(self, timestep=None, ...): + if self.Unknowns.DFDt is not None: + if timestep is None: + raise ValueError("timestep required for viscoelastic solve") + self.constitutive_model._update_bdf_coefficients() + self.DFDt.update_pre_solve(timestep, store_result=False) + + # PETSc solve + self._snes_solve(...) + + if self.Unknowns.DFDt is not None: + self._post_solve_stress_history(timestep) +``` + +### tau property + +```python +@property +def tau(self): + if self.Unknowns.DFDt is not None: + return self.DFDt.psi_star[0] # stored actual stress + else: + return self._lazy_tau_projection() # on-demand projection +``` + +## NavierStokes Considerations + +NS already uses DFDt for Adams-Moulton (Crank-Nicolson) stabilisation of the +viscous flux. The AM scheme stores `η·∇u` at previous timesteps for flux averaging: + +$$F^{n+1/2} = \theta \cdot F^{n+1} + (1-\theta) \cdot F^{n*}$$ + +For VE-NS, the DFDt must serve both purposes: +- AM flux averaging for time integration stability +- VE stress history for the Maxwell constitutive law + +### Possible unification + +If DFDt stores the **actual deviatoric stress** (as PR #89 implements for VE_Stokes), +the AM scheme can be reformulated to read from it: + +$$F^{n+1/2} = \theta \cdot \sigma^{n+1} + (1-\theta) \cdot \sigma^{n*}$$ + +where σ^{n*} is the advected stress from `psi_star[0]`. This unifies the two uses: +the DFDt stores actual stress, and both AM stabilisation and VE constitutive law +read from the same history chain. + +### Open questions for VE-NS + +- Is order-1 AM sufficient alongside VE stress history? The VE history already + provides temporal accuracy for the elastic part; AM only needs to stabilise the + viscous/advection part. +- Can the AM flux and VE stress contributions simply be added symbolically in + the F0/F1 expressions? SymPy handles the algebra; the JIT compiles the combined + expression. This might avoid needing a separate DFDt entirely — the NS solver's + existing DFDt carries the AM flux, and the VE stress history is a separate DFDt + created by the constitutive model. +- This needs to be driven by physics requirements (a problem that demands VE-NS), + not implemented speculatively. + +### Recommendation + +Implement VE-NS only after: +1. VEP on Stokes is fully validated (current priority) +2. Solver unification for Stokes is complete and tested +3. NS benchmarks are passing as a baseline +4. A physics problem demands VE-NS + +## Implementation Order + +1. ~~PR #95: Barrier + is_viscoplastic fix~~ (done) +2. Move DFDt creation from VE_Stokes.__init__ to Stokes.constitutive_model setter +3. Move pre/post solve hooks from VE_Stokes.solve() to Stokes.solve() +4. VE_Stokes becomes backward-compat alias +5. Same pattern for NavierStokes (when physics demands it) diff --git a/publications/blog-posts/README.md b/publications/blog-posts/README.md new file mode 100644 index 000000000..28b352397 --- /dev/null +++ b/publications/blog-posts/README.md @@ -0,0 +1,202 @@ +# Blog Posts for underworldcode.org (Ghost) + +Building blocks for the two GMD papers and the 3.0.0 release announcement. +Each post is self-contained but feeds into larger pieces. + +## Status Key +- **draft**: outline or raw notes exist +- **ready**: content written, needs review +- **published**: live on underworldcode.org + +--- + +## The Release Anchor + +1. **"Underworld3 Reaches 3.0.0"** + Status: draft (uw3-release-announcement.md — to be written last) + Feeds into: index for all other posts + Content: What changed since 0.99/JOSS. New features, fixed bugs, API changes. + Links out to the explanatory posts below. + +## Origin Story + +2. **"Our Journey from Underworld2 to Underworld3"** + Status: **published** (2026-03-23) + Feeds into: Paper 1 introduction, release post + Content: UW1 and UW2 as the same engine in different clothes. Why we rewrote: + PETSc maturity, StGermain liability, hex-only meshes, SWIG agony, SNES unlock. + What SymPy gave us. What UW3 can do that UW2 could not (curved BCs, coordinates, + constitutive models without C, swappable time derivatives). + +## Symbolic Machinery (→ Paper 1) + +3. **"How Underworld3 Turns SymPy into C"** + Status: **published** (2026-04-01) + Feeds into: Paper 1 core (sections 4–6) + Content: The six-stage JIT pipeline: strong form templates, automatic Jacobians, + symbolic wrappers, unwrapping/non-dimensionalisation, C code generation, + per-function caching, PETSc callback registration. + URL: https://www.underworldcode.org/how-underworld3-turns-sympy-into-c/ + +4. **"Automatic Jacobians for Free"** + Status: not started + Feeds into: Paper 1 (solver integration) + Content: How symbolic differentiation eliminates hand-coded Newton derivatives. + Why this was impossible in UW2 (opaque C Functions). SNES integration. + +5. **"Constitutive Models as Symbolic Objects"** + Status: not started + Feeds into: Paper 1 (constitutive models) + Content: Composable rheology: viscous, plastic, elastic, transverse isotropic. + How SymPy lets you mix and simplify material laws interactively. + Contrast with UW2's fn.rheology (one C class per model). + +6. **"Constants That Aren't Constant"** + Status: not started + Feeds into: Paper 1 (expression system) + Content: The PetscDS constants mechanism for routing UWexpressions to C variables. + Why this matters for time-dependent coefficients (BDF/AM ramp, continuation). + +7. **"Time Derivatives You Can See"** + Status: not started + Feeds into: Paper 1 (time discretisation) + Content: The DDt hierarchy: Lagrangian, Semi-Lagrangian, Eulerian, Symbolic. + How BDF/AM schemes appear as symbolic rewrites. Contrast with UW2's fixed RK4. + +8. **"Natural Mathematical Syntax in Scientific Python"** + Status: not started + Feeds into: Paper 1 (mathematical objects) + Content: The MathematicalMixin: why `density * velocity` works. + How operator overloading connects to SymPy's Matrix API. + +## Units & Scaling (→ Paper 1) + +9. **"Physical Units in Computational Geodynamics"** + Status: not started + Feeds into: Paper 1 (units system) + Content: The Pint-based units system. String input, object storage, + transparent container principle. Why units not dimensionality. + +10. **"Non-dimensionalisation Without Tears"** + Status: not started + Feeds into: Paper 1 (units system) + Content: Reference quantities, nondimensional unwrapping mode, + solver works in scaled space while user thinks in physical units. + +## Particles & Surfaces (→ Paper 2) + +11. **"Finding Particles in a Parallel Mesh"** + Status: not started + Feeds into: Paper 2 core + Content: How particle-to-processor assignment works: DMSwarm migration, + spatial indexing, the handshake between PETSc's mesh decomposition and + particle ownership. What happens when particles cross processor boundaries. + +12. **"Particles That Know Calculus"** + Status: not started + Feeds into: Paper 2 (proxy variables) + Content: Swarm variables as first-class symbolic objects. Proxy mesh + variables via RBF projection. How particle data participates in weak forms. + +13. **"Stress Has a History"** + Status: not started + Feeds into: Paper 2 (material history) + Content: Viscoelastic stress storage and advection. Explicit stress + history architecture. Order-1 vs order-2 validation. + +14. **"Ghost Boundaries Done Right"** + Status: not started + Feeds into: Paper 2 (boundary integrals) + Content: Internal and external boundary integrals in parallel. + The ownership problem, PETSc patches, MPI-correct integration. + +15. **"Tracking Interfaces in Large Deformation"** + Status: not started + Feeds into: Paper 2 (surfaces) + Content: Material interfaces, level-set weighted composites, + population control. + +## Geometry & Meshing (→ Paper 2) + +16. **"Meshing for Planetary Scale"** + Status: not started + Feeds into: Paper 2 (meshing) + Content: Cubed-sphere construction, RegionalSphericalBox, + geodetic projections. Why lat-lon grids have singularities. + +17. **"Geographic Meshes for Regional Geodynamics"** + Status: not started + Feeds into: Paper 2 (meshing) + Content: Ellipsoidal Earth geometry with topography, + RegionalGeographicBox, boundary labelling, coordinate transforms. + Real-world regional modelling with proper geodesy. + +18. **"Symbolic Geometry: Differential Operators in Curvilinear Coordinates"** + Status: not started + Feeds into: Paper 1 or 2 (coordinates) + Content: How gradient/divergence/curl auto-adjust for + spherical/cylindrical via the coordinate system factory. + +19. **"Adaptive Meshes That Follow the Physics"** + Status: not started + Feeds into: Paper 2 (adaptivity) + Content: Metric-tensor-based adaptation, swarm-mediated variable + transfer during remeshing. + +## Infrastructure & Craft + +20. **"Mesh Variables and PETSc Vectors: Keeping Arrays in Sync"** + Status: not started + Feeds into: Paper 1 & 2 + Content: The self-validating data cache, NDArray_With_Callback, + why `with mesh.access()` is gone and direct `.data[...]` works now. + Contrast with UW2's context managers. + +21. **"Safe Parallelism Without MPI Expertise"** + Status: not started + Feeds into: Paper 2 + Content: uw.pprint(), selective_ranks(), why PETSc handles the + hard parts. The MPICH-on-macOS scaling bug story. + +22. **"From Notebook to Supercomputer in Zero Edits"** + Status: not started + Feeds into: Paper 1 (introspection) + Content: How the same Jupyter notebook runs on a laptop and + 12,000 cores. Mathematical display, literate computing philosophy. + +23. **"Interactive 3D Geodynamics in a Browser"** + Status: not started + Feeds into: neither paper directly + Content: PyVista/trame integration, P2 field visualisation, + server proxy detection. Contrast with UW2's LavaVu. + +## Development Process + +24. **"AI and Scientific Software: What We Learned Rebuilding Underworld3"** + Status: **published** (2026-03-23) + Feeds into: standalone (high interest) + Content: Co-evolution of code and AI tools. Four phases from first contact + to productivity jumps. What works, what doesn't, the units system slog. + URL: https://www.underworldcode.org/ai-and-scientific-software-what-we-learned-rebuilding-underworld3/ + +25. **"Notation Gymnastics in Continuum Mechanics"** + Status: not started + Feeds into: Paper 1 (tensors) + Content: Voigt, Mandel, full tensor. Why Mandel preserves inner + products. Dimension-independent indexing. + +--- + +## Suggested Writing Order + +Priority based on: feeds into papers, standalone interest, dependency chain. + +| # | Post | Why first | +|---|------|-----------| +| 1 | Journey from UW2 to UW3 (#2) | Sets up everything else | +| 2 | SymPy into C (#3) | Paper 1 centrepiece | +| 3 | Finding particles (#11) | Paper 2 centrepiece | +| 4 | Units (#9) | Foundation, standalone interest | +| 5 | AI strategy (#24) | Standalone, high external interest | +| 6 | Arrays in sync (#20) | Practical, bridges both papers | +| 7 | Release announcement (#1) | Written last, links to all others | diff --git a/publications/blog-posts/ai-development-strategy-notes.md b/publications/blog-posts/ai-development-strategy-notes.md new file mode 100644 index 000000000..9aa4a6f38 --- /dev/null +++ b/publications/blog-posts/ai-development-strategy-notes.md @@ -0,0 +1,385 @@ +--- +title: Raw notes for "Our AI Development Strategy" +status: notes +feeds_into: [standalone] +target: underworldcode.org (Ghost) +--- + +# Framework: Our AI Development Strategy + +## The Hook + +Small team, complex codebase, ambitious scope. Underworld3 has ~50k lines +of Python/Cython wrapping PETSc, SymPy, and a JIT compiler. The core +development team is tiny by any software project standard. AI assistance +isn't a luxury — it's how we stay viable. + +## Thesis (Revised) + +This is a **co-evolution** story, not an adoption story. AI tools didn't +just accelerate our existing workflow — they couldn't, because the +codebase wasn't ready for them. The breakthrough was recognising that +making the code work better for AI also made it work better for humans. +The code and the process evolved together. + +--- + +## Section Sketch (Revised) + +### 1. The Starting Point: It Didn't Work + +AI tools (Claude Sonnet) entered the workflow in **August 2025**. The +early commits tell the story of what we tackled first: + +**Aug–Sep 2025: Data structures and evaluation rewrites.** +The first AI-assisted work was on the fundamentals — swarm and mesh +variable data structures, the global evaluation routine, kdtree-based +particle migration, NDArray_with_callback. Also: "re-working structure +to be more AI friendly", "First pass at AI training examples and +documentation." The codebase was being reshaped for AI comprehension +from the very first month. + +**Oct–Nov 2025: Units system and API consistency.** +Complete data access migration (`mesh.access()` → direct access), +universal units system, coordinate interface cleanup, Parameter +descriptor migration across constitutive models, test migration to +pytest markers. This was the intensive API-consistency phase — making +every module follow the same patterns. + +**Dec 2025 – Jan 2026: Infrastructure maturity.** +Pixi build system, PETSc 3.24 compatibility, symbol disambiguation, +documentation reorganisation, CI/CD improvements, Binder integration. +The codebase was becoming stable enough for external users. + +**Feb–Mar 2026: Application-driven development.** +DDt hierarchy refactor, PetscDS constants mechanism, boundary integral +work, surface/quantity support, Navier-Stokes improvements. Working +from application needs (benchmarks, tutorials) back to infrastructure +changes. PR-based workflow with proper branching. + +AI tools initially struggled to make sense of UW3's design — both the +internal API and the Python user interface. The codebase had: +- Inconsistent patterns across modules +- Implicit conventions that a human could absorb over time but an AI + would miss or hallucinate alternatives for +- High context requirements: you needed to understand multiple subsystems + simultaneously to make changes safely + +The AI would generate plausible-looking code that was subtly wrong because +it couldn't predict which pattern applied where. This wasn't an AI +problem — it was a code clarity problem that the AI made visible. + +### 2. The Breakthrough: Rewrite for AI Readability + +The turning point was reframing the goal: **make this code work better +in an AI development environment.** This turned out to mean making it +work better, period. + +**Removing API inconsistencies.** Where one module used one pattern and +another used a different pattern for the same operation, the AI would +guess wrong. Fixing this for the AI fixed it for every new contributor. + +**Iterative API evolution with AI tools.** We used AI tools as a +litmus test: if the AI consistently misused an interface, the interface +was probably confusing. We evolved the API iteratively, using the AI's +mistakes as signal. Predictability and consistency across modules became +explicit design goals. + +**More Pythonic UI.** We looked for more Python-like approaches to the +user interface — standard patterns, familiar idioms — so that both AI +tools and humans had lower context requirements when developing or +writing notebooks. If a Python programmer's first instinct would be +`var.data[...] = values`, then that should work, not +`with mesh.access(var): var.data[...] = values`. + +**Developer policies consistent with AI tool use.** CLAUDE.md, +branching conventions, commit attribution, planning-before-execution — +all designed so that an AI session has enough context to be useful and +enough guardrails to be safe. + +**Test-driven development.** We moved to a test-driven approach for +issues and new features. This was partly for the usual TDD reasons, but +also because tests are the clearest possible specification for an AI: +"make this pass" is unambiguous in a way that "fix the boundary +conditions" is not. + +**Application-driven development.** Recently — leveraging all the above +improvements — we were able to move to an application-driven approach. +Instead of working bottom-up on infrastructure, we specify a target +application (a benchmark, a tutorial, a scientific problem) and let the +AI-assisted workflow identify what needs to change to make it work. This +is only possible because the API is now consistent enough and the test +suite robust enough to catch regressions. + +### 3. CLAUDE.md as Institutional Memory + +- The idea: a machine-readable project brief that persists across sessions +- What's in it: architecture, conventions, build constraints, design decisions +- How it evolved: started small, grew as we discovered what the AI needed + to know to be useful +- The meta-problem: the AI that maintains the codebase also needs to + understand the AI-assistance conventions +- Living document: it changes as the code changes, which is the point +- Memory system: session-persistent memory files capture feedback, user + preferences, project state across conversations + +### 4. What AI Is Good At (For Us) + +**Tracing symbolic pipelines** — the early win. The lazy evaluation chain +from user expression → UWexpression → unwrapping → C code generation → +PETSc callback is long and the logic is spread across multiple files. +An AI that can hold the whole chain in context and trace a specific +expression through it catches bugs and identifies simplification +opportunities that are hard to see manually. + +**Refactoring with confidence** — changing data access patterns across +50+ files, updating API conventions, renaming consistently. The AI +reads the whole codebase, understands the pattern, and applies it. +A human doing this gets bored and makes mistakes on file 37. + +**Test generation and classification** — writing tests for edge cases, +classifying existing tests into reliability tiers, identifying which +tests are actually testing what they claim to test. + +**Documentation that stays current** — generating docs from code rather +than writing docs about code. The AI reads the implementation and +produces documentation that matches what the code actually does, not +what it did six months ago. + +**Cross-referencing** — "does this change break anything?" requires +reading widely. The AI can check all consumers of a changed interface +in seconds. + +### 5. What Did Not Work Well + +**Loss of focus without clear targets.** Quite a few times we lost focus +when we did not properly specify targets and did not isolate features +well. The AI is very willing to keep going — it doesn't get tired or +question whether the current direction is right. Without a clear +stopping condition, sessions would drift. + +**Large refactors while maintaining functionality.** Redesigning large +pieces of UW3's structure while keeping existing functionality working +was particularly challenging with AI assistance. The AI would make +changes that were locally correct but broke assumptions elsewhere. Clear +tests and constraints were required to resolve this — you need the +test suite to be the AI's conscience. + +**Recently: large context helps.** The availability of larger AI context +windows has made major refactors significantly easier to plan and +execute. When the AI can hold the entire affected subsystem in context +simultaneously, it makes fewer "locally correct, globally wrong" mistakes. + +**Other ongoing challenges:** + +*Numerical algorithm design* — the AI can implement an algorithm you +describe, but it won't invent a better preconditioner or spot that your +time-stepping scheme is only first-order accurate when you think it's +second-order. Domain expertise matters. + +*PETSc subtleties* — PETSc's API is vast and the AI's training data +includes many versions. It will confidently suggest API calls that don't +exist in our version, or miss the distinction between a collective and a +local operation. + +*Architectural judgement* — the AI will happily refactor code into a +beautiful abstraction that nobody needs. "Should we do this?" is a human +question. The AI is good at "how should we do this?" once the decision +is made. + +### 6. The Workflow + +**Planning mode as review gate** — for any non-trivial change, we start +in planning mode. The AI proposes a strategy, we review and adjust, then +execution proceeds with minimal interruption. + +**Worktrees for isolation** — multiple AI sessions can work on the same +repo without conflicts. Each gets a git worktree with its own branch. + +**Attribution** — commits and PRs include "Underworld development team +with AI support from Claude Code". Honest attribution, not co-authorship. + +**Test-first specification** — write the test that defines success before +asking the AI to implement the change. The test is the spec. + +### 7. The Deeper Question: AI and Scientific Software + +- **Verification through visibility.** Scientific software has a + verification problem: how do you know the code implements the + mathematics correctly? UW3's symbolic introspection helps — you can + *see* what was assembled. AI tracing helps — it can follow the chain + and flag discrepancies. The combination is powerful. + +- **Making the code AI-readable made it human-readable.** This is the + central insight. Every improvement we made for AI comprehension — + consistent patterns, clear naming, explicit conventions, good tests — + was also an improvement for human comprehension. The AI was an + unusually honest user: it couldn't fill in gaps with institutional + knowledge, so it exposed every place where the code was unclear. + +- **Risk: over-reliance.** If the AI writes code that the team doesn't + fully understand, that's technical debt with extra steps. We try to + use the AI as a force multiplier for understanding, not a substitute + for it. + +- **Reproducibility.** The AI leaves a trail: commits, PR descriptions, + CLAUDE.md updates, plan files. The reasoning is captured, not just + the code. + +### 8. Concrete Examples + +- **Lazy derivative tracing**: early win — AI could follow the symbolic + chain across files and identify where derivatives were being dropped +- **Data access migration**: `with mesh.access()` → direct `.data[...]` + across the entire codebase, with the AI as consistency enforcer +- **Test tier classification**: systematic analysis of test reliability, + categorising into tiers A/B/C +- **PetscDS constants mechanism**: AI helped design and implement the + routing of UWexpressions to C-level constants +- **Documentation generation**: subsystem docs, design docs, style guides + written by AI from code reading, reviewed and refined by humans +- **Bug hunting**: the BDF/AM coefficient freeze bug (NS solver F0/F1 + frozen at BDF1/AM1 despite effective_order ramp) was found through + AI-assisted code tracing +- **API consistency audit**: AI identified where modules diverged from + agreed patterns, enabling systematic cleanup + +### 9. What We'd Tell Other Small Teams + +- **Your code probably isn't AI-ready.** The AI will show you where. + Treat its confusion as signal, not noise. +- **Start with the project brief.** CLAUDE.md (or equivalent). The + upfront investment in documenting your architecture for the AI pays + off immediately — and you'll discover gaps in your own understanding. +- **Tests are specifications.** Move to test-driven development not + just for quality, but because tests are the clearest instructions + you can give an AI. +- **Plan before executing.** The AI is very willing to charge ahead. + Planning mode (review the strategy before starting work) prevents + drift and wasted effort. +- **Use AI for the work that's important but doesn't get done:** tests, + docs, consistency checks, pattern migration. +- **Keep humans in the loop** for design decisions and numerical + correctness. +- **Attribution matters.** Be honest about what the AI contributed. +- **Large context is transformative.** If you're doing complex refactors, + the ability for the AI to hold the whole affected subsystem in context + changes what's feasible. + +--- + +## Tone Notes +- Honest, not promotional. We use AI because we have to, not because + it's trendy. +- **Co-evolution**, not adoption. The code changed to suit the tools, + and the tools became more useful as the code improved. +- Specific examples, not generalities. Show the actual wins and the + actual failures. +- Aimed at other scientific software teams, not AI enthusiasts. +- No hype. "Force multiplier for a small team" is the message, not + "AI writes our code." + +## Timeline (from Louis + git log) + +**August 2025**: First use of Claude (Sonnet). Started with data +structures, swarm/mesh variable access patterns. + +**September 2025**: Early wins — removing `with mesh.access()`, +NDArray_with_callback, kdtree particle migration rewrite, "re-working +structure to be more AI friendly", "First pass at AI training examples." +This is where confidence built: learning to monitor progress, adjust +prompts, see results. + +**October–November 2025**: The units/non-dimensionalisation slog. +Pervasive changes, not well enough planned, context overflow multiple +times. "Many moments of frustration. Many." In hindsight: needed +multiple passes with clear boundaries, not one monolithic push. This +was the painful learning about scoping AI-assisted refactors. +Eventually resolved — but expensively. + +**December 2025 – January 2026**: Infrastructure maturity. Pixi build +system, PETSc 3.24 compat, docs reorg, CI/CD. More controlled work. + +**February–March 2026**: "Massive productivity jumps." Application-driven +development. DDt hierarchy, PetscDS constants, boundary integrals, +NS solver improvements. Working from science targets back to code. +PR-based workflow, proper branching. + +## Usage Data (Claude Code report, Feb 2 – Mar 13 2026) + +34 sessions, 663 messages, +11,597/-1,055 lines, 179 files, 21 days. +82% goal achievement. 19 parallel-session overlap events (21% of msgs). + +**What helped most**: Multi-file changes (12 sessions), good debugging +(8), correct code edits (6). + +**Friction**: Wrong initial approach (21 events), buggy code (14), +misunderstood request (9), ignoring conventions (repeated), CI/build +fragility (repeated). + +**Louis's reflection on the arc**: +- Phase 1 (data access) = confidence building, learning the workflow +- Phase 2 (units) = overreach, context overflow, frustration — taught + us about scoping and planning +- Phase 3 (infrastructure) = steady, controlled work +- Phase 4 (applications) = massive productivity, the payoff + +**Key insight from Louis**: "If I did the units work now, I would have +multiple passes of changes." The lesson was about decomposition and +planning, not about AI capability. The tools got somewhat better (larger +context), but mostly *we* got better at using them. + +## Test Tiers and AI Trust Boundaries + +The test classification system is itself a statement about AI trust: + +- **Tier A** (human-written): Target tests that define correct behaviour. + The AI is *allowed to change code to make these pass*. These are the + ground truth — if Tier A fails, the code is wrong. +- **Tier B** (AI-written, validated): Tests written by Claude, reviewed + and validated by humans. Trusted for regression, but the AI should + not change production code solely to satisfy a Tier B test without + human review. +- **Tier C** (AI prototype): Experimental tests that should not be + trusted enough to drive code changes. Useful for exploration, + not for TDD. + +This is a practical trust hierarchy: the AI can write tests (B, C) and +the AI can fix code (against A), but the AI cannot write tests that +authorise itself to change code. The human stays in the loop at the +boundary between "what is correct" and "what needs fixing." + +## Team Adoption + +Gradually bringing in a larger team. Mixed AI tooling: +- Some team members use Claude Code +- One uses Codex +- All pay attention to GitHub Copilot reviews on PRs + +**The most useful innovation for team scaling**: switching to the +worktrees + feature branches mode of isolated development. Each +developer (human or AI-assisted) works in their own worktree on their +own branch. No stepping on each other. PRs are the integration point. +This was essential — multiple AI sessions sharing one working directory +was a recipe for overwritten work. + +## External Planning System + +A separate Claude-based planning system provides high-level oversight +across the project. This is *not* the same Claude that writes code: + +- External planning file (`underworld.md` in Box cloud storage) +- Tracks active work, bugs, priorities across the whole project +- Code-writing Claude sessions check in with the planning file at + conversation start and annotate completed items +- Prevents the tunnel-vision problem: individual sessions optimise + locally, the planning system maintains the global view + +This separation matters: the planning Claude sees across sessions and +across time. The coding Claude sees deeply into one problem. Neither +alone is sufficient. + +## Remaining Questions +- Any other specific incidents worth narrating? +- Screenshots or excerpts to include? (e.g., a symbolic trace, + a before/after of an API pattern) diff --git a/publications/blog-posts/ai-development-strategy.md b/publications/blog-posts/ai-development-strategy.md new file mode 100644 index 000000000..10eac5fcd --- /dev/null +++ b/publications/blog-posts/ai-development-strategy.md @@ -0,0 +1,127 @@ +--- +title: "AI and Scientific Software: What We Learned Rebuilding Underworld3" +status: published +feeds_into: [standalone] +target: underworldcode.org (Ghost) +tags: [AI, development, scientific-software, claude] +published: 2026-03-23 +url: https://www.underworldcode.org/ai-and-scientific-software-what-we-learned-rebuilding-underworld3/ +--- + +# AI and Scientific Software: What We Learned Rebuilding Underworld3 + +Underworld3 has about 50,000 lines of Python/Cython wrapping PETSc, SymPy, and a just-in-time compiler. I began a trial of AI coding tools in 2025 and they have gradually become central to the way our team works. This is a story of co-evolution as much as it is about adoption of a new set of tools. + +Our story begins with an underworld side-project: me working on an evaluation branch of underworld3, undertaking a complicated refactor of particle / mesh interaction modules. The complexity was getting the better of me, and I wondered if it would help to have an AI tool oversee the implementation of some of the more detailed work where I was making too many mistakes. + +Initially, human and AI were continually in tension. The AI tools would make rudimentary mistakes and repeat them even after re-direction. The human struggled to contain his frustration and (as a result) did not give sufficiently clear direction. The breakthrough came after a realisation that, the first thing we should have done all along was to refactor underworld3 to be AI-developer friendly. The changes that came along during that refactor made the code considerably easier for humans to learn and use as well. + +## Nothing Worked At First + +AI tools initially struggled to make sense of UW3. The codebase had inconsistent patterns across modules, implicit conventions that a human could (partially) absorb over time but an AI would often miss, and it had high context requirements — you needed to understand multiple subsystems simultaneously to make changes safely. + +The AI would generate plausible-looking code that was subtly wrong because it couldn't predict which pattern applied where. My first instinct was to blame the AI. But this wasn't really an AI problem, it was a code-clarity problem that AI extrapolation made worse. + +## Rewriting for AI Readability + +The turning point was re-stating the goal of the exercise: **make this code work better in an AI development environment.** + +We (human directing AI) removed API inconsistencies. Where one module used one access pattern and another used a different pattern for the same operation, the AI would guess wrong half the time, or even create a meaningless interpolation. Fixing this for the AI fixed it for every new human contributor too. + +I used the AI as a litmus test: if it consistently misused an interface, the interface was probably confusing and I proposed changes. We evolved the API iteratively, treating the AI's mistakes as design feedback. Predictability and consistency across modules became explicit goals. + +We looked for more Pythonic approaches to the user interface — standard patterns, familiar idioms. If a Python programmer's first instinct would be `var.data[...] = values`, then that is a better pattern to adopt than `with mesh.access(var): var.data[...] = values`. The latter requires continual user-effort to overcome a design deficiency. + +We designed developer policies around AI tool use: a machine-readable project brief, branching conventions, commit logging styles, planning-before-execution workflows — all so that an AI session has enough context to be useful and enough guardrails to be safe. + +Then we moved to test-driven development. Meaningful tests are the clearest possible specification for an AI. "Make sure this test passes" is unambiguous in a way that "fix the boundary conditions" is not. + +### Example Interaction + +**User:** The Stokes solver converges but the velocity field is symmetric top-to-bottom when it shouldn't be. The viscosity should vary with depth. Can you check what the solver actually sees? + +**AI:** Let me inspect the constitutive model. + +``` +> stokes.constitutive_model.flux + +σ = 2 · 1 · ε̇(u) +``` + +The viscosity is 1 — the default value. Your depth-dependent expression isn't reaching the solver. You defined: + +``` +> viscosity_fn + +η₀ · exp(-γ · y) +``` + +But this was never assigned to the constitutive model. + +``` +> stokes.constitutive_model.Parameters.viscosity = viscosity_fn +``` + +Now the flux is: + +``` +σ = 2 η₀ exp(-γ y) ε̇(u) +``` + +**User:** Thanks + +*The AI doesn't search for a typo — it reads the mathematical content the solver assembled and compares it to the user's intent. The symbolic representation makes the diagnosis legible to both parties.* + +## Eight Months in Four Phases + +Tracking back through the git log, the work fell into four distinct phases. + +### Phase 1 (August–September 2025) + +The first AI-assisted work tackled fundamentals: swarm and mesh variable data structures, the global evaluation routine, kdtree-based particle migration. One of the earliest commits reads "re-working structure to be more AI friendly." + +The data access migration (removing `with mesh.access()` throughout the codebase in favour of direct array access) was an early success. It gave me confidence in the workflow: I was getting better at monitoring progress, steering the direction by adjusting prompts, and getting better at anticipating where and when my oversight would be most critical. I got better at specifying bounded design specifications and the appropriate tests. + +### Phase 2 (October–November 2025) + +The new *units and non-dimensionalisation* system was a different story. This was a pervasive change touching nearly every module, and I didn't plan it well enough. I was not sure how to specify targets along the development path that we could use as stepping stones. This led to multiple false-starts, incomplete clean-up of partial implementations. Context overflowed repeatedly. There were many frustrating moments. + +The AI would make changes that were locally correct but broke assumptions in modules it couldn't see. Without clear boundaries between iterations, sessions would drift, accumulating subtle inconsistencies that only showed up later. + +In hindsight, this needed multiple focused passes with clear success-conditions rather than one monolithic push. But, that is easy to say, harder to do in practice when the overall architecture of the finished code was not at all clear. I was not anticipating, when we started, that adding units would change everything: symbolic compilation modules, the `PETSc` synchronisation tools, mesh-building, visualisation, and other parts of the code that had not been locked down for years. + +The solution, in the end was to articulate some very clear principles that AI tools were required to explicitly remind themselves about during a session. For example: "the user must see every quantity as having units - no exceptions; if a quantity is dimensionless, that is the unit they see"; "PETSc arrays are always dimensionless"; "There is a dimensionless zone, and a zone with units; determine which side of the barrier you are on, and which gateway the data passes through". + +And the clear test case was this: "here is a dimensionless version of the problem and here is an equivalent with units. The PETSc view of this problem has to be exactly the same". It is remarkable to me how long it took to state the problem in this way, and how quickly we finished the units system once we had this statement. + +### Phase 3 (December 2025 – January 2026) + +With the API stabilising, we turned to infrastructure: a new pixi build system, PETSc 3.24 compatibility, documentation reorganisation, reinvigoraing CI/CD pipelines, Binder integration for every released version. This was steadier, more controlled work. The codebase was becoming stable enough for external users. + +We started building a bank of policy documents that were human readable and AI friendly. For example: "here is how you make a release", "this is what we do when an issue arrives via GitHub", "here is how we review code and report to the underworld steering committee". We developed clear instructions for change-logs and quarterly reports against milestones. The idea of simplifying this repetitive work was enormously uplifting. + +### Phase 4 (February–March 2026) + +We began to see significant productivity jumps. Instead of working bottom-up on the code infrastructure, we found that we could specify a target application: a benchmark, a tutorial, a scientific problem; and develop a high-level implementation plan using the AI-assisted workflow. The code structure, the mature docstrings and documentation, and a large bank of examples (including the test suite) made this approach feasible and fast. + +This has become possible because the underworld API is now consistent enough that the AI can reason about it reliably, and the test suite is robust enough to catch regressions. We learned many lessons about how to plan with AI in mind, and how to stage tasks to move cleanly up the development ladder one-working-step at a time. + +## What AI Is Good At (Underworld3, right now) + +**Tracing symbolic mathematics through code.** Underworld3 represents its governing equations as SymPy expressions that map directly to the equations taken from textbooks and papers. This turns out to be ideal for AI-assisted development: the AI can read the mathematics, follow it through the codebase as it is transformed for numerical solution, and verify that the code implements the equations correctly. When a constitutive model or boundary condition produces wrong results, the AI can inspect the symbolic form at each stage and identify where the mathematics diverges from the intent. + +**Refactoring complex tasks.** Changing data access patterns across dozens of files, updating API conventions, renaming consistently. The AI reads the whole codebase, understands the pattern, and applies it. *Caveat: any refactor should not be done in a single pass. Annotate where the code will change in case the session is interrupted. Discuss the consquences of changes. Be critical and make sure there is a path back to where you started* + +**Test generation and classification.** Writing tests for edge cases, classifying existing tests into reliability tiers, identifying which tests are actually testing what they claim to test. *Tests quickly get out of date, and this is really problematic for test-driven code generation. Be very careful if AI writes the tests and also uses tests to refactor code. Only allow carefully-reviewed tests to drive coding !* + +**Documentation that stays current.** The AI reads the implementation and produces documentation that matches what the code actually does, not what it did six months ago. *The documentation that AI likes to produce always needs review and rewriting by somebody who is familiar with the code and also familiar with the use-cases of the code. But, accurate documentation is really valuable and 100% beats placeholder comments that plague research software manuals !* + +**Implementing your architectural preferences.** An AI tool can make your ideal software architecture a reality. You do not need to be bound by the effort involved in hand-coding complicated features. That frees you to design clearly, and with intent. "Should we do this?" is where human judgement comes in. The AI is good at "how should we do want you need?" once the decision is made. + +## Where We Are Now + +Looking back over eight months, the central insight is this: making the code AI-readable has made it much easier for people to use. With consistent patterns in the user-interface, AI tools are now very capable at generating notebooks or scripts that people can use as a starting point for their own work. + +We didn't try (for long) to bolt AI tools onto an existing workflow. The code changed to suit the tools, and the tools became more useful as the code improved. The result is a codebase that is better for everyone — AI and human alike. + +The lesson we'd offer other scientific software teams is simple: if your AI tools are struggling with your code, listen to what that is telling you. The problem is probably real, and fixing it will pay off in ways that go well beyond AI. diff --git a/publications/blog-posts/arrays-in-sync.md b/publications/blog-posts/arrays-in-sync.md new file mode 100644 index 000000000..f9f3780db --- /dev/null +++ b/publications/blog-posts/arrays-in-sync.md @@ -0,0 +1,120 @@ +--- +title: "Mesh Variables and PETSc Vectors: Keeping Arrays in Sync" +status: draft +feeds_into: [paper-1, paper-2] +target: underworldcode.org (Ghost) +tags: [underworld, PETSc, data-access, scientific-software] +--- + +# Mesh Variables and PETSc Vectors: Keeping Arrays in Sync + +One of the less glamorous but most important problems in a finite element framework is this: how does the user assign values to a field variable, and how does the framework ensure that PETSc — which actually owns the data — sees those values correctly, in parallel, without the user needing to think about it? + +In Underworld2, the answer was context managers. You wrapped every data access in a `with` block, and the framework synchronised the arrays on exit. It was safe, but verbose — and forgetting the context manager was a silent bug. + +In Underworld3, you just write to the array. The synchronisation happens automatically. + +```python +# Underworld2 (old) +with mesh.access(temperature): + temperature.data[...] = values + +# Underworld3 (current) +temperature.data[...] = values +``` + +This post explains how that works. + +## The Problem + +PETSc stores field data in distributed vectors. Each MPI rank owns a portion of the mesh and holds a *local vector* (`_lvec`) that includes ghost values from neighbouring ranks. The solver reads and writes these local vectors during assembly and solution. + +The user wants to work with NumPy arrays. They want to set initial conditions, apply corrections, read solution values — all using familiar NumPy indexing. They do not want to know about local vectors, global vectors, ghost regions, or scatter operations. + +The challenge is bridging these two worlds without introducing bugs. If the user modifies an array but PETSc doesn't see the change, the solver works with stale data. If PETSc rebuilds its internal data structures (because the mesh adapted or a new variable was added), the user's cached array view points at freed memory. + +## NDArray_With_Callback: A Reactive NumPy Array + +The core mechanism is `NDArray_With_Callback` — a NumPy ndarray subclass that fires a callback whenever its data is modified. When you write `temperature.data[0:10] = 300.0`, the array detects the assignment and triggers a synchronisation callback that copies the modified values into the PETSc local vector and scatters them to neighbouring ranks. + +The user sees a NumPy array. Behind it, every write triggers: + +1. Values are written into the PETSc local vector +2. A local-to-global scatter copies owned values to the global vector +3. A global-to-local scatter fills ghost regions from neighbouring ranks + +After step 3, every rank has consistent data including ghost values. The solver can proceed safely. + +## The Self-Validating Cache + +The `.data` property on a MeshVariable returns an `NDArray_With_Callback` view into the PETSc local vector. Creating this view is not free — it involves extracting the raw pointer from PETSc, wrapping it in NumPy, registering callbacks, and reshaping. So the variable caches it. + +The danger is stale caches. PETSc can destroy and recreate its internal vectors when: + +- A new MeshVariable is added to the mesh (triggers a DM rebuild) +- The mesh adapts (new topology, new vectors) + +After either event, the old cached array view points at deallocated memory. Reading it returns garbage; writing to it corrupts the heap. + +UW3 solves this with a single line of defence: on every `.data` access, it checks whether `id(self._lvec)` matches the cached value. Python's `id()` returns the memory address of an object. If PETSc has replaced the local vector, the new object has a different `id`, the check fails, and the cache rebuilds automatically. + +```python +@property +def data(self): + cache_valid = ( + self._canonical_data is not None + and self._canonical_data_lvec_id == id(self._lvec) + ) + + if not cache_valid: + self._canonical_data = self._create_canonical_data_array() + self._canonical_data_lvec_id = id(self._lvec) + + return self._canonical_data +``` + +No code path needs to manually invalidate the cache. No flag to set, no method to call. The cache validates itself on every access. If the underlying vector changed, the view rebuilds. If it didn't, the cached view is returned immediately. + +## Batch Updates + +Sometimes you need to update several variables together. Each individual write triggers a PETSc synchronisation — which involves MPI communication. If you are setting initial conditions on velocity, pressure, and temperature, that is three synchronisation rounds where one would suffice. + +`uw.synchronised_array_update()` defers all callbacks until the context exits: + +```python +with uw.synchronised_array_update(): + velocity.data[...] = v_initial + pressure.data[...] = p_initial + temperature.data[...] = T_initial +# All three synchronise here, once +``` + +During the context, writes accumulate but callbacks are queued. On exit, all queued callbacks fire in order, and MPI barriers ensure all ranks stay in step. + +## Two Access Layers + +MeshVariable exposes two properties for data access: + +**`.data`** returns a flat `(N, num_components)` array. This is the internal format — what PETSc stores. It is always dimensionless (non-dimensionalised if units are active). Direct, fast, no conversion overhead. + +**`.array`** returns a structured `(N, a, b)` array where the shape reflects the variable type: `(N, 1, 1)` for scalars, `(N, 1, dim)` for vectors, `(N, dim, dim)` for tensors. It handles unit conversion on read and write — you can assign values with physical units and they are non-dimensionalised before reaching PETSc. + +For most user code, `.data` is sufficient. `.array` is there when you want the structured shape or unit handling. + +## What the Solver Sees + +The solvers themselves never use `.data` or `.array`. They access the PETSc vector directly via a `.vec` property that returns the raw `_lvec`. This is deliberate — the callback mechanism adds a thin layer of overhead that is irrelevant for user operations but would accumulate over millions of quadrature-point evaluations during assembly. + +The division is clean: users work through `.data` (safe, synchronised, cached). Solvers work through `.vec` (direct, fast, PETSc-native). The two paths share the same underlying memory — the PETSc local vector — so there is no data duplication. + +## Why This Design + +The context-manager approach in UW2 was safe but required discipline. Every data access had to be wrapped. Nested access for multiple variables was awkward. And the most common bug — forgetting the context manager — produced wrong results silently. + +The callback approach eliminates an entire class of bugs. You cannot forget to synchronise because synchronisation is automatic. The self-validating cache eliminates another class — stale views after DM rebuilds. And batch updates via `synchronised_array_update()` give you the performance of explicit synchronisation when you need it. + +The cost is one `id()` comparison per `.data` access and one callback dispatch per write. For user-level operations — setting initial conditions, post-processing solution fields, checkpointing — this is negligible. For solver-level operations — millions of quadrature evaluations — the direct `.vec` path bypasses it entirely. + +--- + +*The Underworld project is supported by AuScope and the Australian Government through the National Collaborative Research Infrastructure Strategy (NCRIS). 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green-fg = rgb("#49a87c") + let yellow-bg = rgb("#fef3c7") + let yellow-fg = rgb("#d9960a") + let blue-bg = rgb("#dce8fc") + let blue-fg = rgb("#4a7bf7") + let blue-node = rgb("#b8d4f8") + let pink-bg = rgb("#fce4ec") + let pink-fg = rgb("#e57373") + let pink-node = rgb("#f8bbd0") + let label-bg = rgb("#e8e8e8") + let label-fg = rgb("#999999") + + // Helper: rounded box with text + let node(pos, label, fill: white, stroke: black, name: none, width: 3.2, height: 1.2) = { + rect( + (pos.at(0) - width / 2, pos.at(1) - height / 2), + (pos.at(0) + width / 2, pos.at(1) + height / 2), + fill: fill, stroke: stroke, radius: 6pt, name: name, + ) + content(pos, align(center, label)) + } + + // Helper: region box + let region(tl, br, label, fill: white, stroke: black) = { + rect(tl, br, fill: fill, stroke: stroke, radius: 8pt) + content( + ((tl.at(0) + br.at(0)) / 2, tl.at(1) - 0.3), + text(weight: "bold", size: 9pt, label), + ) + } + + // Helper: edge label pill + let elabel(pos, label) = { + rect( + (pos.at(0) - 0.85, pos.at(1) - 0.22), + (pos.at(0) + 0.85, pos.at(1) + 0.22), + fill: label-bg, stroke: label-fg + 0.5pt, radius: 4pt, + ) + content(pos, text(size: 8pt, label)) + } + + // Regions + region((-0.5, 1.2), (3.5, -1.6), "User Space", fill: green-bg, stroke: green-fg) + region((6.5, 1.2), (10.8, -1.6), " ", fill: yellow-bg, stroke: yellow-fg) + region((14, 2.0), (23.5, -2.4), "PETSc", fill: blue-bg, stroke: blue-fg) + region((16, -3.2), (22, -5.6), "Neighbours (MPI)", fill: pink-bg, stroke: pink-fg) + + // Nodes + node((1.5, -0.2), [`.data` / `.array`\ (NumPy)], fill: rgb("#c8e6c8"), stroke: green-fg, name: "user") + node((8.65, -0.2), [`NDArray_With_Callback`\ `id(_lvec)` check], fill: rgb("#fde68a"), stroke: yellow-fg, name: "cache", width: 3.6) + node((16.5, -0.2), [Local Vector\ (with ghosts)], fill: blue-node, stroke: blue-fg, name: "lvec") + node((21.0, -0.2), [Global Vector\ (owned DOFs)], fill: blue-node, stroke: blue-fg, name: "gvec") + node((19.0, -4.4), [Ghost Exchange], fill: pink-node, stroke: pink-fg, name: "mpi", width: 2.6, height: 1.0) + + // Arrows: user → cache → lvec + line((3.1, -0.2), (6.85, -0.2), mark: (end: ">", fill: black), stroke: 0.8pt) + elabel((5.0, 0.3), "callback") + + line((10.45, -0.2), (14.9, -0.2), mark: (end: ">", fill: black), stroke: 0.8pt) + elabel((12.7, 0.3), "pack") + + // Arrows: lvec → gvec (top arc) + bezier( + (17.5, 0.6), (20.0, 0.6), + (18.2, 1.5), (19.3, 1.5), + mark: (end: ">", fill: black), stroke: 0.8pt, + ) + elabel((18.75, 1.55), "localToGlobal") + + // Arrows: gvec → lvec (bottom arc) + bezier( + (20.0, -1.0), (17.5, -1.0), + (19.3, -1.9), (18.2, -1.9), + mark: (end: ">", fill: black), stroke: 0.8pt, + ) + elabel((18.75, -1.95), "globalToLocal") + + // Arrows: lvec ↔ mpi (dashed) + line( + (16.0, -0.8), (17.8, -3.9), + mark: (end: ">", fill: black), stroke: (dash: "dashed", thickness: 0.6pt), + ) + elabel((16.0, -2.4), "scatter") + + line( + (20.2, -3.9), (17.2, -0.8), + mark: (end: ">", fill: black), stroke: (dash: "dashed", thickness: 0.6pt), + ) + elabel((20.0, -2.4), "fill ghosts") +}) diff --git a/publications/blog-posts/sympy-to-c-pipeline-notebook.ipynb b/publications/blog-posts/sympy-to-c-pipeline-notebook.ipynb new file mode 100644 index 000000000..240bc711f --- /dev/null +++ b/publications/blog-posts/sympy-to-c-pipeline-notebook.ipynb @@ -0,0 +1,832 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ad33afb4", + "metadata": {}, + "source": [ + "# How Underworld3 Turns SymPy into C\n", + "\n", + "This notebook accompanies the blog post of the same name.\n", + "It walks through the pipeline from user-facing SymPy expressions\n", + "to compiled C callbacks registered with PETSc." + ] + }, + { + "cell_type": "markdown", + "id": "165e2659", + "metadata": {}, + "source": [ + "## At the User Level\n", + "\n", + "We set up a Stokes flow problem with a temperature-dependent\n", + "(Frank-Kamenetskii) viscosity. This is a standard thermal convection\n", + "setup — simple enough to follow, complex enough to show the pipeline." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "90b2941f", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:47.873552Z", + "iopub.status.busy": "2026-03-30T05:37:47.873471Z", + "iopub.status.idle": "2026-03-30T05:37:51.287125Z", + "shell.execute_reply": "2026-03-30T05:37:51.286829Z", + "shell.execute_reply.started": "2026-03-30T05:37:47.873543Z" + } + }, + "outputs": [], + "source": [ + "import underworld3 as uw\n", + "import sympy" + ] + }, + { + "cell_type": "markdown", + "id": "c26feb4a", + "metadata": {}, + "source": [ + "### The mesh" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "9ec8b556", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.287582Z", + "iopub.status.busy": "2026-03-30T05:37:51.287445Z", + "iopub.status.idle": "2026-03-30T05:37:51.414338Z", + "shell.execute_reply": "2026-03-30T05:37:51.413992Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.287571Z" + } + }, + "outputs": [], + "source": [ + "mesh = uw.meshing.UnstructuredSimplexBox(\n", + " minCoords=(0.0, 0.0),\n", + " maxCoords=(1.0, 1.0),\n", + " cellSize=0.1,\n", + " qdegree=3,\n", + ")\n", + "\n", + "x,y = mesh.X" + ] + }, + { + "cell_type": "markdown", + "id": "7e0ef0e0", + "metadata": {}, + "source": [ + "### Parameters as UWexpressions\n", + "\n", + "Each parameter is a symbolic name with a concrete value.\n", + "These behave like SymPy symbols in expressions but carry their values\n", + "for the compiler to extract later. (Units can be added via `uw.quantity()`\n", + "but we keep things dimensionless here to focus on the pipeline.)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "442ca4bf", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.414834Z", + "iopub.status.busy": "2026-03-30T05:37:51.414732Z", + "iopub.status.idle": "2026-03-30T05:37:51.416732Z", + "shell.execute_reply": "2026-03-30T05:37:51.416423Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.414823Z" + } + }, + "outputs": [], + "source": [ + "# Parameters — symbolic names with concrete values (dimensionless here)\n", + "eta_0 = uw.expression(r\"\\eta_0\", 1.0) # reference viscosity\n", + "gamma = uw.expression(r\"\\gamma\", 13.8) # FK sensitivity\n", + "Ra = uw.expression(\"Ra\", 1e6) # Rayleigh number" + ] + }, + { + "cell_type": "markdown", + "id": "8a79d397", + "metadata": {}, + "source": [ + "### Mesh variables\n", + "\n", + "Velocity, pressure, and temperature are mesh variables — fields\n", + "defined at every point in the mesh. We create them explicitly\n", + "so that they have readable names in the symbolic output." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0caafbd8", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.417135Z", + "iopub.status.busy": "2026-03-30T05:37:51.417043Z", + "iopub.status.idle": "2026-03-30T05:37:51.488051Z", + "shell.execute_reply": "2026-03-30T05:37:51.487690Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.417123Z" + } + }, + "outputs": [], + "source": [ + "v = uw.discretisation.MeshVariable(r\"u\", mesh, mesh.dim, degree=2)\n", + "p = uw.discretisation.MeshVariable(r\"p\", mesh, 1, degree=1, continuous=True)\n", + "T = uw.discretisation.MeshVariable(r\"T\", mesh, 1, degree=2)" + ] + }, + { + "cell_type": "markdown", + "id": "d6986e0f", + "metadata": {}, + "source": [ + "### The Stokes solver\n", + "\n", + "We pass our velocity and pressure variables to the solver." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "0b8932fe", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.488405Z", + "iopub.status.busy": "2026-03-30T05:37:51.488319Z", + "iopub.status.idle": "2026-03-30T05:37:51.505280Z", + "shell.execute_reply": "2026-03-30T05:37:51.504962Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.488395Z" + } + }, + "outputs": [], + "source": [ + "stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p)" + ] + }, + { + "cell_type": "markdown", + "id": "263bfa5d", + "metadata": {}, + "source": [ + "### Building the constitutive law\n", + "\n", + "Frank-Kamenetskii viscosity: $\\eta = \\eta_0 \\exp(-\\gamma T)$\n", + "\n", + "This is ordinary SymPy arithmetic combining UWexpressions (parameters)\n", + "and a MeshVariable (spatial field). Nothing is evaluated yet." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "0e2904ca", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.507497Z", + "iopub.status.busy": "2026-03-30T05:37:51.507359Z", + "iopub.status.idle": "2026-03-30T05:37:51.520761Z", + "shell.execute_reply": "2026-03-30T05:37:51.520494Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.507486Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\eta_0 e^{- \\gamma {T}(\\mathbf{x})}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([[\\eta_0*exp(-\\gamma*{T}(N.x, N.y))]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "viscosity_fn = eta_0 * sympy.exp(-gamma * T)\n", + "viscosity_fn" + ] + }, + { + "cell_type": "markdown", + "id": "e1ff9dc2", + "metadata": {}, + "source": [ + "### Assigning the constitutive model and body force" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "d8f38ac0", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.521127Z", + "iopub.status.busy": "2026-03-30T05:37:51.521046Z", + "iopub.status.idle": "2026-03-30T05:37:51.525082Z", + "shell.execute_reply": "2026-03-30T05:37:51.524391Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.521118Z" + } + }, + "outputs": [], + "source": [ + "stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel\n", + "stokes.constitutive_model.Parameters.shear_viscosity_0 = viscosity_fn\n", + "stokes.bodyforce = sympy.Matrix([0, -Ra * T[0, 0]])" + ] + }, + { + "cell_type": "markdown", + "id": "9d739a6f", + "metadata": {}, + "source": [ + "### Boundary conditions — free-slip on all walls" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "32d350aa", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.525952Z", + "iopub.status.busy": "2026-03-30T05:37:51.525685Z", + "iopub.status.idle": "2026-03-30T05:37:51.534494Z", + "shell.execute_reply": "2026-03-30T05:37:51.533627Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.525940Z" + } + }, + "outputs": [], + "source": [ + "stokes.add_dirichlet_bc((sympy.oo, 0.0), \"Top\")\n", + "stokes.add_dirichlet_bc((sympy.oo, 0.0), \"Bottom\")\n", + "stokes.add_dirichlet_bc((0.0, sympy.oo), \"Left\")\n", + "stokes.add_dirichlet_bc((0.0, sympy.oo), \"Right\")" + ] + }, + { + "cell_type": "markdown", + "id": "12067cf0", + "metadata": {}, + "source": [ + "## Stage 1: The Strong Form Template\n", + "\n", + "The Stokes equation in strong form is:\n", + "\n", + "$$-\\nabla \\cdot \\underbrace{\\boldsymbol{\\sigma}}_{\\mathbf{F_1}}\n", + " - \\underbrace{\\mathbf{f}}_{F_0} = 0$$\n", + "\n", + "The solver decomposes this into $\\mathbf{F}_1$ (the stress flux — everything\n", + "under the divergence) and $F_0$ (the body force — everything else).\n", + "We can inspect each piece separately.\n", + "\n", + "Note that `.sym` let's us see through to the inner symbolic representation of an object" + ] + }, + { + "cell_type": "markdown", + "id": "37bdee93", + "metadata": {}, + "source": [ + "### The body force ($F_0$)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "07758e0d-9bb4-4a93-9500-a6447e64ea38", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.535483Z", + "iopub.status.busy": "2026-03-30T05:37:51.535058Z", + "iopub.status.idle": "2026-03-30T05:37:51.540432Z", + "shell.execute_reply": "2026-03-30T05:37:51.540006Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.535469Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}0\\\\Ra {T}(\\mathbf{x})\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[ 0],\n", + "[Ra*{T}(N.x, N.y)]])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stokes.F0.sym" + ] + }, + { + "cell_type": "markdown", + "id": "a7d82dc4", + "metadata": {}, + "source": [ + "### The constitutive stress ($\\mathbf{F}_1$)\n", + "\n", + "The constitutive model defines the stress as a function of the strain rate.\n", + "Our FK viscosity appears inside it. Note the presence of a penalty term that \n", + "helps enforce incompressibility. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "623a1cd8-85f9-4012-ae3f-9d9206302991", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.540953Z", + "iopub.status.busy": "2026-03-30T05:37:51.540863Z", + "iopub.status.idle": "2026-03-30T05:37:51.568700Z", + "shell.execute_reply": "2026-03-30T05:37:51.568434Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.540944Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}2 \\eta {u}_{ 0,0}(\\mathbf{x}) + \\uplambda \\left({u}_{ 0,0}(\\mathbf{x}) + {u}_{ 1,1}(\\mathbf{x})\\right) - {p}(\\mathbf{x}) & 2 \\eta \\left(\\frac{{u}_{ 0,1}(\\mathbf{x})}{2} + \\frac{{u}_{ 1,0}(\\mathbf{x})}{2}\\right)\\\\2 \\eta \\left(\\frac{{u}_{ 0,1}(\\mathbf{x})}{2} + \\frac{{u}_{ 1,0}(\\mathbf{x})}{2}\\right) & 2 \\eta {u}_{ 1,1}(\\mathbf{x}) + \\uplambda \\left({u}_{ 0,0}(\\mathbf{x}) + {u}_{ 1,1}(\\mathbf{x})\\right) - {p}(\\mathbf{x})\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[2*\\eta*{u}_{ 0,0}(N.x, N.y) + \\uplambda*({u}_{ 0,0}(N.x, N.y) + {u}_{ 1,1}(N.x, N.y)) - {p}(N.x, N.y), 2*\\eta*({u}_{ 0,1}(N.x, N.y)/2 + {u}_{ 1,0}(N.x, N.y)/2)],\n", + "[ 2*\\eta*({u}_{ 0,1}(N.x, N.y)/2 + {u}_{ 1,0}(N.x, N.y)/2), 2*\\eta*{u}_{ 1,1}(N.x, N.y) + \\uplambda*({u}_{ 0,0}(N.x, N.y) + {u}_{ 1,1}(N.x, N.y)) - {p}(N.x, N.y)]])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stokes.F1.sym" + ] + }, + { + "cell_type": "markdown", + "id": "fa8c5cce", + "metadata": {}, + "source": [ + "### The viscosity parameter inside the model" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "eefa3a70", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.569101Z", + "iopub.status.busy": "2026-03-30T05:37:51.569009Z", + "iopub.status.idle": "2026-03-30T05:37:51.572832Z", + "shell.execute_reply": "2026-03-30T05:37:51.572610Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.569092Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\eta_0 e^{- \\gamma {T}(\\mathbf{x})}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([[\\eta_0*exp(-\\gamma*{T}(N.x, N.y))]])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stokes.constitutive_model.Parameters.shear_viscosity_0.sym" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "1d062706-e649-4501-85ff-b18f686431ec", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.573396Z", + "iopub.status.busy": "2026-03-30T05:37:51.573314Z", + "iopub.status.idle": "2026-03-30T05:37:51.586023Z", + "shell.execute_reply": "2026-03-30T05:37:51.585759Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.573387Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}- \\eta_0 \\gamma {T}_{,0}(\\mathbf{x}) e^{- \\gamma {T}(\\mathbf{x})}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([[-\\eta_0*\\gamma*{T}_{,0}(N.x, N.y)*exp(-\\gamma*{T}(N.x, N.y))]])" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "stokes.constitutive_model.Parameters.shear_viscosity_0.sym.diff(x)" + ] + }, + { + "cell_type": "markdown", + "id": "65377103", + "metadata": {}, + "source": [ + "These are all live SymPy expressions. The solver has not evaluated anything —\n", + "it stores them symbolically and defers compilation until `solve()` is called.\n", + "Note that the constitutive flux contains the strain rate of the unknown\n", + "velocity field, and the FK viscosity with its dependence on temperature." + ] + }, + { + "cell_type": "markdown", + "id": "41e78d8f", + "metadata": {}, + "source": [ + "## Stage 2: Automatic Jacobians\n", + "\n", + "The solver differentiates $F_0$ and $\\mathbf{F}_1$ with respect to the unknowns\n", + "to produce four Jacobian blocks $G_0$–$G_3$ for PETSc's Newton solver.\n", + "\n", + "We can see what this means by differentiating the viscosity ourselves.\n", + "The viscosity depends on $T$, so any Jacobian term involving\n", + "$\\partial\\mathbf{F}_1/\\partial T$ will contain this derivative:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "baf5aa83", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.586417Z", + "iopub.status.busy": "2026-03-30T05:37:51.586327Z", + "iopub.status.idle": "2026-03-30T05:37:51.596174Z", + "shell.execute_reply": "2026-03-30T05:37:51.595532Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.586407Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\left[\\begin{matrix}\\left[\\left[\\begin{matrix}- \\eta_0 \\gamma e^{- \\gamma {T}(\\mathbf{x})}\\end{matrix}\\right]\\right]\\end{matrix}\\right]\\right]$" + ], + "text/plain": [ + "[[[[-\\eta_0*\\gamma*exp(-\\gamma*{T}(N.x, N.y))]]]]" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sympy.diff(viscosity_fn, T)" + ] + }, + { + "cell_type": "markdown", + "id": "3ede0948", + "metadata": {}, + "source": [ + "SymPy computes exact symbolic derivatives. No finite-difference\n", + "approximations, no hand-coding." + ] + }, + { + "cell_type": "markdown", + "id": "440ae550", + "metadata": {}, + "source": [ + "## The Symbolic Wrappers\n", + "\n", + "Let's look at what the expressions are actually made of." + ] + }, + { + "cell_type": "markdown", + "id": "2673d034", + "metadata": {}, + "source": [ + "### UWexpression: symbol with a value" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c3bceda9", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.597333Z", + "iopub.status.busy": "2026-03-30T05:37:51.596972Z", + "iopub.status.idle": "2026-03-30T05:37:51.603408Z", + "shell.execute_reply": "2026-03-30T05:37:51.603012Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.597321Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Type: \n", + "In an expression: 2*\\eta_0*\\gamma\n", + "Stored value: 1.00000000000000\n" + ] + } + ], + "source": [ + "# eta_0 is a SymPy symbol...\n", + "print(f\"Type: {type(eta_0)}\")\n", + "print(f\"In an expression: {2 * eta_0 * gamma}\")\n", + "\n", + "# ...but it carries a value\n", + "print(f\"Stored value: {eta_0.value}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "db59c6aa", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.604221Z", + "iopub.status.busy": "2026-03-30T05:37:51.604120Z", + "iopub.status.idle": "2026-03-30T05:37:51.608159Z", + "shell.execute_reply": "2026-03-30T05:37:51.607788Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.604210Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\eta_0 = 1.00000000000000$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Display it — renders as LaTeX in the notebook\n", + "eta_0" + ] + }, + { + "cell_type": "markdown", + "id": "e6707e7c", + "metadata": {}, + "source": [ + "### MeshVariable symbols: spatial field data" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "e7a36b29", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.608994Z", + "iopub.status.busy": "2026-03-30T05:37:51.608707Z", + "iopub.status.idle": "2026-03-30T05:37:51.611588Z", + "shell.execute_reply": "2026-03-30T05:37:51.611332Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.608981Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}{T}(\\mathbf{x})\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([[{T}(N.x, N.y)]])" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# The temperature variable's symbolic face\n", + "T.sym" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "3ad3e3cc", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.612317Z", + "iopub.status.busy": "2026-03-30T05:37:51.612071Z", + "iopub.status.idle": "2026-03-30T05:37:51.616463Z", + "shell.execute_reply": "2026-03-30T05:37:51.615771Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.612306Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}{u}_{ 0 }(\\mathbf{x}) & {u}_{ 1 }(\\mathbf{x})\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([[{u}_{ 0 }(N.x, N.y), {u}_{ 1 }(N.x, N.y)]])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# The velocity variable — a vector of symbols\n", + "v.sym" + ] + }, + { + "cell_type": "markdown", + "id": "646d674b", + "metadata": {}, + "source": [ + "### Coordinates: also symbolic" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "0d2a0351", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.617020Z", + "iopub.status.busy": "2026-03-30T05:37:51.616925Z", + "iopub.status.idle": "2026-03-30T05:37:51.619829Z", + "shell.execute_reply": "2026-03-30T05:37:51.619552Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.617010Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\mathrm{x} & \\mathrm{y}\\end{matrix}\\right]$" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Mesh coordinates as SymPy symbols\n", + "mesh.X" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "796117c6", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.620300Z", + "iopub.status.busy": "2026-03-30T05:37:51.620217Z", + "iopub.status.idle": "2026-03-30T05:37:51.625358Z", + "shell.execute_reply": "2026-03-30T05:37:51.624801Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.620291Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\mathrm{y} Ra$" + ], + "text/plain": [ + "N.y*Ra" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Use them in expressions — depth-dependent body force\n", + "depth_force = Ra * mesh.X[1]\n", + "depth_force" + ] + }, + { + "cell_type": "markdown", + "id": "3632f256", + "metadata": {}, + "source": [ + "### UWexpression values" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "56f2aa2b", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-30T05:37:51.625963Z", + "iopub.status.busy": "2026-03-30T05:37:51.625869Z", + "iopub.status.idle": "2026-03-30T05:37:51.630365Z", + "shell.execute_reply": "2026-03-30T05:37:51.629572Z", + "shell.execute_reply.started": "2026-03-30T05:37:51.625952Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "eta_0 = 1.00000000000000\n", + "gamma = 13.8000000000000\n", + "Ra = 1000000.00000000\n" + ] + } + ], + "source": [ + "# Each expression carries its current value\n", + "print(f\"eta_0 = {eta_0.value}\")\n", + "print(f\"gamma = {gamma.value}\")\n", + "print(f\"Ra = {Ra.value}\")" + ] + }, + { + "cell_type": "markdown", + "id": "6101bd57", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "Everything you see in this notebook — the parameters, the viscosity law,\n", + "the $F_0$/$\\mathbf{F}_1$ terms, the constitutive flux — is simultaneously:\n", + "\n", + "- **Human-readable mathematics** (rendered in the notebook)\n", + "- **A complete specification for C code generation** (the JIT compiler reads it)\n", + "- **Symbolically differentiable** (for automatic Jacobians)\n", + "\n", + "The compiler just reads what was there all along." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/publications/blog-posts/sympy-to-c-pipeline-notebook.py b/publications/blog-posts/sympy-to-c-pipeline-notebook.py new file mode 100644 index 000000000..4298bd377 --- /dev/null +++ b/publications/blog-posts/sympy-to-c-pipeline-notebook.py @@ -0,0 +1,223 @@ +# --- +# jupyter: +# jupytext: +# text_representation: +# extension: .py +# format_name: percent +# kernelspec: +# display_name: Python 3 +# language: python +# name: python3 +# --- + +# %% [markdown] +# # How Underworld3 Turns SymPy into C +# +# This notebook accompanies the blog post of the same name. +# It walks through the pipeline from user-facing SymPy expressions +# to compiled C callbacks registered with PETSc. + +# %% [markdown] +# ## At the User Level +# +# We set up a Stokes flow problem with a temperature-dependent +# (Frank-Kamenetskii) viscosity. This is a standard thermal convection +# setup — simple enough to follow, complex enough to show the pipeline. + +# %% +import underworld3 as uw +import sympy + +# %% [markdown] +# ### The mesh + +# %% +mesh = uw.meshing.UnstructuredSimplexBox( + minCoords=(0.0, 0.0), + maxCoords=(1.0, 1.0), + cellSize=0.1, + qdegree=3, +) + +# %% [markdown] +# ### Parameters as UWexpressions +# +# Each parameter is a symbolic name with a concrete value. +# These behave like SymPy symbols in expressions but carry their values +# for the compiler to extract later. (Units can be added via `uw.quantity()` +# but we keep things dimensionless here to focus on the pipeline.) + +# %% +# Parameters — symbolic names with concrete values (dimensionless here) +eta_0 = uw.expression(r"\eta_0", 1.0) # reference viscosity +gamma = uw.expression(r"\gamma", 13.8) # FK sensitivity +Ra = uw.expression("Ra", 1e6) # Rayleigh number + +# %% [markdown] +# ### Mesh variables +# +# Velocity, pressure, and temperature are mesh variables — fields +# defined at every point in the mesh. We create them explicitly +# so that they have readable names in the symbolic output. + +# %% +v = uw.discretisation.MeshVariable(r"u", mesh, mesh.dim, degree=2) +p = uw.discretisation.MeshVariable(r"p", mesh, 1, degree=1, continuous=True) +T = uw.discretisation.MeshVariable(r"T", mesh, 1, degree=2) + +# %% [markdown] +# ### The Stokes solver +# +# We pass our velocity and pressure variables to the solver. + +# %% +stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) + +# %% [markdown] +# ### Building the constitutive law +# +# Frank-Kamenetskii viscosity: $\eta = \eta_0 \exp(-\gamma T)$ +# +# This is ordinary SymPy arithmetic combining UWexpressions (parameters) +# and a MeshVariable (spatial field). Nothing is evaluated yet. + +# %% +viscosity_fn = eta_0 * sympy.exp(-gamma * T) +viscosity_fn + +# %% [markdown] +# ### Assigning the constitutive model and body force + +# %% +stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = viscosity_fn +stokes.bodyforce = sympy.Matrix([0, -Ra * T[0, 0]]) + +# %% [markdown] +# ### Boundary conditions — free-slip on all walls + +# %% +stokes.add_dirichlet_bc((sympy.oo, 0.0), "Top") +stokes.add_dirichlet_bc((sympy.oo, 0.0), "Bottom") +stokes.add_dirichlet_bc((0.0, sympy.oo), "Left") +stokes.add_dirichlet_bc((0.0, sympy.oo), "Right") + +# %% [markdown] +# ## Stage 1: The Strong Form Template +# +# The Stokes equation in strong form is: +# +# $$-\nabla \cdot \underbrace{\boldsymbol{\sigma}}_{\mathbf{F_1}} +# - \underbrace{\mathbf{f}}_{F_0} = 0$$ +# +# The solver decomposes this into $\mathbf{F}_1$ (the stress flux — everything +# under the divergence) and $F_0$ (the body force — everything else). +# We can inspect each piece separately. + +# %% [markdown] +# ### The body force ($F_0$) + +# %% +stokes.bodyforce + +# %% [markdown] +# ### The constitutive stress ($\mathbf{F}_1$) +# +# The constitutive model defines the stress as a function of the strain rate. +# Our FK viscosity appears inside it. + +# %% +stokes.constitutive_model.flux + +# %% [markdown] +# ### The viscosity parameter inside the model + +# %% +stokes.constitutive_model.Parameters.shear_viscosity_0 + +# %% [markdown] +# These are all live SymPy expressions. The solver has not evaluated anything — +# it stores them symbolically and defers compilation until `solve()` is called. +# Note that the constitutive flux contains the strain rate of the unknown +# velocity field, and the FK viscosity with its dependence on temperature. + +# %% [markdown] +# ## Stage 2: Automatic Jacobians +# +# The solver differentiates $F_0$ and $\mathbf{F}_1$ with respect to the unknowns +# to produce four Jacobian blocks $G_0$–$G_3$ for PETSc's Newton solver. +# +# We can see what this means by differentiating the viscosity ourselves. +# The viscosity depends on $T$, so any Jacobian term involving +# $\partial\mathbf{F}_1/\partial T$ will contain this derivative: + +# %% +sympy.diff(viscosity_fn, T) + +# %% [markdown] +# SymPy computes exact symbolic derivatives. No finite-difference +# approximations, no hand-coding. + +# %% [markdown] +# ## The Symbolic Wrappers +# +# Let's look at what the expressions are actually made of. + +# %% [markdown] +# ### UWexpression: symbol with a value + +# %% +# eta_0 is a SymPy symbol... +print(f"Type: {type(eta_0)}") +print(f"In an expression: {2 * eta_0 * gamma}") + +# ...but it carries a value +print(f"Stored value: {eta_0.value}") + +# %% +# Display it — renders as LaTeX in the notebook +eta_0 + +# %% [markdown] +# ### MeshVariable symbols: spatial field data + +# %% +# The temperature variable's symbolic face +T.sym + +# %% +# The velocity variable — a vector of symbols +v.sym + +# %% [markdown] +# ### Coordinates: also symbolic + +# %% +# Mesh coordinates as SymPy symbols +mesh.X + +# %% +# Use them in expressions — depth-dependent body force +depth_force = Ra * mesh.X[1] +depth_force + +# %% [markdown] +# ### UWexpression values + +# %% +# Each expression carries its current value +print(f"eta_0 = {eta_0.value}") +print(f"gamma = {gamma.value}") +print(f"Ra = {Ra.value}") + +# %% [markdown] +# ## Summary +# +# Everything you see in this notebook — the parameters, the viscosity law, +# the $F_0$/$\mathbf{F}_1$ terms, the constitutive flux — is simultaneously: +# +# - **Human-readable mathematics** (rendered in the notebook) +# - **A complete specification for C code generation** (the JIT compiler reads it) +# - **Symbolically differentiable** (for automatic Jacobians) +# +# The compiler just reads what was there all along. diff --git a/publications/blog-posts/sympy-to-c-pipeline.md b/publications/blog-posts/sympy-to-c-pipeline.md new file mode 100644 index 000000000..160d63487 --- /dev/null +++ b/publications/blog-posts/sympy-to-c-pipeline.md @@ -0,0 +1,188 @@ +--- +title: "How Underworld3 Turns SymPy into C" +status: published +published: 2026-04-01 +url: https://www.underworldcode.org/how-underworld3-turns-sympy-into-c/ +feeds_into: [paper-1] +target: underworldcode.org (Ghost) +tags: [underworld, SymPy, PETSc, JIT, scientific-software] +--- + +# How Underworld3 Turns SymPy into C + +In a [previous post](/our-journey-from-underworld2-to-underworld3/) we described why Underworld3 uses SymPy as its expression language and what that choice made possible. Here we'll go one level deeper: what actually happens between the moment you write a mathematical expression in Python and the moment PETSc receives a finite element term in the form of compiled C? The answer is a pipeline with six stages, and understanding it explains most of what makes UW3 tick. + +## At the User Level + +A typical Underworld3 setup might look like this: + +```python +import underworld3 as uw +import sympy + +# Parameters as UWexpressions — symbolic names with concrete values and units +eta_0 = uw.expression("eta_0", uw.quantity(1e21, "Pa*s")) # reference viscosity +gamma = uw.expression("gamma", 13.8) # FK sensitivity (dimensionless) +rho = uw.expression("rho", uw.quantity(3300, "kg/m**3")) # density +gravity = uw.expression("g", uw.quantity(9.8, "m/s**2")) # gravitational acceleration + +# Temperature is a mesh variable — a field solved on the mesh +T = uw.discretisation.MeshVariable("T", mesh, 1, degree=2) + +# Frank-Kamenetskii viscosity: η = η₀ exp(-γ T) +# This is a SymPy expression built from UWexpressions and a MeshVariable +viscosity_fn = eta_0 * sympy.exp(-gamma * T) + +# Set up the Stokes solver +stokes = uw.systems.Stokes(mesh) +stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = viscosity_fn +stokes.bodyforce = -rho * gravity +stokes.solve() +``` + +The viscosity here is a SymPy expression. `eta_0` and `gamma` are UWexpressions (symbols that carry values), `T` is a mesh variable (a symbol that represents spatial field data), and `sympy.exp` is ordinary SymPy. The solver does not care what the expression contains — constant, field-dependent, nonlinear — it handles them all the same way. What happens behind `solve()` is the subject of this post. + +## Stage 1: The Strong Form Template + +Every UW3 solver defines a strong-form PDE template. For Stokes flow, this is: + +$$ +-\nabla \cdot \underbrace{\boldsymbol{\sigma}(u, \nabla u)}_{\mathbf{F_1}} - \underbrace{\mathbf{f}(u, \nabla u)}_{F_0} = 0 +$$ + +The solver decomposes this into two symbolic properties: $\mathbf{F_1}$ (flux-like terms: everything under a divergence operator, which is then paired with gradients of the test function in the weak form) and ${F_0}$ (force-like terms: everything else). For Stokes, $\mathbf{F_1}$ contains the constitutive stress minus the pressure, while ${F_0}$ contains the body force and any time-derivative contributions. + +These are ordinary SymPy expressions. You can inspect them and they render beautifully in a notebook. + + + +*[Screenshot: F0 and F1 as rendered in a Jupyter notebook — the full mathematical form of the body force and constitutive stress, with the Frank-Kamenetskii viscosity visible inside the flux.]* + +The solver does not evaluate these expressions. It stores them symbolically and defers everything until the moment they are converted (compiled) into C functions. + +## Stage 2: Automatic Jacobians + +PETSc's Newton solver (SNES) needs not just the residual but its derivative with respect to the unknowns. In many finite element codes, someone has to derive these by hand and code them in C. In UW3, SymPy does it. We did not use PETSc Newton solvers in Underworld2 because we had no systematic way to produce Jacobians for arbitrary user-defined constitutive models contructed from python functions. + +The solver takes F0 and F1 and differentiates them with respect to the unknown field and its gradient, producing four Jacobian blocks: + +``` +G0 = ∂F0/∂u G1 = ∂F0/∂(∇u) +G2 = ∂F1/∂u G3 = ∂F1/∂(∇u) +``` + +This is `sympy.derive_by_array()` applied to the user's constitutive law. For a simple linear viscosity, G3 is just the viscosity tensor. For a nonlinear rheology (strain-rate-dependent, pressure-dependent, with yield criteria) the derivatives can be complex, and SymPy computes them exactly. No finite-difference approximations, no hand-coding. What is more, they can be checked through introspection and interaction because they are symbolic before and after differentiation. + +## The Symbolic Wrappers + +Before we describe how expressions are compiled, it helps to understand how they are constructed. UW3 does not use plain SymPy symbols. It wraps them in objects that carry extra information — and the reason is lazy evaluation. + +**UWexpression.** A SymPy Symbol that holds a value inside it. When you write `eta = uw.expression("eta", 1e21)`, you get a symbol that behaves like any SymPy variable in an expression tree — you can multiply it, differentiate through it, simplify around it — but it also knows that its current value is $10^{21}$. The expression tree stays symbolic for as long as you want to inspect or manipulate it. When the JIT compiler finally needs a number, it reaches inside the wrapper and extracts the value. + +Why not use a plain SymPy symbol? Because a plain symbol `eta` is purely abstract — it has no value. And a plain number `1e21` cannot participate in symbolic differentiation. UWexpression bridges the gap: symbolic identity for the algebra, concrete value for the compiler. What's more, differentiation is lazy: we can differentiate an expression and, if we change sub-expressions or their values, the result will be computed correctly at the time we *use* the derivative. + +**MeshVariable symbols.** When you create a mesh variable for velocity or temperature, it acquires a `.sym` property — a SymPy Matrix of special symbols that represent the field. These symbols know they are *spatial data living on the mesh*, not parameters. At compile time, they get patched to C array accessors: the velocity unknown becomes `petsc_u[0]`, an auxiliary temperature field becomes `petsc_a[3]`. + +Spatial gradients of mesh variables are also symbols. When you write `T.diff(x)`, UW3 intercepts the call and returns a dedicated gradient symbol — it does not try to evaluate the derivative. This symbol represents $\partial T / \partial x$ abstractly, and at compile time it gets patched to `petsc_u_x[0]` or `petsc_a_x[0]`. PETSc provides the numerical gradient value at each quadrature point during assembly. + +This means the two kinds of derivative in UW3 work together naturally. The automatic Jacobian derivation (Stage 2) uses SymPy's chain rule to differentiate *through* gradient symbols: if the stress depends on $\nabla u$, and the Jacobian needs $\partial \mathbf{F}_1 / \partial (\nabla u)$, SymPy applies the chain rule symbolically, and the gradient symbols survive into the generated C as array references. No derivative is ever evaluated numerically until PETSc runs the compiled callback at a quadrature point. + +**Coordinates.** The mesh coordinates themselves are SymPy symbols. `mesh.X[0]` is $x$, `mesh.X[1]` is $y$. You use them in expressions naturally — `rho * g * mesh.X[1]` for a depth-dependent body force — and at compile time they become `petsc_x[0]`, `petsc_x[1]`. In spherical coordinates, the same mechanism provides $r$, $\theta$, $\phi$ with the correct differential geometry, and `sympy.diff(f, x)` gives $df/dx$ in whatever coordinate system the mesh uses. + +**UWQuantity.** An expression that carries physical units (via Pint). If the user specifies `eta = uw.quantity(1e21, "Pa*s")`, the units track through all arithmetic. At compile time, quantities are non-dimensionalised — the solver always works in scaled, dimensionless space. The units exist for the user's benefit: display, validation, dimensional analysis. PETSc never sees them. + +The point of all these wrappers is that the expression tree the user builds is simultaneously human-readable mathematics (inspect it, render it in a notebook, check the units) and a complete specification for C code generation. Nothing is lost between the two views. + +## Stage 3: Unwrapping + +With that context, the next step is easy to follow. The expressions coming out of Stage 2 are full of these user-facing wrappers. Before generating C code, the compiler must resolve them to pure SymPy — extracting values, stripping units, mapping field symbols to array indices. + +Everything that reaches PETSc must be dimensionless. If we want to work with physical units — viscosity in Pa·s, density in kg/m³ — the unwrapping stage needs to non-dimensionalises all values using the reference quantities that we define at the start of the computation. This applies to constants and field data alike. PETSc never sees a unit; it works in scaled, dimensionless space throughout. + +The unwrapping happens in two phases. + +**Phase 1: Extract constants.** The compiler scans the expression tree for UWexpressions that have no spatial or field dependencies — things like viscosity parameters, time-step size, penalty coefficients. These are pulled out, non-dimensionalised, and assigned indices in a flat array. In the generated C code, they appear as `constants[0]`, `constants[1]`, and so on. Their current (dimensionless) values are passed to PETSc at solve time, not baked into the compiled code. + +This is important. If you change (for example) a viscosity parameter between solves, UW3 does not recompile anything. It re-packs the constants array with the new dimensionless value and PETSc picks it up on the next assembly pass. + +**Phase 2: Resolve everything else.** The remaining UWexpressions — field variables, coordinates, compound expressions — are recursively unwrapped to their underlying SymPy forms. Coordinate symbols are resolved to their SymPy BaseScalar representations. Any remaining UWQuantities are non-dimensionalised. + +The result is a set of pure SymPy expressions with two kinds of atoms: constants (indexed placeholders) and field variables (which will be patched to C array references in the next stage). + +## Stage 4: C Code Generation + +Now the compiler turns SymPy into C. Each mesh variable in the expression — the unknown field, its gradient, auxiliary fields like temperature or pressure — gets patched with a C accessor string. The unknown field `u` becomes `petsc_u[0]`; its x-gradient becomes `petsc_u_x[0]`; an auxiliary mesh variable becomes `petsc_a[offset]`. Coordinate variables become `petsc_x[0]`, `petsc_x[1]`, `petsc_x[2]`. + +SymPy's C99 code printer then converts the patched expression to a C string. The compiler wraps this in a function with the exact signature that PETSc's DMPlex assembly expects: + +```c +void fn_residual_F1( + PetscInt dim, PetscInt Nf, PetscInt NfAux, + const PetscInt uOff[], const PetscInt uOff_x[], + const PetscScalar petsc_u[], // unknown field values + const PetscScalar petsc_u_x[], // unknown field gradients + const PetscInt aOff[], const PetscInt aOff_x[], + const PetscScalar petsc_a[], // auxiliary fields + const PetscScalar petsc_a_x[], // auxiliary field gradients + PetscReal petsc_t, // time + const PetscReal petsc_x[], // coordinates + PetscInt numConstants, + const PetscScalar constants[], // runtime parameters + PetscScalar out[] // output +) { + out[0] = constants[0] * petsc_u_x[0] + ...; +} +``` + +A linear viscous Stokes problem generates a handful of simple functions. A nonlinear rheology with pressure-dependent yielding generates longer ones, but the process is identical: **SymPy handles the complexity**. + +## Stage 5: Compilation and Loading + +The generated C code, a Cython wrapper, and a build script are written to a temporary directory. A subprocess call to `python setup.py build_ext --inplace` compiles everything to a shared library. The library is loaded via Python's import machinery, and function pointers are extracted. + +Compilation can be expensive, a second or more per function, so UW3 caches aggressively. The cache operates at the level of *individual functions*, not entire solvers. Each of the F0, F1, G0–G3 residual and Jacobian callbacks is hashed independently based on its *structural form*: the expression with constants replaced by placeholders. Two consequences follow. + +First, changing a parameter value (viscosity, density, time-step size) does not trigger recompilation. The structural form has not changed — only the values in the constants array, which are updated cheaply at solve time. + +Second, functions that are shared between solvers are compiled once. If a Stokes solver and an advection-diffusion solver both reference the same temperature field with the same constitutive expression, the cached compiled function is reused. In a coupled multiphysics problem with several solvers, this avoids a great deal of redundant compilation. + +Each JIT module gets a random symbol prefix to avoid name clashes when multiple compiled libraries coexist in the same process. + +## Stage 6: PETSc Takes Over + +The function pointers are registered with PETSc's `DMPlex` via `PetscDSSetResidual()` and `PetscDSSetJacobian()`. From this point, PETSc owns the assembly. During each Newton iteration, PETSc loops over mesh elements, evaluates the compiled functions at quadrature points, and assembles the global residual and Jacobian matrices. + +Before each solve, UW3 packs the current values of all constants and passes them to PETSc via `PetscDSSetConstants()`. This is how time-varying parameters, continuation parameters, and BDF/Adams-Moulton coefficients reach the compiled C code without recompilation. + +The user calls `solver.solve()`. PETSc runs Newton iterations, calling back into the JIT-compiled functions thousands or millions of times. The SymPy expressions that the user wrote in a notebook are now running as native C inside PETSc's optimised assembly loops. + +## The Complete Chain + +To summarise the pipeline for a single constitutive model: + +1. **User writes** SymPy expressions for stress, body force, boundary conditions +2. **Solver derives** Jacobian blocks automatically via symbolic differentiation +3. **Compiler extracts** runtime constants (parameters that can change between solves) +4. **Compiler unwraps** remaining expressions to pure SymPy, patches field variables to C accessors +5. **SymPy prints** the expressions as C99 code inside PETSc-compatible function signatures +6. **Subprocess compiles** to a shared library, which is cached and loaded +7. **PETSc registers** the function pointers and uses them during finite element assembly +8. **At each solve**, current constant values are packed and passed to PETSc + +The entire chain is transparent. At any stage, you can inspect what the code has done: view the symbolic expression, view the generated C, view the Jacobian that SymPy derived. In a Jupyter notebook, the solver will render the mathematics it assembled. This is what we mean when we say UW3 is *self-describing*. + +## Why This Design + +Other finite element frameworks take a different approach. FEniCS and Firedrake use the Unified Form Language (UFL) to describe the *weak form* directly. The user writes the variational problem; the framework compiles it. This is elegant and powerful, but the user works with the weak form themselves which, for many people, is a non-trivial step, especially for complex constitutive models with multiple coupled fields. + +UW3 starts from the *strong form* — the same form that appears in textbooks and publications. The framework handles the weak-form transformation, the Jacobian derivation, and the code generation. The cost is that we rely on PETSc's pointwise function template, which constrains the weak form to a specific decomposition. The benefit is that domain scientists work at the level of equations, not variational calculus. + +For geodynamics, where constitutive models are complex, nonlinear, and frequently changed during model development, this trade-off has worked well. The barrier to trying a new rheology is writing a Python class, not deriving a weak form and coding its Jacobian in C. + +--- + +*The Underworld project is supported by AuScope and the Australian Government through the National Collaborative Research Infrastructure Strategy (NCRIS). Source code: [github.com/underworldcode/underworld3](https://github.com/underworldcode/underworld3)* diff --git a/publications/blog-posts/uw2-to-uw3-journey-notes.md b/publications/blog-posts/uw2-to-uw3-journey-notes.md new file mode 100644 index 000000000..2af2e84bf --- /dev/null +++ b/publications/blog-posts/uw2-to-uw3-journey-notes.md @@ -0,0 +1,97 @@ +--- +title: Raw notes for "Our Journey from Underworld2 to Underworld3" +status: notes +feeds_into: [paper-1, release-post] +--- + +# Source Material: Louis's Account + +## The Three Eras + +### Underworld1: XML-composed modular C code +- Modular design with XML tools to compose modules into a working code +- **Pro**: Completely deterministic +- **Con**: Deterministic → inflexible, difficult to work with + +### Underworld2: Python wrapper over C engine +- Original motivation: interoperability with other codes/tools +- Functions and variables made for a near-Python programming experience +- That carried forward into parallel very nicely +- UWGeodynamics (Beucher) provided a higher-level structured interface + +### Underworld3: Clean break +- PETSc DMPlex directly, no StGermain +- SymPy symbolic layer +- JIT compilation + +## The Motivations (in Louis's priority order) + +### 1. PETSc maturity gap +- Started using PETSc for UW1 when it was very immature +- Had our own FE engine on top +- Solvers and meshing were very primitive as a result +- Too much maintenance — wanted to leverage modern PETSc capabilities +- **Could not use SNES (nonlinear solvers) with UW2 strategy** + +### 2. StGermain was a liability +- UW3 was an opportunity to set it aside +- XML component loading, C object lifecycle, dlopen gymnastics +- A framework from a different era + +### 3. Meshing limitations +- Only hex meshes with regular shapes in UW2 +- Wanted spherical and elliptical meshes — "not possible with UW2 (believe me we tried)" +- DMPlex in modern PETSc provided unstructured mesh support + +### 4. Build system / deployment +- "The agony of SWIG" +- Impossibility of maintaining the software stack +- Parallel / HPC horrors +- The sheer number of .py files from SWIG meant loading on HPC filesystems would often randomly fail + +### 5. Introspection (a bonus, not the original driver) +- SymPy + PETSc pointwise C injection made this "a fabulous step up" +- But it was NOT originally the motivation — it emerged from the design choice +- The ability to see, simplify, and differentiate the mathematical structure came for free once SymPy was chosen + +## What Was Preserved +- The particle-in-cell philosophy +- Python-first user interface +- Parallel safety by design +- The idea of composable mathematical objects (Functions → SymPy expressions) +- PETSc underneath (but now used properly) + +## What We Still Miss from UW2 +- **Particle machinery** — UW2's particle infrastructure is still ahead in some respects: + - Population control is not yet as good in UW3 + - The move to level-set-based material representations (MultiMaterialConstitutiveModel) + is more general but less intuitive than UW2's integer-key material mapping + (`fn.branching.map` with swarm variable keys was very natural) + +## How the Design Evolved After the Break +- **Lazy evaluation became central** — started as an implementation detail, now + defines the architecture. Expressions are built symbolically, derivatives are + deferred, compilation happens only when the solver needs C callbacks. +- **Lazy derivatives** — the ability to symbolically differentiate constitutive + models (for Jacobians) without evaluating them is what makes SNES integration + seamless. This was not an original design goal but became the keystone. +- **Templated problem descriptions** — lazy evaluation enables symbolic problem + templates (Stokes, Navier-Stokes, Darcy) where the user fills in constitutive + laws and the framework handles the rest. The template *is* the mathematics. +- **We leaned in** — once introspection and lazy evaluation proved powerful, the + design deliberately embraced them. SymPy went from "convenient expression + language" to "the way the code thinks about physics". +- **AI-assisted discovery** — tracing the logic of lazy derivatives and the + compilation pipeline was one of the early Claude-assisted wins. AI could + follow the symbolic chain from user expression through unwrapping to generated + C code, identifying bugs and simplification opportunities that were hard to + see manually. This fed back into making the pipeline more transparent. + +## Key Narrative Points for the Blog Post +- The rewrite was driven by **infrastructure pain** (StGermain, SWIG, primitive PETSc usage, hex-only meshes) more than by feature ambition +- SymPy introspection was a **happy consequence** of good design choices, not the goal — but then we leaned in hard +- Lazy evaluation and lazy derivatives became the architectural keystone — enabling symbolic templates, automatic Jacobians, and SNES integration +- The Function concept from UW2 was the right idea — but implemented in the wrong layer (opaque C). Moving it to SymPy made it inspectable and composable +- SNES was the solver unlock — UW2's solver strategy couldn't leverage PETSc's nonlinear solver framework +- Particle machinery is still catching up — an honest assessment, not everything is better yet +- AI assistance accelerated the maturation of the symbolic pipeline — a concrete example for the AI strategy post diff --git a/publications/blog-posts/uw2-to-uw3-journey.md b/publications/blog-posts/uw2-to-uw3-journey.md new file mode 100644 index 000000000..8270e3b9b --- /dev/null +++ b/publications/blog-posts/uw2-to-uw3-journey.md @@ -0,0 +1,72 @@ +--- +title: "Our Journey from Underworld2 to Underworld3" +status: published +published: 2026-03-23 +feeds_into: [paper-1, release-post] +target: underworldcode.org (Ghost) +tags: [underworld, geodynamics, scientific-software, PETSc, SymPy] +--- + +# Our Journey from Underworld2 to Underworld3 + +Underworld is a finite element code for geodynamics — mantle convection, lithospheric deformation, subduction, ice flow. We solve coupled, nonlinear PDEs with complex rheologies in the large-deformation limit, using Lagrangian particles to track material history. The project has been running for twenty years across three major incarnations, and this post explains why we threw out the engine and started again. + +## UW1 and UW2: The Same Wolf; different clothes + +Underworld1 assembled simulations from modular C components via XML configuration files: deterministic, reproducible, and rigid. Changing the physics meant writing C code and registering it in the XML framework. The target audience narrowed to people who could write C in a specific component architecture and, you'd have to admit, this is not a recipe for widespread adoption. + +Underworld2 wrapped that C engine in Python. The original motivation was interoperability with the scientific Python ecosystem, but Python brought something we had not anticipated. The `Function` class gave users a composable interface for describing mathematics: build a viscosity from temperature dependence, yielding criteria, and material properties, all in Python. The Jupyter notebook became the natural home for model development. Romain Beucher's UWGeodynamics module showed that a structured geodynamics interface could sit comfortably on top of the core API. + +The Function concept was the seed of a great idea. But underneath the Python layer, UW2 ran the same StGermain engine, the same finite element assembly routines, the same structured hex meshes. Python made Underworld usable by a much wider community. It did not make the engine extensible. + +In some ways, UW2 delayed the inevitable. It was successful enough that the case for a full rewrite was hard to make. The Python layer papered over the cracks in the C engine, and because models ran and papers got published, the accumulated friction took years to become unbearable. + +## Why We Finally Started Again + +The pressures that drove the rewrite existed in UW1. UW2 inherited all of them. + +**PETSc outgrew us.** We started using PETSc when it was quite immature for our purposes. We built our own finite element engine on top — our own assembly, our own solvers, our own mesh management. Although we could see that PETSc had DMPlex for unstructured meshes, SNES for nonlinear solvers, and the pointwise function interface for weak-form assembly, we could not use any of that. Our architecture sat *beside* PETSc rather than on top of it. The inability to leverage SNES was particularly painful — nonlinear problems are the bread and butter of geodynamics, and we had locked ourselves out of PETSc's Newton solver framework. + +**StGermain.** XML component loading, C object lifecycle management, dlopen gymnastics. Error messages from the C layer were cryptic. The `_function.py` source devoted 70 lines to producing useful error reports when something went wrong. UW3 was the opportunity to set all of this straight. + +**Hex meshes only.** UW2 could only build structured hexahedral meshes with regular shapes. We wanted spherical shells for mantle convection, ellipsoidal geometry for regional models. We tried to make spherical meshes work within UW2 (and we certainly tried hard) but the mesh infrastructure was too tightly coupled to the Cartesian assumption. DMPlex gave us unstructured meshes, gmsh import, cubed-sphere construction, and adaptive refinement. + +**The build system.** StGermain depended on PETSc, which depended on MPI and HDF5. SWIG generated Python bindings — thousands of `.py` files. On HPC filesystems, the sheer number of small files meant that `import underworld` would sometimes randomly fail. Docker became the recommended installation path, which solved the build problem but created others. The whole situation consumed far too much of the team's energy. + +## Functions v2: SymPy Shall Provide + +We chose SymPy as UW3's expression language for practical reasons: we needed a mature symbolic algebra library in Python that could represent PDEs. We got much more than we thought we would:- + +**Introspection.** Every constitutive model, every boundary condition, every time derivative in UW3 is a SymPy expression. You can ask the code to show you the mathematics at any point. In a Jupyter notebook, the solver renders the weak form it assembled, the Jacobian it computed, the constitutive law after simplification. This turns out to be extraordinarily useful for debugging and for teaching — you can see what the solver actually solves, not what you hope it solves. + +**Lazy evaluation.** Expressions build up symbolically, but nothing evaluates until the solver needs concrete numbers. Derivatives for Newton iteration are computed symbolically and deferred until compilation. This started as an implementation detail — a natural consequence of choosing SymPy — but it became the architectural keystone. Lazy evaluation enables *symbolic problem templates*: the Stokes solver, the Navier-Stokes solver, the Darcy solver are all defined as *equation* templates where the user fills in constitutive laws and the framework handles weak-form assembly, Jacobian derivation, and C code generation automatically. + +**Automatic Jacobians.** Because a constitutive model is a symbolic expression, the framework differentiates it exactly. No hand-coded Jacobian contributions. No finite-difference approximations. This is what finally unlocked PETSc's SNES for us — the symbolic layer provides exactly the derivatives that Newton's method needs. And this does not just apply to Newton methods. If you want to solve adjoint problems, being able to create symbolic derivatives of the entire strong form is essential. + +UW2's Function class was the right idea but we did not have sufficient depth in our implementation to cover arbitrarily complex operations. Functions were opaque C objects: you could compose them but not inspect, simplify, or differentiate them. Moving that concept into SymPy made it transparent. What started as a convenient expression language became the way the code thinks about physics. That evolution was not planned, but recognising it and embracing it shaped the best parts of UW3's design. + +## What UW3 Can Do That UW2 Could Not + +The architectural changes are not abstract — they unlock concrete capabilities that we needed for years and could not build. + +**Boundary conditions on curved surfaces.** PETSc's native boundary condition machinery assumes you can enumerate DOFs on a flat boundary and set their values directly. That breaks down on curved surfaces — a no-slip condition on a spherical shell, a free-slip condition on an irregular interface. In UW2, we had no good answer for this. UW3 uses a penalty approach: boundary conditions are expressed as additional terms in the weak form, weighted by a large penalty parameter. This is more flexible than it sounds. The same framework handles seepage boundary conditions (where fluid can leave but not enter a surface), frictional boundaries, and slip conditions on curved faults. These are not edge cases in geodynamics — they are everyday requirements that UW2 could not meet cleanly. + +**Coordinates without assumptions.** UW2 was hardwired Cartesian. Every differential operator assumed x, y, z on a flat grid. UW3 defines coordinate systems through SymPy, and the differential operators — gradient, divergence, curl — auto-adjust for the geometry. Write your governing equations once; run them in Cartesian, cylindrical, or spherical coordinates without changing the physics. The same Stokes solver template works for a rectangular box and a spherical shell. The coordinate system supplies the metric tensors and Jacobians; the user supplies the constitutive law. This is what makes spherical and geographic meshes practical, not just possible. + +**Constitutive models without C.** In UW2, adding a new rheology meant writing C code in the StGermain framework, compiling it, and wrapping it in Python. The barrier was high enough that most users never tried. In UW3, a constitutive model is a Python class with SymPy expressions for the stress-strain relationship. A domain scientist can write a new rheology — transverse isotropy, pressure-dependent plasticity, composite diffusion-dislocation creep — and test it in a notebook in an afternoon. The framework differentiates it for the Jacobian automatically. This is a direct consequence of the SymPy choice, but it is one capability that users find extremely helpful. + +**Time derivatives as swappable objects.** UW2 had one time integration approach: explicit particle advection with second-order Runge-Kutta. UW3 treats the time derivative as a symbolic object with multiple implementations — Lagrangian (particles follow the flow), Semi-Lagrangian (unconditionally stable characteristic tracing), and Eulerian (fixed grid with advection correction). All are symbolic, all participate in the weak form, and you can swap between them without rewriting the solver. The schemes support variable-order BDF and Adams-Moulton integration with automatic order ramping for stability at startup. Changing the time discretisation of a problem is a one-line change, not a restructuring of the code. + +## What's Not Finished + +Not everything is better yet. The particle machinery in UW3 is still catching up to UW2 in some respects. Population control — maintaining a good particle distribution as the mesh deforms and particles cluster or deplete — is not yet as robust. The move from integer-keyed material mapping (`fn.branching.map` in UW2, which was beautifully simple) to level-set weighted composite representations is more general but less intuitive. There is work to do, and these are areas where contributions are welcome. + +## Where We Are + +Underworld3 3.0.0 marks the point where the new architecture is mature enough to replace UW2 as the production tool. The symbolic pipeline is solid. The solver framework leverages modern PETSc properly. The mesh infrastructure handles the geometries that geodynamics actually needs. And the Python interface — the part of UW2 that actually worked — is better than ever, because SymPy makes it legible all the way down. + +In upcoming posts, we go deeper into the machinery: how SymPy expressions become C code, how particles navigate a parallel mesh, how the units system tracks physical dimensions through the pipeline, and how we build geographic meshes for regional models. + +--- + +*The Underworld project is supported by AuScope and the Australian Government through the National Collaborative Research Infrastructure Strategy (NCRIS).* diff --git a/publications/particles-surfaces/exports/.gitkeep b/publications/particles-surfaces/exports/.gitkeep new file mode 100644 index 000000000..e69de29bb diff --git a/publications/particles-surfaces/figures/.gitkeep b/publications/particles-surfaces/figures/.gitkeep new file mode 100644 index 000000000..e69de29bb diff --git a/publications/particles-surfaces/myst.yml b/publications/particles-surfaces/myst.yml new file mode 100644 index 000000000..bf6031ef8 --- /dev/null +++ b/publications/particles-surfaces/myst.yml @@ -0,0 +1,82 @@ +version: 1 + +project: + title: "Lagrangian Particles and Surface Tracking in Underworld3: Symbolic Integration of Material History" + description: > + Describes the particle (swarm) and surface-tracking implementation in + Underworld3 — parallel DMSwarm management, proxy mesh variables via RBF + projection, boundary and internal surface integrals, and how particle + data participates in the symbolic expression framework. + keywords: + - geodynamics + - particles + - Lagrangian methods + - surface tracking + - parallel computing + - PETSc + - Python + license: CC-BY-4.0 + open_access: true + bibliography: + - references.bib + authors: + - name: Louis Moresi + orcid: 0000-0003-3685-174X + corresponding: true + affiliations: + - anu-rses + - name: John Mansour + orcid: 0000-0001-5865-1664 + affiliations: + - monash + - name: Julian Giordani + orcid: 0000-0003-4515-9296 + affiliations: + - usyd + # Add other authors as appropriate + affiliations: + - id: anu-rses + institution: Australian National University + department: Research School of Earth Sciences + ror: https://ror.org/019wvm592 + city: Canberra + country: Australia + - id: monash + institution: Monash University + department: School of Earth, Atmospheric & Environmental Science + city: Melbourne + country: Australia + - id: usyd + institution: University of Sydney + city: Sydney + country: Australia + + exports: + # Draft / preprint (Typst — fast, no TeX needed) + - format: typst + template: lapreprint-typst + output: exports/paper-preprint.pdf + + # GMD submission (LaTeX — required by Copernicus) + - format: pdf + template: egu_copernicus + journal_name: gmd + running_author: "Moresi et al." + output: exports/paper-gmd.pdf + + # EarthArXiv preprint + - format: pdf + template: eartharxiv + output: exports/paper-eartharxiv.pdf + + # LaTeX source bundle for arXiv upload + - format: tex + template: arxiv_two_column + output: exports/arxiv-submission.zip + + # Word for collaborators + - format: docx + output: exports/paper.docx + +site: + template: article-theme diff --git a/publications/particles-surfaces/paper.md b/publications/particles-surfaces/paper.md new file mode 100644 index 000000000..9b738bf8e --- /dev/null +++ b/publications/particles-surfaces/paper.md @@ -0,0 +1,81 @@ +--- +title: "Lagrangian Particles and Surface Tracking in Underworld3: Symbolic Integration of Material History" +short_title: Particles and Surfaces in Underworld3 +subject: Methods for Geoscientific Model Development +abstract: | + Placeholder abstract. +date: 2026-03-22 +--- + +# Introduction + + + + +# Background: Particle-in-Cell and Lagrangian Integration Points + + + + +# Swarm Implementation + +## PETSc DMSwarm + +## Parallel decomposition and migration + +## Population control + + +# Proxy Mesh Variables + +## RBF projection from particles to mesh + +## Symbolic participation: swarm variables as UWexpressions + + +# Material History and Time Derivatives + +## Stress history for viscoelasticity + +## Advection of stored fields + +## BDF/Adams–Moulton schemes on particles + + +# Boundary and Surface Integrals + +## External boundary integrals + +## Internal surfaces and interfaces + +## The ghost-ownership problem in parallel + + +# Examples + +## Subduction with material tracking + +## Viscoelastic lithosphere with stress history + +## Two-phase flow with a tracked interface + + +# Discussion + + +# Code and data availability + +Underworld3 is open-source software released under the LGPLv3 licence. +Source code, documentation, and example notebooks are available at +[https://github.com/underworldcode/underworld3](https://github.com/underworldcode/underworld3). + +# Author contributions + +# Competing interests + +The authors declare that they have no conflict of interest. + +# Acknowledgements + +# References diff --git a/publications/particles-surfaces/references.bib b/publications/particles-surfaces/references.bib new file mode 100644 index 000000000..0faeaaba2 --- /dev/null +++ b/publications/particles-surfaces/references.bib @@ -0,0 +1,43 @@ +% References for Paper 2: Lagrangian Particles and Surfaces in Underworld3 +% Starter set — extend as writing progresses. + +@article{moresiLagrangianIntegrationPoint2003, + title = {A {{Lagrangian}} Integration Point Finite Element Method for Large Deformation Modeling of Viscoelastic Geomaterials}, + author = {Moresi, L. and Dufour, F. and M{\"u}hlhaus, H.-B.}, + year = {2003}, + journal = {Journal of Computational Physics}, + volume = {184}, + number = {2}, + pages = {476--497}, + doi = {10.1016/S0021-9991(02)00031-1} +} + +@techreport{balayPETScTAOUsers2024, + title = {{{PETSc}}/{{TAO Users Manual V}}.3.21}, + author = {Balay, S. and others}, + year = {2024}, + number = {ANL--21/39-Rev-3.21}, + doi = {10.2172/2337606} +} + +@article{mansourUnderworld2PythonGeodynamics2020, + title = {Underworld2: {{Python Geodynamics Modelling}} for {{Desktop}}, {{HPC}} and {{Cloud}}}, + author = {Mansour, John and Giordani, Julian and Moresi, Louis and others}, + year = {2020}, + journal = {JOSS}, + volume = {5}, + number = {47}, + pages = {1797}, + doi = {10.21105/joss.01797} +} + +@article{moresiComputationalApproachesStudying2007, + title = {Computational Approaches to Studying Non-Linear Dynamics of the Crust and Mantle}, + author = {Moresi, L. and Quenette, S. and Lemiale, V. and M{\'e}riaux, C. and Appelbe, B. and M{\"u}hlhaus, H.-B.}, + year = {2007}, + journal = {Physics of the Earth and Planetary Interiors}, + volume = {163}, + number = {1}, + pages = {69--82}, + doi = {10.1016/j.pepi.2007.06.009} +} diff --git a/publications/sympy-machinery/exports/.gitkeep b/publications/sympy-machinery/exports/.gitkeep new file mode 100644 index 000000000..e69de29bb diff --git a/publications/sympy-machinery/figures/.gitkeep b/publications/sympy-machinery/figures/.gitkeep new file mode 100644 index 000000000..e69de29bb diff --git a/publications/sympy-machinery/myst.yml b/publications/sympy-machinery/myst.yml new file mode 100644 index 000000000..ae6cc6d9c --- /dev/null +++ b/publications/sympy-machinery/myst.yml @@ -0,0 +1,89 @@ +version: 1 + +project: + title: "Symbolic PDE Assembly in Underworld3: From SymPy Expressions to Parallel Finite Element Solvers" + description: > + Describes the design philosophy and implementation of the symbolic + equation-assembly pipeline in Underworld3 — from user-facing SymPy + expressions through JIT compilation to PETSc weak-form callbacks. + keywords: + - geodynamics + - finite elements + - symbolic computing + - SymPy + - PETSc + - code generation + - Python + license: CC-BY-4.0 + open_access: true + bibliography: + - references.bib + authors: + - name: Louis Moresi + orcid: 0000-0003-3685-174X + corresponding: true + affiliations: + - anu-rses + - name: John Mansour + orcid: 0000-0001-5865-1664 + affiliations: + - monash + - name: Julian Giordani + orcid: 0000-0003-4515-9296 + affiliations: + - usyd + - name: Matt Knepley + orcid: 0000-0002-2292-0735 + affiliations: + - buffalo + affiliations: + - id: anu-rses + institution: Australian National University + department: Research School of Earth Sciences + ror: https://ror.org/019wvm592 + city: Canberra + country: Australia + - id: monash + institution: Monash University + department: School of Earth, Atmospheric & Environmental Science + city: Melbourne + country: Australia + - id: usyd + institution: University of Sydney + city: Sydney + country: Australia + - id: buffalo + institution: University at Buffalo + department: Computer Science and Engineering + city: Buffalo + country: United States + + exports: + # Draft / preprint (Typst — fast, no TeX needed) + - format: typst + template: lapreprint-typst + output: exports/paper-preprint.pdf + + # GMD submission (LaTeX — required by Copernicus) + - format: pdf + template: egu_copernicus + journal_name: gmd + running_author: "Moresi et al." + output: exports/paper-gmd.pdf + + # EarthArXiv preprint + - format: pdf + template: eartharxiv + output: exports/paper-eartharxiv.pdf + + # LaTeX source bundle for arXiv upload + - format: tex + template: arxiv_two_column + output: exports/arxiv-submission.zip + + # Word for collaborators + - format: docx + output: exports/paper.docx + +site: + template: article-theme diff --git a/publications/sympy-machinery/paper.md b/publications/sympy-machinery/paper.md new file mode 100644 index 000000000..68525e9fe --- /dev/null +++ b/publications/sympy-machinery/paper.md @@ -0,0 +1,179 @@ +--- +title: "Symbolic PDE Assembly in Underworld3: From SymPy Expressions to Parallel Finite Element Solvers" +short_title: Symbolic PDE Assembly in Underworld3 +subject: Methods for Geoscientific Model Development +abstract: | + We describe the design and implementation of the symbolic equation-assembly + pipeline in Underworld3, an open-source Python framework for geodynamics + modelling. Users specify governing equations in strong form using SymPy, + the Python computer-algebra system. Underworld3 automatically derives the + corresponding finite element weak forms, computes exact Jacobians for + Newton iteration, and just-in-time compiles the resulting expressions to C + callbacks consumed by PETSc. The pipeline preserves full symbolic + introspection at every stage, so that the mathematical structure of a + model — constitutive laws, boundary conditions, time discretisation — can + be displayed, simplified, and validated interactively in a Jupyter notebook + before the same script is deployed on a parallel cluster. We present the + architecture of this pipeline, discuss design trade-offs between symbolic + generality and numerical performance, and illustrate the approach with + examples drawn from mantle convection, lithospheric deformation, and + porous-media flow. +date: 2026-03-22 +--- + +# Introduction + + + +Geodynamics modelling requires solving coupled, nonlinear partial differential +equations (PDEs) with complex, spatially varying constitutive laws. The +distance between the textbook statement of a problem and the numerical code +that solves it is large: users must manually derive weak forms, compute +Jacobian contributions for Newton solvers, and express the result in a +low-level language that the solver library can consume. Each of these steps +is error-prone, opaque to collaborators, and a barrier to rapid prototyping. + +Several projects have addressed parts of this gap. The Unified Form Language +(UFL) and FEniCS ecosystem [@loggAutomatedSolutionDifferential2012] allow +users to write weak forms symbolically in Python and compile them to efficient +C/C++ kernels. Firedrake [@daviesAutomaticFiniteelementMethods2022] extends +this with composable solvers via PETSc. TerraFERMA +[@wilsonTerraFERMARansparent2017] provides a high-level options system for +multiphysics coupling. In all of these, the user works at the level of the +*weak form*, which already requires a non-trivial derivation from the +governing equations. + +Underworld3 takes a different approach. Users write the *strong form* of the +governing equations as standard SymPy expressions — the same notation found +in textbooks and journal papers. The framework then: + +1. maps these expressions onto the PETSc pointwise-function template + [@knepleyAchievingHighPerformance2013], +2. symbolically differentiates to produce exact Jacobian contributions, +3. JIT-compiles the result to C shared libraries via Cython + [@behnel2011cython], and +4. hands function pointers to PETSc for parallel assembly and solution. + +The entire pipeline is transparent: at any point the user can inspect the +SymPy expression tree, view the generated C code, or display the +mathematical form in a Jupyter notebook. This paper describes the design, +implementation, and rationale for this pipeline. + + +# Design Philosophy + + + +## Strong-form-first + +## SymPy as the algebra engine + +## Deferred evaluation and lazy compilation + + +# The PETSc Pointwise-Function Template + + + +The PETSc `DMPlex` finite element infrastructure provides a template for +residual and Jacobian assembly based on pointwise callback functions +[@knepleyAchievingHighPerformance2013; @balayPETScTAOUsers2024]. Rather +than requiring users to write element-level integration routines, PETSc +decomposes the weak form into contributions that depend on the trial +function value ($f_0$) and its gradient ($f_1$), and similarly for the +Jacobian ($g_0, g_1, g_2, g_3$). + +$$ +\mathcal{F}(u) \sim \sum_e \epsilon_e^T \left[ + B^T\, W\, f_0(u^q, \nabla u^q) + + D^T\, W\, f_1(u^q, \nabla u^q) +\right] = 0 +$$ (eq:petsc-weak-form) + +The user's responsibility reduces to providing C functions for $f_0$, $f_1$ +and the corresponding Jacobian blocks $g_0 \ldots g_3$. This is precisely +what Underworld3 generates from the symbolic strong form. + + +# From Strong Form to Weak Form: The Symbolic Pipeline + +## UWexpression: the symbolic wrapper + + + +## Expression unwrapping and compilation + + + +## Constitutive models as symbolic objects + + + +## Time discretisation + + + + +# JIT Compilation + +## Cython code generation + +## Symbol-to-C mapping + +## Shared-library loading and PETSc callback registration + + +# Solver Integration + +## Template solvers: Stokes, Navier–Stokes, Darcy, Poisson + +## Nonlinear iteration and automatic Jacobians + +## Boundary conditions as symbolic expressions + + +# Introspection and the Notebook Experience + +## Mathematical display of assembled forms + +## Dimensional analysis via the units system + +## From notebook prototype to HPC script + + +# Examples + +## Mantle convection with composite rheology + +## Lithospheric extension with plasticity + +## Darcy flow with heterogeneous permeability + + +# Discussion + + + + +# Code and data availability + +Underworld3 is open-source software released under the LGPLv3 licence. +Source code, documentation, and example notebooks are available at +[https://github.com/underworldcode/underworld3](https://github.com/underworldcode/underworld3). + +# Author contributions + + + +# Competing interests + +The authors declare that they have no conflict of interest. + +# Acknowledgements + +AuScope provides direct support for the core development team behind the +Underworld codes. AuScope is funded by the Australian Government through +the National Collaborative Research Infrastructure Strategy, NCRIS. + +# References diff --git a/publications/sympy-machinery/references.bib b/publications/sympy-machinery/references.bib new file mode 100644 index 000000000..43d4ef21e --- /dev/null +++ b/publications/sympy-machinery/references.bib @@ -0,0 +1,146 @@ +% References for Paper 1: Symbolic PDE Assembly in Underworld3 +% Seeded from the JOSS paper bibliography; extend as needed. + +@techreport{balayPETScTAOUsers2024, + title = {{{PETSc}}/{{TAO Users Manual V}}.3.21}, + author = {Balay, S. and Abhyankar, S. and Adams, M. and Benson, S. and Brown, J. and Brune, P. and Buschelman, K. and Constantinescu, E. and Dalcin, L. and Dener, A. and Eijkhout, V. and Faibussowitsch, J. and Gropp, W. and Hapla, V. and Isaac, T. and Jolivet, P. and Karpeev, D. and Kaushik, D. and Knepley, M. and Kong, F. and Kruger, S. and May, D. and McInnes, L. and Mills, R. and Mitchell, L. and Munson, T. and Roman, J. and Rupp, K. and Sanan, P. and Sarich, J. and Smith, B. and Zampini, S. and Zhang, H. and Zhang, H. and Zhang, J.}, + year = {2024}, + month = mar, + number = {ANL--21/39-Rev-3.21}, + doi = {10.2172/2337606} +} + +@article{behnel2011cython, + title = {Cython: {{The}} Best of Both Worlds}, + author = {Behnel, Stefan and Bradshaw, Robert and Citro, Craig and Dalcin, Lisandro and Seljebotn, Dag Sverre and Smith, Kurt}, + year = {2011}, + journal = {Computing in Science \& Engineering}, + volume = {13}, + number = {2}, + pages = {31--39}, + doi = {10.1109/mcse.2010.118} +} + +@article{dalcinpazklercosimo2011, + title = {Parallel Distributed Computing Using {{Python}}}, + author = {Dalcin, Lisandro D. and Paz, Rodrigo R. and Kler, Pablo A. and Cosimo, Alejandro}, + year = {2011}, + journal = {Advances in Water Resources}, + volume = {34}, + number = {9}, + pages = {1124--1139}, + doi = {10.1016/j.advwatres.2011.04.013} +} + +@article{daviesAutomaticFiniteelementMethods2022, + title = {Towards Automatic Finite-Element Methods for Geodynamics via {{Firedrake}}}, + author = {Davies, D. Rhodri and Kramer, Stephan C. and Ghelichkhan, Sia and Gibson, Angus}, + year = {2022}, + journal = {Geosci. Model Dev.}, + volume = {15}, + number = {13}, + pages = {5127--5166}, + doi = {10.5194/gmd-15-5127-2022} +} + +@book{hughesFiniteElementMethod1987, + title = {The Finite Element Method: Linear Static and Dynamic Finite Element Analysis}, + author = {Hughes, Thomas J. R.}, + year = {1987}, + publisher = {Prentice Hall}, + address = {Englewood Cliffs, N.J.}, + doi = {10.1016/0045-7825(87)90013-2} +} + +@article{knepleyAchievingHighPerformance2013, + title = {Achieving {{High Performance}} with {{Unified Residual Evaluation}}}, + author = {Knepley, Matthew G. and Brown, Jed and Rupp, Karl and Smith, Barry F.}, + year = {2013}, + journal = {arXiv:1309.1204 [cs]}, + eprint = {1309.1204}, + archiveprefix = {arXiv} +} + +@book{loggAutomatedSolutionDifferential2012, + title = {Automated {{Solution}} of {{Differential Equations}} by the {{Finite Element Method}}: {{The FEniCS Book}}}, + editor = {Logg, Anders and Mardal, Kent-Andre and Wells, Garth}, + year = {2012}, + series = {Lecture {{Notes}} in {{Computational Science}} and {{Engineering}}}, + volume = {84}, + publisher = {Springer Berlin Heidelberg}, + doi = {10.1007/978-3-642-23099-8} +} + +@article{mansourUnderworld2PythonGeodynamics2020, + title = {Underworld2: {{Python Geodynamics Modelling}} for {{Desktop}}, {{HPC}} and {{Cloud}}}, + author = {Mansour, John and Giordani, Julian and Moresi, Louis and Beucher, Romain and Kaluza, Owen and Velic, Mirko and Farrington, Rebecca and Quenette, Steve and Beall, Adam}, + year = {2020}, + journal = {JOSS}, + volume = {5}, + number = {47}, + pages = {1797}, + doi = {10.21105/joss.01797} +} + +@article{meurerSymPySymbolicComputing2017, + title = {{{SymPy}}: Symbolic Computing in {{Python}}}, + author = {Meurer, Aaron and Smith, Christopher P. and Paprocki, Mateusz and others}, + year = {2017}, + journal = {PeerJ Computer Science}, + volume = {3}, + pages = {e103}, + doi = {10.7717/peerj-cs.103} +} + +@article{moresiLagrangianIntegrationPoint2003, + title = {A {{Lagrangian}} Integration Point Finite Element Method for Large Deformation Modeling of Viscoelastic Geomaterials}, + author = {Moresi, L. and Dufour, F. and M{\"u}hlhaus, H.-B.}, + year = {2003}, + journal = {Journal of Computational Physics}, + volume = {184}, + number = {2}, + pages = {476--497}, + doi = {10.1016/S0021-9991(02)00031-1} +} + +@incollection{moresiChapter23Literate2023, + title = {Chapter 23 - {{Literate}}, {{Reusable}}, {{Geodynamic Modeling}}}, + booktitle = {Dynamics of {{Plate Tectonics}} and {{Mantle Convection}}}, + author = {Moresi, Louis}, + year = {2023}, + pages = {573--582}, + publisher = {Elsevier}, + doi = {10.1016/B978-0-323-85733-8.00010-X} +} + +@article{wilsonTerraFERMARansparent2017, + title = {{TerraFERMA}: The Transparent Finite Element Rapid Model Assembler for Multiphysics Problems in Earth Sciences}, + author = {Wilson, Cian R. and Spiegelman, Marc and Van Keken, Peter E.}, + year = {2017}, + journal = {Geochem. Geophys. Geosyst.}, + volume = {18}, + number = {2}, + pages = {769--810}, + doi = {10.1002/2016GC006702} +} + +@article{heisterHighAccuracyMantle2017, + title = {High Accuracy Mantle Convection Simulation through Modern Numerical Methods -- {{II}}: Realistic Models and Problems}, + author = {Heister, Timo and Dannberg, Juliane and Gassm{\"o}ller, Rene and Bangerth, Wolfgang}, + year = {2017}, + journal = {Geophysical Journal International}, + volume = {210}, + number = {2}, + pages = {833--851}, + doi = {10.1093/gji/ggx195} +} + +@incollection{zhong705NumericalMethods2015, + title = {7.05 - {{Numerical Methods}} for {{Mantle Convection}}}, + booktitle = {Treatise on {{Geophysics}} ({{Second Edition}})}, + author = {Zhong, S. J. and Yuen, D. A. and Moresi, L. N. and Knepley, M. G.}, + year = {2015}, + pages = {197--222}, + publisher = {Elsevier}, + doi = {10.1016/B978-0-444-53802-4.00130-5} +} From 9fda3c1ad73298fddc90aee6283d92af3aed7619 Mon Sep 17 00:00:00 2001 From: Thyagarajulu Gollapalli Date: Sat, 4 Apr 2026 17:25:27 +1100 Subject: [PATCH 067/537] add missing packages to petsc during hpc build --- petsc-custom/build-petsc.sh | 2 ++ 1 file changed, 2 insertions(+) diff --git a/petsc-custom/build-petsc.sh b/petsc-custom/build-petsc.sh index f55e3278e..63d816297 100755 --- a/petsc-custom/build-petsc.sh +++ b/petsc-custom/build-petsc.sh @@ -293,6 +293,7 @@ configure_petsc() { --download-cmake=1 \ --download-bison=1 \ --with-petsc4py=1 \ + --with-slepc4py=1 \ --with-make-np=40 ;; gadi) @@ -304,6 +305,7 @@ configure_petsc() { --with-hdf5-dir="${HDF5_DIR}" \ --download-fblaslapack=1 \ --with-petsc4py=1 \ + --with-slepc4py=1 \ --with-make-np=40 \ --with-shared-libraries=1 \ --with-cxx-dialect=C++11 \ From 90123353c575dfcfd0b591aca7ae8b61300d4e21 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Tue, 7 Apr 2026 13:54:49 -0700 Subject: [PATCH 068/537] Normalise Gamma_N: unit boundary normal for consistent penalty scaling MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit mesh.Gamma_N now returns Gamma / |Gamma| — a unit normal regardless of element size. mesh.Gamma remains the raw (un-normalised) PETSc face normal whose magnitude scales with edge length (2D) / face area (3D). This fixes a scaling issue where: - penalty * Gamma.dot(v) * Gamma had effective penalty ~ penalty * h² - Nitsche gamma/h * Gamma.dot(v) * Gamma scaled as h (should be 1/h) With normalised Gamma_N, both penalty and Nitsche terms are now mesh-independent at the symbolic level. Updated Nitsche BC code to use the normalised matrix form. JIT extension updated to register ccode on the raw Gamma base scalars. Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 14 +++++------- .../discretisation/discretisation_mesh.py | 22 +++++++++++++------ src/underworld3/utilities/_jitextension.py | 6 +++-- 3 files changed, 25 insertions(+), 17 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 62c411630..88d09c7f7 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -2193,10 +2193,9 @@ class SNES_Vector(SolverBaseClass): mesh = self.mesh dim = mesh.dim - # Surface normal components - n = [mesh.Gamma_N.x, mesh.Gamma_N.y] - if dim == 3: - n.append(mesh.Gamma_N.z) + # Surface normal components (normalised) + Gamma_N = mesh.Gamma_N + n = [Gamma_N[i] for i in range(dim)] # Constraint direction: defaults to surface normal if direction is not None: @@ -3233,16 +3232,15 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): mesh = self.mesh dim = mesh.dim - # Surface normal components. By default use PETSc's facet normal. + # Surface normal components. By default use normalised PETSc facet normal. if normal is not None: if isinstance(normal, sympy.MatrixBase): n = [normal[i] for i in range(dim)] else: n = list(normal) else: - n = [mesh.Gamma_N.x, mesh.Gamma_N.y] - if dim == 3: - n.append(mesh.Gamma_N.z) + Gamma_N = mesh.Gamma_N + n = [Gamma_N[i] for i in range(dim)] # Constraint direction: defaults to surface normal if direction is not None: diff --git a/src/underworld3/discretisation/discretisation_mesh.py b/src/underworld3/discretisation/discretisation_mesh.py index 4b11dbd6e..7802dd938 100644 --- a/src/underworld3/discretisation/discretisation_mesh.py +++ b/src/underworld3/discretisation/discretisation_mesh.py @@ -1451,19 +1451,27 @@ def N(self) -> sympy.vector.CoordSys3D: return self._N @property - def Gamma_N(self) -> sympy.vector.CoordSys3D: - r"""SymPy coordinate system for boundary/surface coordinates. + def Gamma_N(self) -> sympy.Matrix: + r"""Normalised boundary/surface normal as a row matrix. + + Returns ``Gamma / |Gamma|`` so that the result is a unit normal + regardless of element size. Use this for penalty and Nitsche BCs + where mesh-independent scaling is required. Returns ------- - sympy.vector.CoordSys3D - The boundary coordinate system object. + sympy.Matrix + Row matrix of normalised boundary normal components. """ - return self._Gamma + G = self.Gamma + return G / sympy.sqrt(G.dot(G)) @property - def Gamma(self) -> sympy.vector.CoordSys3D: - r"""Boundary coordinate scalars as a row matrix. + def Gamma(self) -> sympy.Matrix: + r"""Raw (un-normalised) boundary coordinate scalars as a row matrix. + + The magnitude scales with face edge length (2D) or face area (3D). + For a unit normal, use :attr:`Gamma_N` instead. Returns ------- diff --git a/src/underworld3/utilities/_jitextension.py b/src/underworld3/utilities/_jitextension.py index d9eb50559..a15e76778 100644 --- a/src/underworld3/utilities/_jitextension.py +++ b/src/underworld3/utilities/_jitextension.py @@ -775,8 +775,10 @@ def _basescalar_ccode(self, printer): return f"petsc_x[{idx}]" type(mesh.N.x)._ccode = _basescalar_ccode - if type(mesh.Gamma_N.x) is not type(mesh.N.x): - type(mesh.Gamma_N.x)._ccode = _basescalar_ccode + # Gamma base scalars (un-normalised face normal) — ensure ccode is registered + Gamma_scalars = mesh._Gamma.base_scalars() + if type(Gamma_scalars[0]) is not type(mesh.N.x): + type(Gamma_scalars[0])._ccode = _basescalar_ccode # Create a custom functions replacement dictionary. # Note that this dictionary is really just to appease Sympy, From 1dfa914f332e1a92e8e083b22dfbf9c4f1044626 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 23 Feb 2026 22:13:47 +1100 Subject: [PATCH 069/537] Add TransientDarcy and Richards solvers with mass-conservative mixed form MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Introduce a Darcy/Richards solver hierarchy for groundwater and variably-saturated flow: - SNES_TransientDarcy: time-dependent groundwater flow with constant storage, BDF time integration, and Adams-Moulton flux weighting - SNES_Richards: nonlinear extension using the mixed (mass-conservative) form ∂θ/∂t rather than C(ψ)·∂ψ/∂t, eliminating mass balance errors from the discrete chain rule (Celia et al. 1990) Supporting additions: - retention_curves module with Gardner and Van Genuchten models, including an Ogata-Banks analytical transient solution - NB16: steady-state Richards equation tutorial - NB17: transient wetting-front benchmark against analytical solution - Tests for transient Darcy diffusion, steady Richards, transient Richards with VG and Gardner models - Updated Params docstring to document named-constants-first convention - Minor updates to notebook index, style guide, and NB14 Underworld development team with AI support from Claude Code --- docs/beginner/parameters.md | 41 +- .../16-Richards-Equation-Groundwater.ipynb | 679 ++++++++++++++++++ .../17-Richards-Transient-Wetting-Front.ipynb | 636 ++++++++++++++++ docs/beginner/tutorials/Notebook_Index.ipynb | 40 +- docs/developer/guides/notebook-style-guide.md | 83 ++- .../Benchmark/Ex_VP_Spiegelman_Benchmark.py | 3 +- src/underworld3/__init__.py | 1 + src/underworld3/systems/__init__.py | 8 + src/underworld3/systems/solvers.py | 463 +++++++++++- src/underworld3/utilities/__init__.py | 2 + src/underworld3/utilities/_params.py | 33 +- src/underworld3/utilities/retention_curves.py | 505 +++++++++++++ tests/test_1005_TransientDarcyCartesian.py | 116 +++ tests/test_1006_RichardsCartesian.py | 267 +++++++ 14 files changed, 2806 insertions(+), 71 deletions(-) create mode 100644 docs/beginner/tutorials/16-Richards-Equation-Groundwater.ipynb create mode 100644 docs/beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb create mode 100644 src/underworld3/utilities/retention_curves.py create mode 100644 tests/test_1005_TransientDarcyCartesian.py create mode 100644 tests/test_1006_RichardsCartesian.py diff --git a/docs/beginner/parameters.md b/docs/beginner/parameters.md index a82b48e23..045dc429d 100644 --- a/docs/beginner/parameters.md +++ b/docs/beginner/parameters.md @@ -16,16 +16,25 @@ This makes scripts portable between interactive development and HPC batch execut ## Basic Usage +The recommended pattern is to define default values as **named constants** before +the `uw.Params` block. This separates "what are the defaults" (easy to find and +edit in a notebook) from "how are they validated and overridden" (the `uw.Params` +machinery). + ```python import underworld3 as uw -# Define parameters with defaults +# --- Default values (edit these in a notebook) --- +RESOLUTION = 0.05 # cell size for mesh +DIFFUSIVITY = 1.0 # material property +MAX_STEPS = 100 # solver iterations + params = uw.Params( - uw_resolution = 0.05, # Cell size for mesh - uw_diffusivity = 1.0, # Material property - uw_max_steps = 100, # Integer parameter - uw_verbose = True, # Boolean flag - uw_solver = "mumps", # String option + uw_resolution = RESOLUTION, + uw_diffusivity = DIFFUSIVITY, + uw_max_steps = MAX_STEPS, + uw_verbose = True, # Boolean flag + uw_solver = "mumps", # String option ) # Use in your model @@ -203,22 +212,30 @@ Example: ```python import underworld3 as uw +# --- Default values (edit these in a notebook) --- +CELL_SIZE = 50.0 # km – target cell size +DEPTH = 660.0 # km – model depth +VISCOSITY = 1e21 # Pa·s – reference viscosity +DENSITY_DIFF = 50.0 # kg/m³ – density contrast +MAX_ITERATIONS = 50 +TOLERANCE = 1e-6 + # Define all configurable parameters at the top params = uw.Params( # Mesh parameters - uw_cell_size = uw.Param(50.0, units="km", + uw_cell_size = uw.Param(CELL_SIZE, units="km", bounds=(10, 200), description="Target cell size"), - uw_depth = uw.Param(660.0, units="km", + uw_depth = uw.Param(DEPTH, units="km", description="Model depth"), # Physical properties - uw_viscosity = uw.Param(1e21, units="Pa*s"), - uw_density_diff = uw.Param(50.0, units="kg/m^3"), + uw_viscosity = uw.Param(VISCOSITY, units="Pa*s"), + uw_density_diff = uw.Param(DENSITY_DIFF, units="kg/m^3"), # Solver settings - uw_max_iterations = 50, - uw_tolerance = 1e-6, + uw_max_iterations = MAX_ITERATIONS, + uw_tolerance = TOLERANCE, ) # Show help (useful at script start) diff --git a/docs/beginner/tutorials/16-Richards-Equation-Groundwater.ipynb b/docs/beginner/tutorials/16-Richards-Equation-Groundwater.ipynb new file mode 100644 index 000000000..fd72579b3 --- /dev/null +++ b/docs/beginner/tutorials/16-Richards-Equation-Groundwater.ipynb @@ -0,0 +1,679 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Notebook 16: Richards Equation \u2014 Groundwater Flow\n", + "\n", + "This notebook introduces the Richards equation for variably-saturated\n", + "porous media flow. We solve a steady-state drainage problem in a\n", + "vertical soil column and validate the numerical solution against an\n", + "exact analytical benchmark.\n", + "\n", + "## Key Concepts\n", + "\n", + "- Richards equation \u2014 nonlinear PDE for unsaturated flow\n", + "- Gardner exponential conductivity model\n", + "- Analytical steady-state solution with gravity\n", + "- Darcy velocity field" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Richards Equation\n", + "\n", + "Water movement in unsaturated soil is governed by the Richards\n", + "equation (Richards, 1931). Three equivalent forms exist:\n", + "\n", + "| Form | Storage term | Flux term | Notes |\n", + "|------|-------------|-----------|-------|\n", + "| Head-based ($\\psi$) | $C(\\psi)\\,\\partial\\psi/\\partial t$ | $\\nabla\\cdot[K(\\psi)(\\nabla\\psi - \\mathbf{s})]$ | Simple, but poor mass balance |\n", + "| Moisture-based ($\\theta$) | $\\partial\\theta/\\partial t$ | $\\nabla\\cdot[D(\\theta)\\nabla\\theta]$ | Conservative, but $D(\\theta)$ singular at saturation |\n", + "| **Mixed** | $\\partial\\theta/\\partial t$ | $\\nabla\\cdot[K(\\psi)(\\nabla\\psi - \\mathbf{s})]$ | Conservative and well-behaved |\n", + "\n", + "The **mixed form** (Celia et al., 1990) is generally preferred because\n", + "writing the storage as $\\partial\\theta/\\partial t$ guarantees mass\n", + "conservation in the discrete system \u2014 the head-based form\n", + "$C(\\psi)\\,\\partial\\psi/\\partial t$ introduces balance errors because the\n", + "discrete chain rule $C(\\psi)\\Delta\\psi \\neq \\Delta\\theta$ when $C$ varies\n", + "sharply across a timestep.\n", + "\n", + "$$\\frac{\\partial \\theta}{\\partial t}\n", + " - \\nabla\\cdot\\bigl[K(\\psi)\\,(\\nabla\\psi - \\mathbf{s})\\bigr] = f$$\n", + "\n", + "where\n", + "- $\\psi$ is the **pressure head** (negative in unsaturated soil),\n", + "- $\\theta(\\psi)$ is the **volumetric water content**,\n", + "- $K(\\psi)$ is the **hydraulic conductivity** (decreases as soil dries out),\n", + "- $\\mathbf{s} = [0, -1]^T$ represents **gravity** (pointing downward),\n", + "- $f$ is any source/sink.\n", + "\n", + "The Underworld solver uses this mixed form when `water_content` is set\n", + "\u2014 discretising the storage term as\n", + "$(\\theta(\\psi^{n+1}) - \\theta(\\psi^n))/\\Delta t$.\n", + "The Jacobian $\\partial\\theta/\\partial\\psi = C(\\psi)$ is computed\n", + "automatically by PETSc. For steady-state problems (where\n", + "$\\partial/\\partial t = 0$) the forms are all identical." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gardner Exponential Model\n", + "\n", + "The **Gardner (1958)** model uses an exponential relationship for\n", + "hydraulic conductivity:\n", + "\n", + "$$K(\\psi) = K_s\\,e^{\\alpha\\psi}, \\qquad \\psi < 0$$\n", + "\n", + "This is simpler than the Van Genuchten model and, crucially,\n", + "admits an **exact analytical solution** for the steady-state\n", + "Richards equation with gravity.\n", + "\n", + "The substitution $u = e^{\\alpha\\psi}$ linearises the ODE, giving\n", + "the exact pressure head profile:\n", + "\n", + "$$\\psi(y) = \\frac{1}{\\alpha}\\,\\ln\\!\\Bigl[\n", + " \\bigl(u_0 - q^*\\bigr)\\,e^{-\\alpha y} + q^*\n", + "\\Bigr]$$\n", + "\n", + "where $u_0 = e^{\\alpha\\psi_0}$, $u_L = e^{\\alpha\\psi_L}$, and\n", + "$q^* = q/K_s = (u_L - u_0\\,e^{-\\alpha L})/(1 - e^{-\\alpha L})$." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:26.899970Z", + "iopub.status.busy": "2026-02-23T08:03:26.899837Z", + "iopub.status.idle": "2026-02-23T08:03:29.371758Z", + "shell.execute_reply": "2026-02-23T08:03:29.371351Z", + "shell.execute_reply.started": "2026-02-23T08:03:26.899959Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy\n", + "import underworld3 as uw\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from underworld3.utilities.retention_curves import (\n", + " gardner_K,\n", + " gardner_theta,\n", + " gardner_steady_state_psi,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Configurable parameters\n", + "\n", + "Default values are defined as named constants below. From the\n", + "command line, override them with PETSc-style flags:\n", + "\n", + "```bash\n", + "python script.py -uw_Ks \"5e-5 m/s\" -uw_alpha \"2.0 1/m\"\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:29.373366Z", + "iopub.status.busy": "2026-02-23T08:03:29.373024Z", + "iopub.status.idle": "2026-02-23T08:03:29.376282Z", + "shell.execute_reply": "2026-02-23T08:03:29.375910Z", + "shell.execute_reply.started": "2026-02-23T08:03:29.373350Z" + } + }, + "outputs": [], + "source": [ + "# --- Default values (edit these in a notebook) ---\n", + "COLUMN_HEIGHT = 1.0 # m \u2014 soil column height\n", + "COLUMN_WIDTH = 0.1 # m \u2014 narrow (\u2248 1-D)\n", + "RES = 32 # \u2014 vertical elements\n", + "KS = 1e-4 # m/s \u2014 saturated hydraulic conductivity\n", + "ALPHA_G = 3.5 # 1/m \u2014 Gardner sorptive number\n", + "THETA_R = 0.05 # \u2014 residual water content\n", + "THETA_S = 0.40 # \u2014 saturated water content\n", + "PSI_TOP = -0.5 # m \u2014 pressure head at top\n", + "PSI_BOTTOM = -3.0 # m \u2014 pressure head at bottom" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:29.376850Z", + "iopub.status.busy": "2026-02-23T08:03:29.376657Z", + "iopub.status.idle": "2026-02-23T08:03:29.382604Z", + "shell.execute_reply": "2026-02-23T08:03:29.382268Z", + "shell.execute_reply.started": "2026-02-23T08:03:29.376834Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\mathrm{K_s} = 1.00 \\times 10^{-04} \\; \\mathrm{meter / second}$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Named expressions for display\n", + "Ks = uw.expression(r\"K_s\", uw.quantity(KS, \"m/s\"), \"saturated conductivity\")\n", + "alpha_g = uw.expression(r\"\\alpha\", uw.quantity(ALPHA_G, \"1/m\"), \"Gardner sorptive number\")\n", + "theta_r = uw.expression(r\"\\theta_r\", THETA_R, \"residual water content\")\n", + "theta_s = uw.expression(r\"\\theta_s\", THETA_S, \"saturated water content\")\n", + "\n", + "Ks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Retention Curves\n", + "\n", + "Let\u2019s visualise how hydraulic conductivity and water content\n", + "change with pressure head for these Gardner parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:29.383126Z", + "iopub.status.busy": "2026-02-23T08:03:29.383012Z", + "iopub.status.idle": "2026-02-23T08:03:29.907990Z", + "shell.execute_reply": "2026-02-23T08:03:29.907225Z", + "shell.execute_reply.started": "2026-02-23T08:03:29.383113Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "

" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "psi_range = np.linspace(-5, 0, 200)\n", + "\n", + "K_vals = KS * np.exp(ALPHA_G * psi_range)\n", + "K_vals[psi_range >= 0] = KS\n", + "\n", + "theta_vals = THETA_R + (THETA_S - THETA_R) * np.exp(ALPHA_G * psi_range)\n", + "theta_vals[psi_range >= 0] = THETA_S\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))\n", + "\n", + "ax1.semilogy(psi_range, K_vals)\n", + "ax1.set_xlabel(r\"Pressure head $\\psi$ (m)\")\n", + "ax1.set_ylabel(r\"$K(\\psi)$ (m/s)\")\n", + "ax1.set_title(\"Hydraulic conductivity\")\n", + "ax1.grid(True, alpha=0.3)\n", + "\n", + "ax2.plot(psi_range, theta_vals)\n", + "ax2.set_xlabel(r\"Pressure head $\\psi$ (m)\")\n", + "ax2.set_ylabel(r\"$\\theta(\\psi)$\")\n", + "ax2.set_title(\"Volumetric water content\")\n", + "ax2.axhline(THETA_S, color=\"grey\", ls=\"--\", lw=0.8, label=r\"$\\theta_s$\")\n", + "ax2.axhline(THETA_R, color=\"grey\", ls=\":\", lw=0.8, label=r\"$\\theta_r$\")\n", + "ax2.legend()\n", + "ax2.grid(True, alpha=0.3)\n", + "\n", + "fig.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Analytical Solution\n", + "\n", + "For a column of height $L$ with boundary conditions\n", + "$\\psi(0) = \\psi_\\text{bottom}$ and $\\psi(L) = \\psi_\\text{top}$,\n", + "the exact steady-state profile is given by\n", + "`gardner_steady_state_psi`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:29.909278Z", + "iopub.status.busy": "2026-02-23T08:03:29.908998Z", + "iopub.status.idle": "2026-02-23T08:03:29.994670Z", + "shell.execute_reply": "2026-02-23T08:03:29.994276Z", + "shell.execute_reply.started": "2026-02-23T08:03:29.909261Z" + }, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "y_exact = np.linspace(0, COLUMN_HEIGHT, 200)\n", + "psi_exact = gardner_steady_state_psi(\n", + " y_exact,\n", + " psi_0=PSI_BOTTOM,\n", + " psi_L=PSI_TOP,\n", + " L=COLUMN_HEIGHT,\n", + " alpha=ALPHA_G,\n", + ")\n", + "\n", + "fig, ax = plt.subplots(figsize=(5, 6))\n", + "ax.plot(psi_exact, y_exact, \"b-\", lw=2, label=\"Analytical\")\n", + "ax.set_xlabel(r\"Pressure head $\\psi$ (m)\")\n", + "ax.set_ylabel(\"Height $y$ (m)\")\n", + "ax.set_title(\"Exact steady-state profile\")\n", + "ax.grid(True, alpha=0.3)\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Numerical Solution with Richards Solver\n", + "\n", + "We solve the same problem numerically using `uw.systems.Richards`,\n", + "stepping forward in time until the transient terms die out and\n", + "we reach steady state." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:29.995465Z", + "iopub.status.busy": "2026-02-23T08:03:29.995228Z", + "iopub.status.idle": "2026-02-23T08:03:30.131412Z", + "shell.execute_reply": "2026-02-23T08:03:30.130717Z", + "shell.execute_reply.started": "2026-02-23T08:03:29.995431Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Structured box element resolution 4 32\n" + ] + } + ], + "source": [ + "mesh = uw.meshing.StructuredQuadBox(\n", + " elementRes=(4, RES),\n", + " minCoords=(0.0, 0.0),\n", + " maxCoords=(COLUMN_WIDTH, COLUMN_HEIGHT),\n", + " qdegree=3,\n", + ")\n", + "\n", + "psi_var = uw.discretisation.MeshVariable(r\"\\psi\", mesh, 1, degree=2)\n", + "v_soln = uw.discretisation.MeshVariable(\"v\", mesh, mesh.dim, degree=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:30.132680Z", + "iopub.status.busy": "2026-02-23T08:03:30.132212Z", + "iopub.status.idle": "2026-02-23T08:03:30.169135Z", + "shell.execute_reply": "2026-02-23T08:03:30.168477Z", + "shell.execute_reply.started": "2026-02-23T08:03:30.132659Z" + } + }, + "outputs": [], + "source": [ + "richards = uw.systems.Richards(mesh, psi_var, v_soln, order=2, theta=0.5, degree=3)\n", + "richards.petsc_options.delValue(\"ksp_monitor\")\n", + "richards.petsc_options[\"snes_rtol\"] = 1.0e-6\n", + "\n", + "psi_sym = psi_var.sym[0]\n", + "\n", + "# Constitutive model: Gardner K(\u03c8) with gravity\n", + "richards.constitutive_model = uw.constitutive_models.DarcyFlowModel\n", + "richards.constitutive_model.Parameters.permeability = gardner_K(\n", + " psi_sym, Ks=KS, alpha=ALPHA_G\n", + ")\n", + "richards.constitutive_model.Parameters.s = sympy.Matrix([0, -1]).T\n", + "\n", + "# Mixed form: \u03b8(\u03c8) for mass-conservative storage term\n", + "richards.water_content = gardner_theta(\n", + " psi_sym,\n", + " theta_r=THETA_R,\n", + " theta_s=THETA_S,\n", + " alpha=ALPHA_G,\n", + ")\n", + "\n", + "richards.f = 0.0\n", + "\n", + "# Boundary conditions\n", + "richards.add_dirichlet_bc([PSI_TOP], \"Top\")\n", + "richards.add_dirichlet_bc([PSI_BOTTOM], \"Bottom\")\n", + "\n", + "# Velocity projector settings\n", + "richards._v_projector.petsc_options[\"snes_rtol\"] = 1.0e-6\n", + "richards._v_projector.smoothing = 1.0e-3" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:30.174229Z", + "iopub.status.busy": "2026-02-23T08:03:30.173895Z", + "iopub.status.idle": "2026-02-23T08:03:30.181463Z", + "shell.execute_reply": "2026-02-23T08:03:30.180723Z", + "shell.execute_reply.started": "2026-02-23T08:03:30.174195Z" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\kappa = Piecewise((0.0001, {\\psi}(N.x, N.y) >= 0), (0.0001*exp(3.5*{\\psi}(N.x, N.y)), True))$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Inspect the solver expressions\n", + "richards.constitutive_model.Parameters.permeability" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:30.182703Z", + "iopub.status.busy": "2026-02-23T08:03:30.182493Z", + "iopub.status.idle": "2026-02-23T08:03:40.806808Z", + "shell.execute_reply": "2026-02-23T08:03:40.806394Z", + "shell.execute_reply.started": "2026-02-23T08:03:30.182683Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Converged after 25 steps (dt = 1000.0 s)\n" + ] + } + ], + "source": [ + "# Initial guess: linear profile from bottom to top\n", + "y = mesh.X[1]\n", + "psi_init = PSI_BOTTOM + (PSI_TOP - PSI_BOTTOM) * y / COLUMN_HEIGHT\n", + "psi_var.array = uw.function.evaluate(psi_init, psi_var.coords)\n", + "\n", + "# Step towards steady state\n", + "dt = 0.1 * COLUMN_HEIGHT / KS # a few diffusive time scales\n", + "\n", + "for step in range(25):\n", + " richards.solve(timestep=dt)\n", + "\n", + "print(f\"Converged after 25 steps (dt = {dt:.1f} s)\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison\n", + "\n", + "Sample the numerical solution along a vertical profile and\n", + "compare with the exact analytical solution." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:40.807514Z", + "iopub.status.busy": "2026-02-23T08:03:40.807393Z", + "iopub.status.idle": "2026-02-23T08:03:41.046305Z", + "shell.execute_reply": "2026-02-23T08:03:41.045975Z", + "shell.execute_reply.started": "2026-02-23T08:03:40.807495Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Max absolute error: 5.4541e-02 m\n" + ] + } + ], + "source": [ + "n_sample = 100\n", + "sample_y = np.linspace(0.02, COLUMN_HEIGHT - 0.02, n_sample)\n", + "sample_x = np.full_like(sample_y, COLUMN_WIDTH / 2)\n", + "sample_pts = np.column_stack([sample_x, sample_y])\n", + "\n", + "psi_numerical = uw.function.evaluate(psi_var.sym[0], sample_pts).squeeze()\n", + "psi_analytical = gardner_steady_state_psi(\n", + " sample_y, PSI_BOTTOM, PSI_TOP, COLUMN_HEIGHT, ALPHA_G\n", + ")\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6), sharey=True)\n", + "\n", + "# Pressure head profile\n", + "ax1.plot(psi_analytical, sample_y, \"b-\", lw=2, label=\"Analytical\")\n", + "ax1.plot(psi_numerical, sample_y, \"ro\", ms=3, label=\"Numerical\")\n", + "ax1.set_xlabel(r\"Pressure head $\\psi$ (m)\")\n", + "ax1.set_ylabel(\"Height $y$ (m)\")\n", + "ax1.set_title(r\"$\\psi(y)$ profile\")\n", + "ax1.legend()\n", + "ax1.grid(True, alpha=0.3)\n", + "\n", + "# Error\n", + "error = psi_numerical - psi_analytical\n", + "ax2.plot(error, sample_y, \"k-\", lw=1)\n", + "ax2.axvline(0, color=\"grey\", ls=\"--\", lw=0.5)\n", + "ax2.set_xlabel(\"Error (m)\")\n", + "ax2.set_title(\"Numerical \u2212 Analytical\")\n", + "ax2.grid(True, alpha=0.3)\n", + "\n", + "fig.suptitle(\n", + " f\"Gardner model: $K_s$ = {KS:.0e} m/s, \"\n", + " rf\"$\\alpha$ = {ALPHA_G} /m\",\n", + " fontsize=12,\n", + ")\n", + "fig.tight_layout()\n", + "plt.show()\n", + "\n", + "print(f\"Max absolute error: {np.max(np.abs(error)):.4e} m\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Darcy Velocity\n", + "\n", + "The Richards solver also computes the Darcy flux\n", + "$\\mathbf{q} = -K(\\psi)(\\nabla\\psi - \\mathbf{s})$.\n", + "At steady state the vertical component should be constant\n", + "(uniform flux through the column)." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T08:03:41.047082Z", + "iopub.status.busy": "2026-02-23T08:03:41.046754Z", + "iopub.status.idle": "2026-02-23T08:03:41.130030Z", + "shell.execute_reply": "2026-02-23T08:03:41.129670Z", + "shell.execute_reply.started": "2026-02-23T08:03:41.047069Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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kJBclUs0d8qRvSH78UpUkaShUqBDs7e3VyVNPSt7y45OTlb57f2RIQJD2qJAnXakClxOmnLzlZCKBT543rFmILPn+UjMhJ8IhQ4aotij5rlKDIVVqsr9FkSJFVMCQCzQ59mToihxvhw8fjtQFmByL/fr1U00KkjdHjhxRwwWMIce7XKDJhYfUqEjaZR9KyU9PhmNJYJAqQTkGpWpPjhlpB5MTtL4d/ntFdjsye5P8fiStMnxGgtWIESNU6Uny8XvJRZlUAwt9c8e3yPbluJJ9Ir8LOX6ltkeGLslwH/k9yvEvQVLaLuX1UlqUY0KCtJR0JfAZI7LHbZ48edQsWVKylAtH2b/ynOSj/Mbkglx+/3KekHyVi4ebN28amWv/25aYMmWKOrdIVbsc4/qLHv1wmu+9SDBajHZFsnL6XnT6m3SFl56s0gNNhltI9/Gwup3Xr19fdQuX3p3SXfzy5cuqx6P0fIxsj10ZpiBd3KWXZty4cVUvtrC69ksvR/mckD1BI2POnDnqvdID1rBLuCHpwi49WKVnqPQKlO7y8rcMkwn5XUL2lJs3b54aZiL5JsNQZFhDWMNBpEu69CiV10hvU+nl2KtXrwg///Xr17oGDRroEiRIoHrhhXXoDxs2TD1//PjxSOfJnj171Hukh6KeDP+RbvnSq1N6R8v+kO81adKkYL0aZR9L3oQkx0vIXouXLl1SPZblO0v+SE/lsPavDKupXLmyGgIiwxSkO78MX/lWr1ohvXOlN6fkkfTWrVSpkhqqYUyvWhmK0L17d7Vt2TcyFOT06dOhXn/hwgVdo0aN1O9DjhMZKiRDe2RYRUT0PUSlt2VIYaUzMtuRnuYybEKOVfn9SM9gGa4RMo8i2nZYvWoNydCLiHrTh0WGY8j+kDRL2mX4l3wXOb70pEe29DpPnDixeo0MJ5H0GfYYjmyeRfa4vXfvnjrG5Hwl7zfMoz/++EN9V9n38n3nzp2rPj/k703+7tKlS6j0hDzviQEDBqjvLj1uQx7HLVu2VL2FY5qd/BOzoZrMSUqF0tYppeIffviBO8OAlLIiMzA9JOmdKFXVkakuJ9sjJTYZ3C+1JfqOSfT9ZMIO6QglM7NFpmnFlBg4bYR0Lb97965qX5WT/MaNG82dJIv58clFhFSFSjW0VG3WqVPHqM+Q6jOpnpTqKFP3+CXtkrZvaeOVqlZpTpAhMtImTaYhTTlSXSwXJtIjPCaxjdNGyIldGuplSIqxvTqtmbR1SfuI9FCUNi5jg6aQYQvSTi0XJgycpCfte/op5aQ9lUHTtKSPiHRUjOmgKVjiJCIiMgKHoxARERmBgZOIiMgINt/GKXMxyiBaGRfE9RSJiGyXTqdTM0ZJb10Z6x0emw+cEjS/NVUdERHZjocPH0bY0c/mA6d+BgrJKOmlpbXSsszIIzMRRXR1RMxHHo/awt+2efJRhqdJQepb0z7afODUV89K0NRi4JR5GiXdDJzMR3Pj8ci8tJZj8lvNdiymEBERGYGBk4iIyAgMnEREREZg4CQiIjICAycREZERGDiJiIi0GjgPHjyImjVrqlkbpDtwZJa+OnDgAAoVKqRWIZfVyLnyBxER2Uzg/Pjxo1rw9e+//47U62UZp2rVqqmlsmS9SVn3ThZpXrduXbSnlYiIbJNFTYDg4eGhbpElpct06dJh8uTJ6m9Z9+706dOYMGEC6tevH40pJSIiW2VRgdNYx44dQ+XKlYM9V6VKFcyfPx9+fn5wcnIK9R4fHx91M5xiST/DhNy0RNIrkxJrLd2WhvnIfLQ0PCbNk4+RfZ2mA+ezZ8+QPHnyYM/J3/7+/nj58iVSpkwZ6j1jx47F8OHDQz0v8xnK1ExaIjvZ29tbHRicco/5aG48HpmXWj8mZWUUqw+cYc0pKBkU1vN6AwYMQO/evUNN6iuTAGtxrlr5npzknfloCXg8Mi+1fkxKJ1OrD5wpUqRQpU5DXl5ecHR0ROLEicN8j4uLi7qFJJmqxVKbHBRaTbslYT4yHy0Nj8mYz8fInkc1fbYtXrw4du/eHey5Xbt2oXDhwmG2bxIREX0viwqcHz58wPnz59VNP9xEHj948CComrVVq1ZBr+/cuTPu37+vql49PT2xYMEC1TGob9++ZvsORERk3SyqqlaGkpQrVy7ob31bZOvWrbFo0SI8ffo0KIiKjBkzYtu2bejVqxemT5+uJk6YOnUqh6IQEZFtBM6yZcsGde4JiwTPkMqUKYOzZ89Gc8qIiIgssKpWy8YcGoMOmzvg1ONT5k4KERFFIwZOE9l6Yyvmn5uPx+8fm+ojiYjIAjFwmsjbL2/VvZuLm6k+koiILBADp4kDZwLXBKb6SCIiskAMnCbi7eOt7hk4iYisGwOnCQTqAvHJ75MpPoqIiCwcA6cpMtHOHsXSFFOPV11ZZYqPJCIiC8XAaSIdC3ZU9/POzlMlUCIisk4MnCbS6IdGiO8SH7ff3Ma+u/tM9bFERGRhGDhNJI5zHLTI00I9nnl6pqk+loiILAwDpwn9XORndb/ecz2uvbxmyo8mIiILwcBpQrmT5UadHHWgg05NwUdERNaHgdPEBpYaqO5XXFqB269vm/rjiYjIzBg4TaxwqsKomqUqAnQB+OPwH6b+eCIiMjMGzmgwqNQgdb/4wmI88P7f+qFERKR9DJzRoES6EiiXoRz8Av0w/sj46NgEERGZCQNnNBlU+mupc+7ZuXj24Vl0bYaIiGIYA2c0kRKne1p3+AT4sNRJRGRFGDijiZ2dXVBb57ST03Du6bno2hQREcUgBs5oJL1r6+Wsp9o6m69vjs9+n6Nzc0REFAMYOKO51Dm7xmykiJsCni898dt/v0Xn5oiIKAYwcEazJLGTYGHthUFVtjtv7YzuTRIRUTRi4IyhKtsuRbqoxy02tMC9t/diYrNERBQNGDhjyLhK41AgRQG8/PQSNVfWxHuf9zG1aSIiMiEGzhgS2yk2NjXZpNo7L3tdVp2FAgIDYmrzRERkIgycMSitW1psbLwRLg4u2HJjC37f83tMbp6IiEyAgTOG/Zjmx6DOQuOOjsPi84tjOglERPQdGDjNoGmepkGTI3Tc2hFHHhwxRzKIiCgKGDjNZHi54aifsz58A3xRd1Vd9rQlItIIBk5zZbydPRbXWax62r749AK1VtZiT1siIg1g4DSjOM5xsLnpZtXT9pLXJTXGM1AXaM4kERHRNzBwmlma+GnUMBXpabv5+maMPjja3EkiIqIIMHBagKKpi2JWjVnq8dD9Q7Ht5jZzJ4mIiMLBwGkh2uRvg58L/wwddGpyhNuvb5s7SUREFAYGTgsyuepkFEtTDG+/vFU9bT/5fTJ3koiIKAQGTgvi7OCMtQ3XInmc5KqzUO+dvc2dJCIiCoGB08Kkjp8ay+sthx3sMPvMbGzw3GDuJBERkQEGTgtUIVMF/Or+q3rcYUsHPHr3yNxJIiKi/8fAaaFGlh+JwqkK4/Xn12i5oSVXUiEishAMnBbc3rmi3grEcYqD/ff2Y9yRceZOEhERMXBatqyJs2J6tenq8eB9g3Hi0QlzJ4mIyOaxxGnhWuVrhSa5myBAF4Bm65vhnc87cyeJiMimMXBaODs7O8ysPhPp3dLjzps76Lqtq7mTRERk0xg4NSCBawI1REVWVFl6cSmWXVxm7iQREdksBk6NKJGuBIaUHqIe//zvz7j1+pa5k0REZJMYODVkUOlBKJ2+ND74fkDTdU3VIthERBSzGDg1xMHeQVXZJoqVCKefnMbAvQPNnSQiIpvDwKnB9TsX1FqgHk88PhF7Huwxd5KIiGwKA6cG1c5RG12LfO1d23VvV9x7e8/cSSIishkMnBo1ofIEFElVBG993qLR2kb44v/F3EkiIrIJDJwa5eLogtUNViOha0KceXoGPbb3MHeSiIhsAgOnhqVzS4cZ5WeoJcjmnJ2DRecXmTtJRERWj4FT48qmLYthZYYFje+88OyCuZNERGTVGDitwO+lfodHFg/Vzll/dX28/fLW3EkiIrJaDJxWQKbiW1ZvmZrP9vab22i9sTUCdYHmThYRkVVi4LQSMinCukbr1Dqem69v5vqdRETRhIHTihRKVQh/e/ytHsusQvvu7jN3koiIrA4Dp5XpULAD2uRvo6pqm6xrgsfvHps7SUREVoWB0wrX75xebTryJc8Hr49eanIEvwA/cyeLiMhqMHBaodhOsbG20Vq4ubjh6MOj6Le7n7mTRERkNRg4rVSWRFmwuM5i9XjyickYsm8Ie9oSEZkAA6eVTwY/stxI9XjkwZFotKYRPvp+NHeyiIg0jYHTBha/Xlh7IZzsnbDOcx1KLSyFR+8emTtZRESaxcBpA6SX7d7We5EkdhKce3YOReYWwcnHJ82dLCIiTWLgtBEl05XEyQ4nkTtZbjz78AylF5bGiksrzJ0sIiLNYeC0IRkTZsSRdkdQI1sN+AT4oPn65uj/X38EBAaYO2lERJrBwGlj4rvEx8bGG/Fbid/U338e+RO1/6kN7y/e5k4aEZEmMHDaIAd7B/xR8Q8sr7ccro6u+Pfmvyg2vxhuvrpp7qQREVk8Bk4b1ixPMxxqewip46XGtZfXUHReUey+vdvcySIismgMnDaucKrCOPXTKRRLU0yt41l1eVVMPj4ZOp3O3EkjIrJIDJyElPFSYn/r/UGTw/fa2QvtNreDj78Pc4eIKAQGTlJcHF2woNYCTKoySS2Mvej8IpRbXE4NXSEiov9h4KRgK6v0LNYT25tvRwLXBDj26BgKzymMc0/PMZeIiP4fAyeFUjlzZTVZQs4kOfH4/WPUWFkDrz69Yk4RETFwUniyJs6KY+2PIUeSHHjy/gk6bOnADkNERAycFBE3VzesqLdCTRC/8dpGzD07lxlGRDaPVbUUoQIpC2BshbHqcc8dPdV4TyIiW2ZxgXPGjBnImDEjXF1dUahQIRw6dCjC1y9fvhz58uVD7NixkTJlSrRt2xavXrE9zpR6Fe+FSpkq4bP/Z7Tb1I5VtkRk0ywqcK5atQo9e/bEwIEDce7cOZQqVQoeHh548OBBmK8/fPgwWrVqhfbt2+PKlStYs2YNTp06hQ4dOsR42q2ZGp5SZxFiO8VWPW233Nhi7iQREZmNIyzIxIkTVRDUB77Jkydj586dmDlzJsaO/VpdaOj48ePIkCEDunfvrv6WkmqnTp0wbty4cLfh4+Ojbnrv3r1T94GBgeqmJZJemeEnJtKdIk4KdC/aHX8c+QMD9wxEtSzVVEC1BjGZj9aM+ci81PoxGdnXWUzg9PX1xZkzZ9C/f/9gz1euXBlHjx4N8z3u7u6qdLpt2zZVMvXy8sLatWtRvXr1cLcjAXj48OGhnn/x4gW+fPkCLZGd7O3trQ4Me/voD2Kts7bGzFMzcfnFZcw+Ohv1s9aHNYjpfLRWzEfmpdaPyffv32srcL58+RIBAQFInjx5sOfl72fPnoUbOKWNs3Hjxiro+fv7o1atWpg2bVq42xkwYAB69+4drMSZNm1aJE2aFPHjx4fWDgqZtEDSHhMn/GRIhn4l+mHgvoGYeG4iOhTrACcHJ2hdTOejtWI+Mi+1fkxK3xpNBU49+ZKG5Eoh5HN6V69eVdW0Q4YMQZUqVfD06VP8+uuv6Ny5M+bPnx/me1xcXNQtJMlULZ40JW9iMu09ivXA1JNTcefNHSy6sAidCneCNYjpfLRWzEfmpZaPycj+/i3mLJEkSRI4ODiEKl1K9WvIUqhhtWuJEiVUsMybN68KntIrd8GCBSqIkunFcY6DgaUGqscjDo7AZ7/PzGYisikWEzidnZ3V8JPdu4OvByl/S5VsWD59+hTqCkGCr+CyWNGnY6GOSOeWTs0oNP3U9GjcEhGR5bGYwCmk7XHevHmqxOjp6YlevXqpoShS9apvn5ThJ3o1a9bE+vXrVa/bO3fu4MiRI6rqtmjRokiVKpUZv4n1r6QyrMww9Xjs4bF45/O1ZzIRkS2wqDZO6eQjkxeMGDFCVbXmzp1b9ZhNnz69+n95znBMZ5s2bVQvqL///ht9+vRBggQJUL58efz5559m/Ba2oWW+lqqq9t7bezhw7wBqZq9p7iQREdle4BS//PKLuoVl0aJFoZ7r1q2bulHMcrR3RLE0xVTg9HzpycBJRDbDoqpqSVtyJcml7q++uGrupBARxRgGToqyXEm/Bk4pcRIR2QoGTooy6Vkr7r+9z1wkIpvBwElRduPVDXWfOVFm5iIR2QwGToqyc8/OqfsCKQowF4nIZjBw0ncHzoIpCzIXichmMHBSlMjMTOefnVePWeIkIlvCwElR8sD7AV5/fg0neyf8kOwH5iIR2QwGToqSs0/PqnsJms4OzsxFIrIZDJwUJewYRES2ioGTooQdg4jIVjFwUpQ8fvdY3WdKmIk5SEQ2hYGTouSD7wd1H98lPnOQiGwKAydFyXvf9+o+rnNc5iAR2RQGTvquEmc853jMQSKyKQycFCUuDi7q/sn7J8xBIrIpDJwUJR5ZPdT9xmsbmYNEZFMYOClK6uaoq+43XNugpt8jIrIVDJwUJVUyV4Groyvuvr2LC88vMBeJyGYwcFKUxHGOo4Kn2OC5gblIRDaDgZNMUl1LRGQrGDgpympmrwkHOwdc8rqE269vMyeJyCYwcFKUJYqVCGUzlFWPWeokIlvBwEkmqa5d77meOUlENoGBk75L3Zx1YQc7HHt0DA+9HzI3icjqMXDSd0kVLxVKpCuhHq/zXMfcJCKrx8BJ361Rrkbqfs3VNcxNIrJ6DJz03ernqq+qa48+PIqbr24yR4nIqjFwkkmqa6tmqaoe99zZk1PwEZFVY+Akk5hUZRKc7J2w7eY2bLq+iblKRFaLgZNMInuS7Ojr3lc97rGjBz76fmTOEpFVYuAkkxlYaiDSuaXDA+8HGH1oNHOWiKwSAyeZdOL3KVWnqMcTjk7AtZfXmLtEZHUYOMmkamevjepZq8Mv0A9dtnVhRyEisjoMnGRSdnZ2mOoxVa3VuffuXqy6soo5TERWhYGTTC5TwkwYUHKAetx7Z2+883nHXCYiq8HASdGiX4l+yJwwM55+eIph+4cxl4nIajBwUrSQqtq/q/2tHk89MRUXn19kThORVWDgpGgjswnVz1kfAboA/PLvLwjUBTK3iUjzGDgp2mcUiuMUB0ceHsGSC0uY20SkeQycFK3SuqXFkDJD1OP+//XHZ7/PzHEi0jQGTop2PYv1RIYEGfD843PMPTuXOU5EmsbASdHO2cEZ/Uv0V4/HHRkHH38f5joRaRYDJ8WINvnbIE38NHj8/jEWnV/EXCcizWLgpBjh4uiCfu791OM/jvwBvwA/5jwRaRIDJ8WYDgU7IHmc5Lj39h5WX1nNnCciTWLgpBgTyykWuv/YXT0ed3QcJ4AnIk1i4KQY9XPhnxHXOa6aSWjn7Z3MfSLSHAZOilEJYyVEx4Id1eM/j/zJ3CcizWHgJLOM63S0d8T+e/tx8vFJ7gEi0hQGTjLLbELN8zQPGtdJRKQlDJxkFr+6/6ru13uux41XN7gXiEgzGDjJLH5I9gNqZKsBHXSYcHQC9wIRaQYDJ5lNn+J91P3aq2u5F4hIMxg4yWwKpiyo7t98eYOPvh+5J4hIExg4yWziu8RXYzqFzGFLRKQFDJxkVqnjpVb3j98xcBKRNjBwklmliJtC3T/78Ix7gog0gYGTzOrV51fqPlGsRNwTRKQJDJxkNjqdDvff3leP0ydIzz1BRJrAwElm4+3jjfe+79XjdG7puCeISBMYOMls9KXNpLGTIrZTbO4JItIEBk4ym/veXwMnS5tEpCUMnGQ2bN8kIi1i4CSzlzjTu7FjEBFpBwMnmQ2raolIixg4yWw++H5Q9wlcE3AvEJFmMHCS2ejnqeUE70SkJQycZPbAqS95EhFpAQMnmU1cp6+BUz8JAhGRFjBwktkkiZ1E3d95c4d7gYg0g4GTzKZiporqftvNbfAL8OOeICJNYOAksymWphiSxUmm5qw9cP8A9wQRaQIDJ5mNg70DamevrR5v8NzAPUFEmsDASWZVJ0cddb/x+kYE6gK5N4jI4jFwklmVz1heDUt58v4Jzjw5w71BRBbP4gLnjBkzkDFjRri6uqJQoUI4dOhQhK/38fHBwIEDkT59eri4uCBz5sxYsGBBjKWXvo+roys8snioxxuvbWR2EpHFs6jAuWrVKvTs2VMFwnPnzqFUqVLw8PDAgwcPwn1Po0aNsGfPHsyfPx/Xr1/HypUrkSNHjhhNN5muupaIyNI5woJMnDgR7du3R4cOHdTfkydPxs6dOzFz5kyMHTs21Ot37NiBAwcO4M6dO0iUKJF6LkOGDDGebvo+1bJWg6O9I66+uArPF57ImTQns5SILJbFBE5fX1+cOXMG/fv3D/Z85cqVcfTo0TDfs3nzZhQuXBjjxo3D0qVLESdOHNSqVQsjR45ErFixwq3alZveu3fv1H1gYKC6aYmkV6fTaS7dIcV3jo+qmati682tmHV6FiZVmRSj27eWfDQ35iPzUuvHZGRfZzGB8+XLlwgICEDy5MmDPS9/P3v2LMz3SEnz8OHDqj10w4YN6jN++eUXvH79Otx2Tim5Dh8+PNTzL168wJcvX6AlspO9vb3VgWFvb1G17kZrmqWpCpwLzy9E99zdEccpToxt25ry0ZyYj8xLrR+T79+/11bg1LOzswv2t3zhkM8ZZor83/Lly+Hm5hZU3dugQQNMnz49zFLngAED0Lt372AlzrRp0yJp0qSIHz8+tET//SXtWj/hN0raCENPDMWt17ew69kudCrUKca2bU35aE7MR+al1o9JKYRFe+D08/NTpcFPnz6phOnbGaMiSZIkcHBwCFW69PLyClUK1UuZMiVSp04dFDRFzpw5VbB99OgRsmbNGuo90vNWbiFJpmrxpCkHhVbTbsge9vil8C/ovas3pp6cilb5WiGOc8yVOq0lH82N+ci81PIxGdnfv9FniQ8fPmD27NkoW7asCljSGSdXrlwqcMqQkJ9++gmnTp0y9mPh7Oyshp/s3r072PPyt7u7e5jvKVGiBJ48eaLSpHfjxg315dOkSWN0Gsi82hZoi4SuCXHt5TXUXVUXPv7/a4smIrIURgXOSZMmqUA5d+5clC9fHuvXr8f58+fVMJBjx45h6NCh8Pf3R6VKlVC1alXcvHnTqMRIFeq8efNU+6Snpyd69eqlhqJ07tw5qJq1VatWQa9v1qwZEidOjLZt2+Lq1as4ePAgfv31V7Rr1y7czkFkuRK4JsDWZltV++buO7vRZF0T+Af6mztZRERRr6qV3q379u1Dnjx5wvz/okWLqqAlw0ck+MlQkbCqS8PTuHFjvHr1CiNGjMDTp0+RO3dubNu2TZVkhTxnOKYzbty4qkTarVs31btWgqiM6xw1apQxX4ssiHtad2xqsgnVV1RXEyK03dQWi+sshr0dq1CJyDLY6aRB0IZJ5yCpcpaeV1rsHCRtwMmSJbO6trkt17eo6toAXQA6F+qMGdVnhNtJ7HtZcz7GJOYj81Lrx2Rk48F3dQ6S4RsXL15UCQs5/kXGUxJFVc3sNbG07lI0X98cs87MQjyXePiz4p/RFjyJiCIryoFTZu2R9kYZOxmSnNxkTCbR92iapyk++n3ET1t+wvij4xHfJT4GlR7ETCUis4pyvVTXrl3RsGFD1e6on3VHf2PQJFPpULADJlaeqB4P3jcYU45PYeYSkTYDp1TPSi/Y8MZYEplKr+K9MLzs19meeu7sifln5zNziUh7gVNm59m/f79pU0MUjsGlB6NP8T7qsVTdrrq8inlFRNpq4/z7779VVa2slynDU5ycnIL9f/fu3U2RPqKgdvPxlcbjvc97zDk7By02tFAzC9XIVoM5RETaCJwrVqxQS37JRANS8jTs7SiPGTjJ1OS4kmEpH/w+YMWlFWiwugG2N9+OchnLMbOJyPKragcNGqQmKpDxLvfu3cPdu3eDbrJqCVF0cLB3wKLai1Arey34BPig5sqaOP7oODObiCw/cMr6mTLTDweMU0xzcnDCqgarUCFjBTVcxWO5By4+v8gdQUSWHThbt26NVavYQYPMw9XRVU3NJ1P0vf3yFlWWVcHt17e5O4jIcts4ZazmuHHjVDtn3rx5Q3UOknUxiaKTdA7a2nQryi4uq0qclZZWwuF2h5EqXipmPBFZXuC8dOkSChQooB5fvnw52P9xWjSKKQljJcTOFjtRckFJ3H5zG5WXVsbBtgeRKFbU14YlIoqWwCmrpBBZghRxU2B3y90oubAkrry4gmrLq+G/Vv8hrnNccyeNiKwQl4Igq5AxYUbsarFLlTRPPD6BeqvqcSFsIjJ/4DRcCzMyHj9+bGx6iKLsh2Q/qHGd+oWwZWWVgEAuNkBEZgycRYoUwU8//YSTJ0+G+xoZ1zl37ly1CPX69etNkUaiSCuauig2NtkIZwdnrPNch05bO8HGl5wlInO2cXp6emLMmDGoWrWq6kVbuHBhpEqVCq6urnjz5g2uXr2KK1euqOfHjx8PDw8PU6eX6JsqZqqIlfVXouGahph/br6qvh1XaRxzjohivsSZKFEiTJgwAU+ePMHMmTORLVs2tR7nzZs31f83b94cZ86cwZEjRxg0yazq5ayHuTXnqseyluefh//kHiEi8/WqlRJmvXr11I3IUrUr0A5vPr9B39190X9PfzV0pWOhjuZOFhFpHHvVklXr494HA0oOUI87b+2M1VdWmztJRKRxDJxk9UaXH41OhTpBBx1arG+BHbd2mDtJRKRhDJxk9WQmq+nVpqPxD43hF+inVlSZemIqe9sSUcwGzocPH0b1rURmWY5sSd0laJanGfwD/dFjRw+03tgan/w+cW8QUcwEzhw5cmDw4MH4+PFjVD+CKEbJ2M5ldZdhUpVJcLBzwNKLS1FiQQnce3uPe4KIoj9w7t69G7t27ULWrFmxcOFCZjlpptq2Z7Geai7bpLGT4vyz8ygyrwgOPDpg7qQRkbUHTnd3d5w4cQJ//PEHhgwZolZK2b9/v2lTRxRNymYoizMdz6BIqiJ4/fk1mv7bFIP3DYZfgB/znIiit3NQq1atcOPGDdSsWRPVq1dH3bp1cevWre/9WKJol9YtrVqCrEOBDqrH7ZjDY1BqYSnceXOHuU9E0durVuYCrVy5Mjp27IjNmzereWr79OmD9+/fm+LjiaKNq6MrZteYjdkVZ8PNxU2trJJ/Vn4sv7icuU5Epg2cs2bNQvv27ZE3b164ubmhYsWKaqq9Ll26YMaMGTh//jxy5cqF06dPR3UTRDGmVuZaONfxHEqmK4n3vu/RYkMLtNzQEu983nEvEFEwdrooLh2RNm1aFCtWLOgmE7u7uLgEe41MCL9ixQpcvnwZlurdu3cq8MuqLvHjx4eWBAYGwsvLC8mSJYO9PYfkmiIfAxGIMYfGYPiB4QjUBSJjgoxYUX8FiqUpZtJ9Z414PDIvtX5MRjYeRDlwRsbz58/V6ikBAZa7JiIDJ4X14zr68CiarWuG+9731dCV4WWHo3/J/mo8KIWNgdN0mJeWHTijtZgiid27d290boIoWrindcf5zufRJHcTBOgCMGjfIFRYUgEPvTnxB5Gts4/uMXNlypSJzk0QRZsErgmwot4KLK6zGHGd4+LA/QPINysf1ntygXYiW8aGMaJvXPy1ytcK5zqdQ+FUhfHmyxvUX10fbTe1xeN3j5l3RDaIgZMoErIkyoIj7Y6gf4n+sIMdFp1fhMxTM6PPzj548fEF85DIhkQ5cD548CDM1SXkOfk/Imuc63ZsxbEqgJZKVwo+AT6YeHwiMk3NhKH7hsL7i7e5k0hElhw4M2bMiBcvQl9pv379Wv0fkbUqnrY4DrQ5gB3Nd6BgyoL44PsBIw6OUAF0/JHxXHGFyMpFOXBKyVLaf0L68OEDXF1dvzddRBZNjv0qWarg9E+nsbbhWuRMklPNedvvv37IMjULpp2Yhvc+nDmLyBo5GvuG3r17B504ZFmx2LFjB/2fjNeUid/z589v2lQSWSj5HdTPVR91ctTB8kvLMXT/ULVMWfcd3fH73t/RIk8L/FzkZ+RNntfcSSUicwXOc+fOBZU4L126BGdn56D/k8f58uVD3759TZU+Ik2QiRGk962M+5x/dj6mnJiC66+uY9aZWepWIm0J/Fz4ZzTI1QAujsFn2CIibYnyzEFt27bFlClTNDdNXUicOYiiY5YW+Vntu7cPM0/PxMZrG+Ef6K+eTxI7Cdrlb4dOhTshU8JMVpX5nO2GeWlpLG7mIFm8WutBkyg6q3DLZyyPNQ3X4EHPBxhRdgTSxE+Dl59eYtzRcaod1GO5B7Zc34KAQMudkpKITFBVa2jPnj3qJhFdIruhBQsWfM9HE1mNlPFSYnCZwRhQagC23tiqSqG7bu/Cjls71C2dWzp0LNgR7Qu2R4q4KcydXCL6hiiXOIcPH67W4JTA+fLlS7x58ybYjYiCc7R3VJ2IdrbYiZvdbqJv8b5IFCsRHng/UHPhpp2UFk3WNsGBewfCHCNNRBpv40yZMiXGjRuHli1bQsvYxknmbJv77PcZa66uUaXQ44+OBz2fK2kudC7UWXU4cnN108ROYhsn89LSWFwbp6+vL9zd3aP6diICEMsplgqOx9ofw9mOZ/FTwZ8Q2yk2rr64qoa0pJqYCh23dMS5p197sxOR+UU5cHbo0EEtUk1EplEgZQHMqTkHT3o/wTSPaarU+cnvE+aenYuCcwrCfb47/rn8D/wC/JjlRFrpHKSf/EBfBJ4zZw7+++8/5M2bF05OTsFeO3HiRNOlksiGSNVs16Jd0aVIFxx6cAgzTs1QS5kde3RM3VLGTanGhHYs1BHJ4yY3d3KJbI5jVCY/0NPPEHT58uVgz4c1FR8RGUd+R6XTl1a3Zx+eYfbp2WoyhacfnmLI/iEYdWgUGv/QGN2KdkOR1EWYvUSW3jnIWrBzEGmpU4tvgC/WXl2LqSem4sTjE0HPF0tTDN2LdlfT/8kqLuagpXy0dMxLK+0cREQxT4JiszzNcLzDcZzocAIt8raAk72T6pHbbH0zpJ+cHmMPjcU7n3fcPUSWVuI0bO8M9oF2dmp1lCxZsqB27dpIlCgRLBlLnKT1q3upxp1zZo4a0iKPhZuLm6rC7VGsh5rmLyZoPR8tCfPSskucUQ6c5cqVw9mzZ9WKKNmzZ1cDtm/evAkHBwfkyJED169fV0H08OHDyJUrFywVAydZy0lKqnGl1+3Yw2Nx7eU19VwcpzjoVKgT+rj3Qap4qaJ1+9aSj5aAeWmlVbVSmqxYsSKePHmCM2fOqCD6+PFjVKpUCU2bNlWPS5cujV69ekV1E0RkZDWujAm98ssVNUdugRQF8NHvIyYen4iMUzLi560/qyXPiOj7RLnEmTp1auzevTtUafLKlStqKj4JnBJM5bFMyWepWOIka726l5+2zIU7+tBoHHl4RD3nYOeA5nmbY0DJAciRJIdJt2et+WgOzEsrLXHKB0uCQnrx4oXauEiQIIGaYYiIYp40lXhk9cChtoewv/V+VMpUCQG6ACy5sAS5pudCwzUNcf7Zee4aIiN9V1Vtu3btsGHDBjx69EiVMOVx+/btUadOHfWakydPIlu2bFHdBBGZKICWyVAGu1ruUj1xa2evDR10alhLgdkFUH1FdRx9eJR5TRTdgXP27NmoUKECmjRpgvTp0yNdunTqsTw3a9Ys9RrpJDRv3ryoboKITKxo6qLY2GQjLna+iKa5m8Lezh7bbm5DiQUlUG5xOfx35z+uzEIU3RMgfPjwAXfu3FE/tsyZMyNu3LjQErZxki23J918dRN/HvlTVd/6BfoFBdeBpQaiZraaRs0CZsv5aGrMSytt49STQClz1ebLl09zQZPI1mVNnBXzas3D7e631bhPV0dXnHx8ErX/qa0mlt/guQGBuuCL1BPZOqMneR85ciTixIkT7gQIepzknUg70rqlxVSPqRhUehAmHZuEv0/9rToO1VtdD3mT58Xg0oNRL2c9VbVLZOuMnuTdz88vzAnfDXGSdyJtShYnGcZWHIu+7n0x6fgkNSfuxecXVQ/c3MlyqwDaIFcDBlCyaZzkPZJ12paI7SDMx+j25vMbTD4+GVNOTIG3j7d6TtYJlQDaMFdDONg78HiMBvxtW3Eb56FDh9CiRQu4u7ur4Shi6dKlapo9ItK+hLESYni54bjX8x6GlRmGBK4JcPXFVTRd11T1wv3o+9HcSSSKcVEOnOvWrUOVKlUQK1YsNUOQj4+Pev79+/cYM2aMKdNIRGYmAXNo2aG41+MeRpYbiXjO8dQi21KF6xfwtfmGyFZEOXCOGjVKjdecO3cunJycgp6X0qcEUiKyPm6ubqoD0c4WOxHLMRa239qOdpvbsect2ZQoB05Z/UQmcQ9J6oXfvn37vekiIgtWPG1xrG20Vs19u+ziMvTd1ZcTJ5DNiHLgTJkyJW7duhXqeWnfzJQp0/emi4gsXLWs1bCw9kL1WHrgjj863txJIrLswNmpUyf06NEDJ06cUMNPZHmx5cuXo2/fvvjll19Mm0oiskgt87XEX5X/Uo8H7B2AlddWmjtJRJY1jtNQv379VJddWdD6y5cvqtrWxcVFBc6uXbuaNpVEZLF6F+8Nr49eauq+vgf7ImPyjKiT8+tCD0TW6LuGo4wePVqttSmroBw/flwtKSYzCxGRbRlbYSza5GujOgk1Xd8Uh+4fMneSiCwncMoAUcObv7+/WjpMVkKRwab654nIdkhzzewas1E5fWV88f+CmitrqhmHiKyR0YFTFqdOmDBhuDf9/xORbXG0d8TMCjNRMm1JNctQ1WVVcffNXXMni8j8bZz79u0LeixLiVWrVk2tuZk6dWpTp42INCa2U2xsbLwRZZeUxWWvy6iyrAoOtzus5sAlstnAWaZMmWB/Ozg4oFixYhyCQkRB0/TJBAnu891x8/VNVFteDfta70M8l3jMIbIKXCOIiEwuVbxU2NVyF5LEToIzT8+g7qq68PH/Oi0nkdYxcBJRtMiWOBu2N9+OuM5xsefuHkw7OY05TVbBJIHTlOtvzpgxAxkzZoSrqysKFSqkVmCJjCNHjsDR0RH58+c3WVqI6PsUTlUYo8qNUo933t7J7CTbbOOsV69esL9l8oPOnTsjTpw4wZ5fv3690YlZtWoVevbsqYJniRIlMHv2bHh4eODq1atIly5duO+TiRhatWqFChUq4Pnz50Zvl4iiT6XMldT9kQdHVHWti6MLs5tsK3DKIp+GZD1OU5k4cSLat2+PDh06qL8nT56MnTt3YubMmRg7dmyE0/81a9ZMdVTauHFjhNuQ5c/0S6AJ/ZhTGYMqNy2R9ErPZq2l29IwH6M3H7Mnyo6ksZPixacXOPHoBEqmK2miLVovHpPmycfIvs7owLlw4ddJnU3N19cXZ86cQf/+/YM9X7lyZRw9ejTC9Ny+fRvLli1TS519iwTg4cOHh3peZj2S0rOWyE6W0rYcGJFZ3ZyYj+Y6HoulKIYtd7bg36v/IptrNh6K35GXFH35KOtJR+tctaYmU/cFBAQgefLkwZ6Xv589exbme27evKkCrbSDSvtmZAwYMAC9e/cOVuJMmzYtkiZNqpZE09pBIe3Lknb+uJiPlnw8umdwV4Hz8ZfHSJaMYzq/Jy8p+vJR+tZoKnCG19FIrhTC6nwkQVaqZ6X0KFP+RZZMRC+3kCRTtXiASt5oNe2WhPkYvfmYPkF6df/w3UMeqzwmLfa3HdnzqMUEziRJkqg2ypClSy8vr1ClUH2R+vTp0zh37lzQaiz6+mwpfe7atQvly5ePsfQTUfjSuX3t3PfQ+yGziTTPYoopzs7OavjJ7t27gz0vf7u7u4d6vVSrXrp0CefPnw+6Se/e7Nmzq8c//vhjDKaeiCITOB+9e4SAwABmFmmaxZQ4hbQ9tmzZEoULF0bx4sUxZ84cPHjwQAVEffvk48ePsWTJElWkzp07d7D3S9uJ1FGHfJ6IzCtlvJSwt7OHX6Afnn14htTxObc1aZdFBc7GjRvj1atXGDFiBJ4+faoC4LZt25A+/df2EXlOAikRaW/llNTxUqs2TrkxcJKW2emkUdCGSa9aGZsqXZa12KtW2oClpM3OQcxHSz8eSy4oiSMPj2BVg1Vo9EMjs6RRK/jbNk8+RjYeWEwbJxHZRjvn/bf3zZ0Uou/CwElEMTbpu5hxegaevH/CXCfNYuAkohjRpUgXZEmUBffe3lMLXL/5/IY5T5rEwElEMSJpnKTY3XK3Wqvzstdl1FhZAx99PzL3SXMYOIkoxmRIkAE7W+xEQteEOPrwKBquaQjfAF/uAdIUBk4iilG5k+XGv83+RWyn2Nh+azvc57vD84Un9wJpBgMnEcW44mmLY1OTTarkeebpGRScUxB/n/xbTZlJZOkYOInILCpmqohLP19C5cyV8cX/C7pt74aqy6uyxy1ZPAZOIjIbmUFoe/PtmFp1KlwdXbHr9i7kmZkHa6+u5V4hi8XASURmJXPYdvuxG852PIuCKQvi9efXqtNQqw2t4P3Fm3uHLA4DJxFZhJxJc+JY+2P4veTvKpguvbgUeWflxYF7B8ydNKJgGDiJyGI4OzhjdIXRONjmIDIlzIQH3g9QbnE59NvdDz7+PuZOHpHCwElEFqdEuhI43+k8OhToAB10GH90PIrOK4pLzy+ZO2lEDJxEZJniucTD3FpzsbHxRiSNnRQXn19E4bmFMWTfELz3eW/u5JENY4mTiCxa7Ry11bCVGtlqqFmGRh4cicxTM2PaiWmcdYjMgoGTiCxe8rjJsbnJZqxtuFatsvLi0wt039EdOafnxD+X/0GgLtDcSSQbwsBJRJpgZ2eH+rnq4/LPlzGz+kwkj5Mcd97cQdN1TVFkbhH8d+c/cyeRbAQDJxFpipODEzoX7oxb3W9hZLmRiOccD2efnkWlpZVQeWllNYkCS6AUnRg4iUiT4jrHxaDSg3C7+210L9odTvZO2H1nt1rrM8vULBhzaAyevn9q7mSSFWLgJCLNr/M5xWMKrnW9hq5FusLNxQ13397FwL0DkXZSWtRbVQ87bu1AQGCAuZNKVoKBk4isgkyYMK3aNDzp8wSLai+Ce1p3BOgCsOHaBngs91A9cUcdHMVJ5Om7MXASkVWRdT5b52+NI+2OqGEsUo2bwDUB7nvfx+B9g5FuUjrU+acOtt3cxlIoRQkDJxFZ9aLZUo37pPcTLKmzBCXTlVSl0E3XN6H6iurIOCUjRhwYgUfvHpk7qaQhDJxEZPViOcVCy3wtcajtIVz55Qp6/thTLaL98N1DDN0/FOknp0etlbWw9cZWlkLpmxg4icim5EqaC5OqTlJtocvqLkPp9KXV8JUtN7ag5sqayDAlA4btH4aH3g/NnVSyUAycRGSTZOHs5nmb40CbA/Ds4onexXojcazEqtp2+IHhKoDWWFEDm69vhn+gv7mTSxaEgZOIbF6OJDnwV5W/8Kj3I6yotwJlM5RVpdB/b/6L2v/URrZp2TD95HR88vtk83lFDJxERMFKoU3zNMW+1vtwvet19C3eV5VCZVxo1+1dVVuodCZ69ekVc82GscRJRBQGmUx+fOXxeNDrAaZ5TEOGBBnw8tNL1Zko3eR06Lmjp1pom2wPAycR0TfGhXYt2hU3u91U1bj5kudTVbZTTkxBpimZ0HJDS7XAtk6nYz7aCAZOIqJIcLR3VNW45zqdw84WO1EuQzk1JnTZxWXIOysv+u3ux3y0EQycRERGLm9WOXNl7G29F6d+OoWGuRqq5/869hcev3vMvLQBDJxERFFUOFVhrG64Ws1IpIMOKy+vZF7aAAZOIqLv1DxPc3W/4tIK5qUNYOAkIvpODXI1UG2g556dg+cLT+anlWPgJCL6TkliJ0HVLFXV4+WXljM/rRwDJxGRiatrOTTFujFwEhGZQK3stRDXOa6aZejYo2PMUyvGwElEZKKJEurmqKseL7/I6lprxsBJRGTi6trVV1fDL8CP+WqlGDiJiEykQqYKSBYnmZrTdved3cxXK8XASURkIjIkpfEPjdVj9q61XgycRETRUF278dpGfPD9wLy1QgycREQm9Nn/syp5ygoqu2+zutYaMXASEZnAnTd3UH91fZRbXA7+gf5I4JoA2ZNkZ95aIUdzJ4CISMve+bzD6IOjMfnEZPgG+MLezh6dCnXCiHIj1IxCZH0YOImIoiAgMAALzy/EwL0D4fXRSz1XKVMlTKwyET8k/UEtP0bWiYGTiMgIMp3ejls7MGDPAFx4fkE9ly1xNvxV+S9Uz1qdAdMGMHASEUXSsYfH0H9Pfxy8f1D9Le2YQ8sMxS9FfoGzgzPz0UYwcBIRfcMVryuqSnbT9U3qbxcHF3Qt2hUDSg5A4tiJmX82hoGTiCgc99/ex9D9Q7HkwhLooFMdf9rmb6tKmWnd0jLfbBQDJxFRCC8+vsDoQ6Mx8/RM1VNW1M9ZH6PKj0KOJDmYXzaOgZOI6P+993mPiccmYsKxCUGz/pTPWB5jK4xF0dRFmU+kMHASkc3z8ffBrNOzMOrQKDVBuyiYsiD+qPAHKmaqyJ6yFAwDJxHZ9FhMmYx9yL4huO99Xz2XNVFWjC4/GvVz1VdtmkQhMXASkU2Oxdx5eyf67uqLKy+uqOdSxUuFYWWGoU3+NnBycDJ3EsmCMXASkc0FTWnH7Lu7b9BYTBlWIsNLYjvFNnfySAMYOInIpqpm++zqgyknpqi/ZU5Z6fiTMFZCcyeNNISBk4hswhf/L2ixvgXWea5Tf0+oNAG9i/dmxx8yGgMnEVm9159fo/Y/tXH4wWE1Nd7iOovRJHcTcyeLNIqBk4is2kffj6i0tBLOPj0LNxc3bGyyEWUzlDV3skjDGDiJyGoF6gLRamMrFTSTxk6Kva33Iney3OZOFmkcBykRkdWS8ZnrPder6lkpaTJokikwcBKRVVp+cbmab1bMqzkP7mndzZ0kshIMnERkletmtt/cXj3uX6I/WuZrae4kkRVh4CQiq1sKrM6qOvAJ8EHt7LUxusLXUieRqTBwEpFVrW5Sc2VNeH30Qr7k+bCs3jLON0smx8BJRFYzK1CLDS1wyesSksdJji1NtyCuc1xzJ4usEAMnEVlND9rN1zfDxcEFm5psQlq3tOZOElkpBk4isorp9CYen6gez681Hz+m+dHcSSIrxsBJRJp39OFRFTxTxk2JZnmamTs5ZOUYOIlI8/bc2aPuK2SqwEnbKdoxcBKR5v139z91XyFjBXMnhWwAAycRad75Z+fVfaGUhcydFLIBDJxEpHn5U+RX97JsGFF0Y+AkIs2rn7O+ul9/bb25k0I2wOIC54wZM5AxY0a4urqiUKFCOHToULivXb9+PSpVqoSkSZMifvz4KF68OHbu3Bmj6SUi86ubo66633d3n1q0mshmAueqVavQs2dPDBw4EOfOnUOpUqXg4eGBBw8ehPn6gwcPqsC5bds2nDlzBuXKlUPNmjXVe4nIdmRNnBV5kuVBgC5ATYJAZDOBc+LEiWjfvj06dOiAnDlzYvLkyUibNi1mzpwZ5uvl//v164ciRYoga9asGDNmjLrfsmVLjKediCykutaT1bUUvRxhIXx9fVWpsX///sGer1y5Mo4ePRqpzwgMDMT79++RKFGicF/j4+Ojbnrv3r0Leq/ctETSq9PpNJduS8N8tI58rJO9DoYdGIZdt3fB+7M34rnEg1aZOy+tRaCR+RjZ11lM4Hz58iUCAgKQPHnyYM/L38+ePYvUZ/z111/4+PEjGjVqFO5rxo4di+HDh4d6/sWLF/jy5Qu0RHayt7e3OjDs7S2q8kBTmI/WkY/JkAyZ3DLhjvcd/HPmH9TOUhtaZe68tBaBRuajFLw0FTj17Ozsgv0tXzjkc2FZuXIlhg0bhk2bNiFZsmThvm7AgAHo3bt3sBKnVAfrOxhp7aCQvJG088fFfDQ3SzgeG/zQAOOOjsOux7vwk/tP0CpLyEtrEGhkPkqnVE0FziRJksDBwSFU6dLLyytUKTSsTkXSNrpmzRpUrFgxwte6uLioW0iSqVo8QOWg0GraLQnz0TryUeaplcC58fpG3Hx9E9mTZIdWmTsvrYWdEfkY2by2mD3i7Oyshp/s3r072PPyt7u7e4QlzTZt2mDFihWoXr16DKSUiCxVvhT5UDNbTQTqAjHy4EhzJ4eslMUETiFVqPPmzcOCBQvg6emJXr16qaEonTt3DqpmbdWqVbCgKX9L22axYsVUaVVuUqdNRLZpWNlh6n7l5ZW49vKauZNDVsiiAmfjxo3VEJMRI0Ygf/78apymjNFMnz69+v+nT58GG9M5e/Zs+Pv7o0uXLkiZMmXQrUePHmb8FkRkTgVTFkTt7LVVqXPQ3kGqnwSRKdnpbPyoks5Bbm5uqpSqxc5B0gYsnaHYDsJ8NDdLOh5l0veCswtCBx16F+uNCZUnaGq5MUvKSy0LNDIfIxsPuEeIyConfZ9Z/evEKROPT0T///qz5Ekmw8BJRFapU+FOmF5tunosPW0H7h3I4EkmwcBJRFbrlyK/YJrHNPV47OGxGLJvCIMnfTcGTiKyal2LdsXkKpPV41GHRmH4gdAzhxEZg4GTiKxej2I9MLHyRPVYAueIAyPMnSTSMAZOIrIJvYr3wvhK49XjofuHYvTB0eZOEmkUAycR2Yy+7n3xR4U/1ONB+wZh7KGx5k4SaRADJxHZlN9K/oYx5ceox7/v/R3jj3wthRJFFgMnEdmcAaUGYGS5r3PZ9vuvHyYf/9p5iCgyGDiJyCYNKj0IQ0oPUY977eyF6Se/jvkk+hYGTiKy6QnhB5QcoB533d4Vc87MMXeSSAMYOInIZsn8taPLj0af4n3U3522dsKqy6vMnSyycAycRARbD54yTKVb0W7q77ab2qpJ4onCw8BJRDZPguekKpNQNUtVfPb/jDr/1MHLTy9tPl8obAycREQAHOwdsKLeCmROmBn3ve+j8drG8A/0Z95QKAycRET/L2GshNjUZBPiOMXB3rt78euuX5k3FAoDJxGRgR+S/YAldZeox5NPTMbSC0uZPxQMAycRUQj1ctbDoFKD1OOOWzvizJMzzCMKwsBJRBSG4eWGo0a2Gvji/wV1V9WF10cv5hMpDJxERGGwt7PHsrrLkC1xNjx89xAN1zSEX4Af84oYOImIwuPm6oaNjTcinnM8HLx/EH12fZ0ogWwbS5xERBHImTQnltVbph5POzkNC88tZH7ZOAZOIqJvqJW9FoaVGaYed/63M04+Psk8s2EMnEREkTC4zGDUzl4bvgG+qLeqHp59eMZ8s1EMnEREkTlZ2tmr8Z05kuTA4/eP0XVbV+abjWLgJCKKpPgu8bG6wWr1eL3netx4dYN5Z4MYOImIjJAneR41vlMHHSYem8i8s0EMnERERupbvK+6X3xhMSdGsEEMnERERiqdvjSKpCqiZhWacWoG88/GMHASEUVh/c5exXqpxwvOLUBAYADz0IYwcBIRRUHdnHWR0DWhmo5vz909zEMbwsBJRBQFro6uaJ6neVCpk2wHAycRURS1K9BO3W+4tgGvPr1iPtoIBk4ioigqkLIA8qfIr2YTWnFpBfPRRjBwEhF9h3b5v5Y6F5xnda2tYOAkIvoOzfM2h7ODM84/O49zT88xL20AAycR0XdIFCsR6uaoqx6zk5BtYOAkIjJRJ6Fll5bhs99n5qeVY+AkIvpOFTNVRIYEGfD2y1usvvJ1EniyXgycRETfeyK1s8dPBX9Sj2efmc38tHIMnEREJqqudbR3xLFHx3Dx+UXmqRVj4CQiMoEUcVOgTo466vHMUzOZp1aMgZOIyER+LvxzUCehdz7vmK9WioGTiMhEymUohxxJcuCD7wcsvbCU+WqlGDiJiEy43NgvhX9Rj6efmg6dTse8tUIMnEREJtQqXyvEcYoDz5ee2H9vP/PWCjFwEhGZkJurG1rmbRlU6iTrw8BJRGRiXYp2Ufcbr23Eo3ePmL9WhoGTiMjEcifLjdLpSyNAF4A5Z+Ywf60MAycRUTToUuRrqVMC50Pvh8xjK8LASUQUDWTFFJm/9vnH5ygwuwB23NrBfLYSDJxERNHAycEJe1rtQcGUBfHq8yt4LPfAwD0D4R/oz/zWOAZOIqJokilhJhxpdyRobOeYw2NQcUlFPH3/lHmuYQycRETRyNXRFdOrT8c/9f9BXOe4OHD/APLPzo9F5xfhvc975r0GMXASEcWAxrkb40zHM8iTLA+8Pnqh7aa2SD4hOZqta4ZtN7fBL8CP+0EjGDiJiGJItsTZcKLDCYwuP1o9/uz/GSsvr0T1FdWRemJqdN/eHScfn+RUfRaOgZOIKAbFcoqF30v9jmtdruFkh5PoXrQ7ksZOihefXmDayWn4cd6PyDkjJyaemYjbr29z31ggBk4iIjNNCF8kdRFM8ZiCx70fY1uzbWiWpxliOcbCzdc3Mf70eGSbng3u890x49QMvPr0ivvJQjBwEhFZwNAVj6weWF5vOZ73fY5FtRehTJoysLezx7FHx9BlWxek+CsFav9TG2uurMFnv8/mTrJNczR3AoiI6H/iucRTk8RXSVEFAbECsPrqaiy9uBTnnp3D5uub1S2+S3w0yNkALfK2QJkMXwMsxRzmNhGRhUoZLyV6Fe+Fs53O4vLPlzGg5ACkc0uHdz7vsOD8ApRfUh7pJ6dH///647LXZXMn12YwcBIRacAPyX7AmApjcLfHXRxocwA/FfwJbi5uavWVP4/8iTwz8yD/rPyYcHQCHr97bO7kWjU7nY0vUf7u3Tu4ubnB29sb8ePHh5YEBgbCy8sLyZIlg709r4GYjzwerUVkf9tf/L+oMaDLLi7D1htb4Rf4v7GguZLmQtn0ZVE2Q1lVnZssTjLYmkAjz5GRjQds4yQi0vCsRPVy1lO3159fY+3Vtao99PCDw7j64qq6zTg9Q72WgdR0GDiJiKxAoliJ0LFQR3WToSsH7x/E/nv7sf/+flx8fpGB1IQYOImIrEzi2IlRN2dddRMMpKbFwElEZOWiEkizJMqCNPHTIEXcFEgZN6W6qcfx/vdYSrkykYOtYeAkIrIxkQmkt17fUreIONk7hQqmKsjGC/44eZzkapIHa8HASURk48IKpJe8LuHZh2dq7dCnH55+ffzhqfpbHsvi3NKL9+G7h+r2LUliJwmz1BryOVl6zdJLsQycREQUKpDKMJaI+Pj74PnH56GDa4hAK/f+gf54+emluklAjkhsp9ihS61hBNykcZKabcYkBk4iIjKai6OLmsVIbhEJ1AWqoTIRBVd9Kfa973t88vuE229uq1tEHOwckDxu8mCl1g4FO6BYmmLRvjcZOImIKNrY29mralq55UmeJ8LXfvT9+M3gKo9ffHyBAF0Anrx/om56VbNUjZE9ycBJREQWIY5zHNWbV24R8QvwU+uXhizF5k+RP0bSycBJRESa4uTghFTxUqmbOXCCUyIiIiMwcBIRERmBgZOIiEjLgXPGjBnImDEjXF1dUahQIRw6dCjC1x84cEC9Tl6fKVMmzJo1K8bSSkREtseiAueqVavQs2dPDBw4EOfOnUOpUqXg4eGBBw8ehPn6u3fvolq1aup18vrff/8d3bt3x7p162I87UREZBssaiHrH3/8EQULFsTMmTODnsuZMyfq1KmDsWPHhnr9b7/9hs2bN8PT0zPouc6dO+PChQs4duxYmNvw8fFRN8OFS9OmTYs3b95ociHrFy9eIGnSpFzImvlodjwemZdaPyYlHiRMmFA7C1n7+vrizJkz6N+/f7DnK1eujKNHj4b5HgmO8v+GqlSpgvnz58PPzw9OTqEnFZYAPHz48FDPS+Z++fIFWjsoZAfLtU9kDgpiPvJ41Ab+ts2Tj+/fv4/U51pM4Hz58iUCAgKQPHnyYM/L38+ePQvzPfJ8WK/39/dXn5cyZcpQ7xkwYAB69+4dqsQpVyRaLHHKZMgscTIfLQGPR+al1o9J6SujqcCpF3JWfLlSiGim/LBeH9bzei4uLuoWkmSqFktt8j21mnZLwnxkPloaHpMxn4+RPY9azNk2SZIkcHBwCFW69PLyClWq1EuRIkWYr3d0dETixImjNb1ERGSbLCZwOjs7q2Elu3fvDva8/O3u7h7me4oXLx7q9bt27ULhwoXDbN8kIiKymsAppO1x3rx5WLBggeop26tXLzUURXrK6tsnW7VqFfR6ef7+/fvqffJ6eZ90DOrbt68ZvwUREVkzi2rjbNy4MV69eoURI0bg6dOnyJ07N7Zt24b06dOr/5fnDMd0ykQJ8v8SYKdPn45UqVJh6tSpqF+/vhm/BRERWTOLGsdpDtKr1s3N7Zvjdiy1x5i06SZLloydg5iPZsfjkXmp9WMysvHAoqpqiYiILB0DJxERkREYOImIiLTaOcgc9E28Uretxfp7mSJKZrvgBAjMR3Pj8ci81PoxqY8D3+r6Y/OBUz83oUy7R0RE9P79e9VJKDw236tWrkiePHmCePHiRTi1nyXSz7P78OFDzfUItiTMR+ajpeExaZ58lJKmBE0Z2hhRCdXmS5ySOWnSpIGWyQHBwMl8tBQ8HpmXWj4mIypp6rFzEBERkREYOImIiIzAwKlhsjza0KFDw1wmjZiPMY3HI/PSVo5Jm+8cREREZAyWOImIiIzAwElERGQEBk4iIiIjMHASEREZgYGTiIjICAycGjVjxgxkzJhRTV5cqFAhHDp0yNxJ0pyxY8eiSJEiarpFWei2Tp06uH79urmTZRX5KtNX9uzZ09xJ0ZzHjx+jRYsWSJw4MWLHjo38+fPjzJkz5k6Wpvj7+2PQoEHq/BgrVixkypQJI0aMUNOrmgoDpwatWrVKnZQGDhyIc+fOoVSpUvDw8MCDBw/MnTRNOXDgALp06YLjx49j9+7d6gdXuXJlfPz40dxJ06xTp05hzpw5yJs3r7mTojlv3rxBiRIl4OTkhO3bt+Pq1av466+/kCBBAnMnTVP+/PNPzJo1C3///Tc8PT0xbtw4jB8/HtOmTTPZNjiOU4N+/PFHFCxYEDNnzgx6LmfOnKrEJFf7FDUvXrxQJU8JqKVLl2Y2GunDhw/quJTakFGjRqnS0uTJk5mPkdS/f38cOXKEtUffqUaNGkiePDnmz58f9Fz9+vVVCX7p0qUwBZY4NcbX11dV3UjJyJD8ffToUbOlyxp4e3ur+0SJEpk7KZokpffq1aujYsWK5k6KJm3evBmFCxdGw4YN1QVcgQIFMHfuXHMnS3NKliyJPXv24MaNG+rvCxcu4PDhw6hWrZrJtmHzq6NozcuXLxEQEKCuqAzJ38+ePTNburROlhPq3bu3+tHlzp3b3MnRnH/++Qdnz55VVbUUNXfu3FG1SHIc/v777zh58iS6d++upotr1aoVszWSfvvtN3URnCNHDjg4OKjz5ejRo9G0aVOYCgOnRoVcO1RO/FpbT9SSdO3aFRcvXlRXpmQcWeuwR48e2LVrl+qsRlEjnVekxDlmzBj1t5Q4r1y5ooIpA6dxfUCWLVuGFStW4IcffsD58+dVnxBZY7N169YwBQZOjUmSJIm6igpZuvTy8gpVCqXI6datm6omO3jwoObXZjUHaTqQ4096d+vJVb7kp3TQ8PHxUccsRSxlypTIlStXsOek78K6deuYdUb49ddfVXtxkyZN1N958uTB/fv3Vf8PUwVOtnFqjLOzszpBSS9QQ/K3u7u72dKlRVJKl5Lm+vXrsXfvXtV9nYxXoUIFXLp0SV3Z629ScmrevLl6zKAZOdKjNuRwKGmnS58+PQ9LI3z69An29sFDmxyDphyOwhKnBkkbSMuWLdXJqXjx4qr7vwxF6dy5s7mTprnOLFKds2nTJjWWU1+KlxXgZfwXRY7kXch24Thx4qixiGwvjrxevXqpi1+pqm3UqJFq45Tfttwo8mrWrKnaNNOlS6eqamXI3sSJE9GuXTuYjI40afr06br06dPrnJ2ddQULFtQdOHDA3EnSHDn8w7otXLjQ3EnTvDJlyuh69Ohh7mRozpYtW3S5c+fWubi46HLkyKGbM2eOuZOkOe/evVPHXrp06XSurq66TJky6QYOHKjz8fEx2TY4jpOIiMgIbOMkIiIyAgMnERGRERg4iYiIjMDASUREZAQGTiIiIiMwcBIRERmBgZOIiMgIDJxEpBky/63MDCMTdsuiBhs3bjTr9vz8/NRqHDIfqsyWJK+TCdmfPHnyXduVSfNlak1ZGUXWNf2We/fuqfSFdVuzZk3Q62QFm0qVKqnFsWVmp44dO6p1VI3d9urVq9X/yRqXMiWgLBQdksxRPHDgQPX/8lmZM2fGggULgv6/bNmyYaZXlqaLLosWLQpzm1++fDHqcxg4iUgzPn78iHz58qnJ4y1hezIvqgSjwYMHq3uZ91jml61Vq1aEnysnawl24ZGJrWSKuMaNG0cqnWnTpsXTp0+D3YYPH66CuYeHh3qNBHNZKzVLliw4ceIEduzYoVZfadOmjVHb3r59u5qHWKb4vHz5slq4XKa0C5lHMm2grIspC0rLHLwrV65US33pSV4Zplc+S+aUlfVIo1P8+PFD5ZXRq/qYbA4iIitg6qnirHHqucDAQN1PP/2kS5gwoZqi8Ny5c2b5nrLtDRs2BHtOplX79ddfdalSpdLFjh1bV7RoUd2+ffvC/YyXL1/qkiZNqrt7926UtheWkydPqtfev38/ws+SaeC+ZejQobp8+fLpoiJ//vy6du3aBf09e/ZsXbJkyXQBAQFBz8m+k7TcvHkz0ttu2rSprkGDBsGemzRpki5NmjTq2BDbt2/Xubm56V69ehXp9MpnxIsXT/fhw4eg5+Tz/vzzT13GjBnV9Hl58+bVrVmzRhdVMp2mpOt7scRJFkmqx+TqOCzHjh1TV+xyhR9VUk0ka/SFJFfBI0eOREyRq319dZGTk5NaGk6q0qRKy5SrOZiSlFSkymvr1q3qat2SJnJv27Ytjhw5ohbWlvVVpfRStWpV3Lx5M8zXy1JTcqxlyJDBZPvzr7/+UvtTqkMjIiW0d+/eIbqWepOVadq3bx+s6lRWVzJcOUS/mIEx69D6+PiEKqHJ5zx69Egt3yVkmT5ZhGLcuHFInTo1smXLhr59++Lz58/hfq6UTGUpMCkl6w0aNAgLFy5Ua5JK6Vgmwm/RogUOHDiAqJKqaak+liUEa9SooSaBNxYDJ1kk+cHLUl/6H6IhCSrSvlKwYMEofbavr2+4/5coUSK12kdMkhO7BCCpupNqsHLlyql2JvlR+/v7R/lzI/qe3+P27dtq7UhZySNFihRwdLSMRZYkXVIdKG16pUqVUm1qcrIuWbKkOvmGJCdxOVl36NDBJNuXCx25mLhw4QKaNWumqgQjIifu5cuXIzrI95K1PA2XGixfvrxaAUjaI+XYePPmDX7//Xf1f3L8RVaVKlXUBaZUw8p3lqrpyZMnB/ucO3fuqGAs1a8bNmxQ/7927Vq1IlFYZCUYea3hvpBqcqkClt+7bDNTpkzqwkQC5+zZs6OUL1JVLBd9EtjlWJELAFnOLbwLq3B9d5mVKBr4+fnpkidPrhs2bFiw5z9+/Kiqc6ZNmxbpqhypRuzSpYuuV69eusSJE6tVE0KuiKKvqgtZ5SjVWn/88Ycuc+bMaiWatGnT6kaNGhVUHVWiRAlV9ZMoUSJd9erVdbdu3Qq17YiqMFu3bq2rXbt2qOf37Nmj0jV37tyg5761vZDfs3Tp0t/8DosXL1af9eXLl2Dbr1evnq5ly5Zhptcw32SFnrC+pzwvVW+GpNpPqv+El5eX2r+jR48O+v/jx4/rnJycdDt37gw3vzw9PXVly5ZVq4fI9gcPHqyzs7PTnT59Wrd69Wr1XJw4cYLdHB0ddY0aNVLvl/0c3qo4+luePHnUd0mQIIGq2pQqTqk+lP/Tr7axbdu2UGnbu3evyt8CBQqofJVVTuT1kr+yPwzTJJ8l39Xe3j7oOVNV1X769EkdIxMmTAj1f8uXL1f57uDgoNLat29f9bf8hiK77cDAQF2/fv3Ud5PPkSp7+Z3Kdzpx4oR6TaVKldT/v337Nuh969atU/tK0hdSx44dVX6FVeUdcn9KvkkVvN639qf8TsIjvw35jt26ddMZg4GTLJa0VWXIkCGo3UQsWrRInTRfv36t/v7999/V8ks7duzQ3b59W7VhyP/v378/6D1yUo8bN676vGvXrunOnz+vK168uGqne/r0qbr5+/uHGQDkBCEnBtmuBKlDhw4FBbO1a9eqk8GNGzdUW1HNmjXVSdewDSmqgVPID9rDwyPo729tL+T3lCDzre+gP8lK0NF78eKFOqlKIAhJToQjRoxQ7VmSbxIAoxI4xb///qtOgqdOndK9f/9elyVLlgjzSr6TXDTJyV6+h5wU48ePr07enz9/1v3zzz/qsbxO2uwMb5JW4evrq/JFbnJhULJkyaC/5VakSBF1ch45cqTKZ7mX4Cb7QbYny/n9/PPPKhDKRZyefK6kX4Lk5cuXVbCeOHGiCtQXL15UFwhy3OnTI58lwUry+cqVK2G2MUY1cC5ZskTlq37fhOXZs2cqz+WCQL6f4f6P7Lb9/f11jx49Uu3KciEh3+n58+fq/1q1aqUu1AxdvXpVvUby1ZDko+zHyZMnB3teLqTk9fJbDrk/Hzx4EPQ6w/0X1u3hw4cR5leHDh10VatW1RmDgZMslhz08sMxPIFLKUo6Jwj50ctV7dGjR4O9r3379kGv0Z/UpaOEofACmuHzsq6fBGHDUl9E5EQl6b106dI3txOZwNm4cWNdzpw5I729sL5nZL6DBALDAC0nMClVGV6wGJKAqC9p6kUlcIpffvlFly1bNl3z5s1ViUMCYHgqV66sa9OmTdDf8t2lBJ4rVy719/Xr19VzBw8e1EWG5Lth5xn995BgahgcJJBKkNV3DpIgLI+PHTsWFDTr1KmjguDSpUt1Z86cUf9/7969cLct/68PNhG9LiqBU75D/fr1I/Xa+fPnq05Ub968+a5tt2zZUl2M6kkpPVasWCo4623cuFEF6ZAlTv3FrnTUCuvYlQuB6CLHeOHChXVt27Y16n2W0ThBFE57hLTRSBuHtPtJG9ahQ4ewa9cu9f9Xr15V46+kM40hab8pUKBAsOeko4KxPD09VUeIChUqhPn/kh4ZhnD8+HG8fPkyqDPPgwcPTNJhRs6v0snEmO2F/J7f+g7ip59+QpEiRfD48WPVkUPaA/WdlqLbhAkTVNplXODp06fDHRbw8OFDtd+lY5h0etGT/Z8uXTqVB9IBRYZJyDhK6aAjx4Dkk7SVyzjLatWqhWrjDGt7efPmDfYaafOWMY/i7t27qmOJ8PLyUm3QDRo0UG100ulG2sukA460q8r3kvbrypUrq9ckTJgw2Hb025YhLSHdunVLdWKRNklJg/4758qVS32+7CvZp0uWLEHRokWDvU/Gnm7bti3cDknym4obNy52796NX3/9FX/88Uewjkzf2vbLly9Ve6V0sJP8l+NF2pUNO+xIG690spPOWjIsRt4j25JhLvoOSYbtsXXq1AnKYz3Jd2mjlg5BcqxLnkpnqqNHj6r0t27dGsaStBQrVgxZs2ZVnzV16lT1/aZPn27U5zBwksV3Euratas6sOUHKictfRDQB45///1XnfANyYBrQ4Y99SIr5A88JOmNKePn5s6dqwa+S3rkZGmqTjkS9DJmzGjU9kJ+z299ByEBRsYqyklYOmFcunQJW7Zs+a60SxD5WrAKPllASNKJRMYXyneRjmCGQcuQ9KCWXsfSYaR48eLBeo+KIUOGoHv37iqYSeDs06eP6uUpJ3r5TiGDpkiSJInqIBOSbEdPgrkEEH3nl969ewf9n6RZtiEdTfSkA4uenJQlYEybNk1NBCBjJw3359u3b9V90qRJQ6VBOskYBiL9haAEbukBLHkpYyNDBl25yJTfggTrsEiAHzp0qAqMcmEqnWxatmxp1LbF4sWLVVCTfSz7Y//+/cECuD4wd+vWTV3MSVCUcZ2jRo2CIelYJJ2I9BfDIUnwTZYsmer9LMeKBHjpFKjv1GQsyXOZ9EH2qZubm/pucqFhmPZIibYyMJEJSFW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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "vy_numerical = uw.function.evaluate(v_soln.sym[0, 1], sample_pts).squeeze()\n", + "\n", + "fig, ax = plt.subplots(figsize=(5, 6))\n", + "ax.plot(vy_numerical, sample_y, \"g-\", lw=1.5)\n", + "ax.set_xlabel(r\"Vertical Darcy flux $q_y$ (m/s)\")\n", + "ax.set_ylabel(\"Height $y$ (m)\")\n", + "ax.set_title(\"Darcy velocity (should be nearly constant)\")\n", + "ax.grid(True, alpha=0.3)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Try It Yourself\n", + "\n", + "Experiment with different parameters to build intuition:\n", + "\n", + "```python\n", + "# Larger \u03b1 \u2192 sharper transition near saturation\n", + "ALPHA_G = 5.0\n", + "\n", + "# Wetter bottom boundary\n", + "PSI_BOTTOM = -1.0\n", + "\n", + "# Higher resolution\n", + "RES = 64\n", + "```\n", + "\n", + "- What happens as $\\alpha \\to 0$? (Hint: the profile should approach linear.)\n", + "- What if the top boundary is fully saturated ($\\psi_\\text{top} = 0$)?\n", + "- The Van Genuchten model is also available \u2014 try replacing\n", + " `gardner_K` with `van_genuchten_K` (no analytical solution,\n", + " but the solver still works).\n", + "- Can you compute mass conservation by integrating $\\theta(\\psi)$\n", + " over the column?\n", + "\n", + "## References\n", + "\n", + "Celia, M. A., Bouloutas, E. T. & Zarba, R. L. (1990). A general\n", + "mass-conservative numerical solution for the unsaturated flow equation.\n", + "*Water Resources Research*, 26(7), 1483\u20131496.\n", + "doi:[10.1029/WR026i007p01483](https://doi.org/10.1029/WR026i007p01483)\n", + "\n", + "Gardner, W. R. (1958). Some steady-state solutions of the unsaturated\n", + "moisture flow equation with application to evaporation from a water table.\n", + "*Soil Science*, 85(4), 228\u2013232.\n", + "\n", + "Mualem, Y. (1976). A new model for predicting the hydraulic conductivity\n", + "of unsaturated porous media. *Water Resources Research*, 12(3), 513\u2013522.\n", + "doi:[10.1029/WR012i003p00513](https://doi.org/10.1029/WR012i003p00513)\n", + "\n", + "Richards, L. A. (1931). Capillary conduction of liquids through porous\n", + "mediums. *Physics*, 1(5), 318\u2013333.\n", + "doi:[10.1063/1.1745010](https://doi.org/10.1063/1.1745010)\n", + "\n", + "Van Genuchten, M. Th. (1980). A closed-form equation for predicting the\n", + "hydraulic conductivity of unsaturated soils. *Soil Science Society of\n", + "America Journal*, 44(5), 892\u2013898.\n", + "doi:[10.2136/sssaj1980.03615995004400050002x](https://doi.org/10.2136/sssaj1980.03615995004400050002x)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/docs/beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb b/docs/beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb new file mode 100644 index 000000000..727e94bce --- /dev/null +++ b/docs/beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb @@ -0,0 +1,636 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cell-0", + "metadata": {}, + "source": [ + "# Notebook 17: Richards Equation — Transient Wetting Front\n", + "\n", + "This notebook solves a **transient** Richards equation problem\n", + "and validates the numerical solution against an exact analytical\n", + "benchmark. A wetting front propagates downward through an\n", + "initially dry soil column after a wet boundary condition is\n", + "applied at the top.\n", + "\n", + "## Key Concepts\n", + "\n", + "- Time-dependent Richards equation with the mixed form\n", + "- Gardner exponential model — linearisation trick\n", + "- Ogata–Banks advection–diffusion solution\n", + "- Wetting-front dynamics and mass conservation" + ] + }, + { + "cell_type": "markdown", + "id": "cell-1", + "metadata": {}, + "source": [ + "## Why a Transient Benchmark?\n", + "\n", + "[Notebook 16](16-Richards-Equation-Groundwater.ipynb) validated\n", + "the Richards solver at steady state, where the time derivative\n", + "vanishes and all formulations agree. A transient test is needed\n", + "to verify that the **mixed form** storage term\n", + "$\\partial\\theta/\\partial t$ is discretised correctly.\n", + "\n", + "### The Gardner Linearisation\n", + "\n", + "The substitution $u = \\exp(\\alpha\\psi)$ transforms the nonlinear\n", + "Richards equation with Gardner conductivity into a **linear**\n", + "advection–diffusion equation:\n", + "\n", + "$$\\frac{\\partial u}{\\partial t}\n", + " = D\\,\\frac{\\partial^2 u}{\\partial z^2}\n", + " + V\\,\\frac{\\partial u}{\\partial z}$$\n", + "\n", + "where $z = L - y$ is depth from the top,\n", + "$D = K_s / (\\alpha\\,\\Delta\\theta)$,\n", + "$V = K_s / \\Delta\\theta$, and\n", + "$\\Delta\\theta = \\theta_s - \\theta_r$.\n", + "\n", + "### Ogata–Banks Solution\n", + "\n", + "For a step change at the top ($z = 0$) from $u_{\\rm dry}$ to\n", + "$u_{\\rm wet}$ with a semi-infinite column, the\n", + "**Ogata–Banks (1961)** solution is:\n", + "\n", + "$$u(z,t) = u_{\\rm dry}\n", + " + (u_{\\rm wet} - u_{\\rm dry})\\,H(z,t)$$\n", + "\n", + "where\n", + "\n", + "$$H(z,t) = \\tfrac{1}{2}\\,\\operatorname{erfc}\\!\\left(\n", + " \\frac{z - Vt}{2\\sqrt{Dt}}\\right)\n", + " + \\tfrac{1}{2}\\,\\exp\\!\\left(\\frac{Vz}{D}\\right)\\,\n", + " \\operatorname{erfc}\\!\\left(\\frac{z + Vt}{2\\sqrt{Dt}}\\right)$$\n", + "\n", + "Converting back: $\\psi(y,t) = \\ln(u)/\\alpha$.\n", + "\n", + "The approximation is valid while the wetting front has not\n", + "yet reached the bottom boundary." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "cell-3", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T11:10:33.051502Z", + "iopub.status.busy": "2026-02-23T11:10:33.051236Z", + "iopub.status.idle": "2026-02-23T11:10:36.713698Z", + "shell.execute_reply": "2026-02-23T11:10:36.713132Z", + "shell.execute_reply.started": "2026-02-23T11:10:33.051490Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import sympy\n", + "import underworld3 as uw\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from underworld3.utilities.retention_curves import (\n", + " gardner_K,\n", + " gardner_theta,\n", + " gardner_transient_psi,\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "cell-4", + "metadata": {}, + "source": [ + "### Configurable parameters\n", + "\n", + "Default values are defined as named constants below. From the\n", + "command line, override them with PETSc-style flags:\n", + "\n", + "```bash\n", + "python script.py -uw_res 64 -uw_alpha \"4.0 1/m\"\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "cell-5", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T11:10:36.714847Z", + "iopub.status.busy": "2026-02-23T11:10:36.714355Z", + "iopub.status.idle": "2026-02-23T11:10:36.725206Z", + "shell.execute_reply": "2026-02-23T11:10:36.724538Z", + "shell.execute_reply.started": "2026-02-23T11:10:36.714827Z" + } + }, + "outputs": [], + "source": [ + "# --- Default values (edit these in a notebook) ---\n", + "COLUMN_HEIGHT = 3.0 # m — tall column so the front stays away from the bottom\n", + "COLUMN_WIDTH = 0.1 # m — narrow (effectively 1-D)\n", + "RES = 64 # — vertical elements\n", + "KS = 1.0 # m/s — saturated hydraulic conductivity (dimensionless-friendly)\n", + "ALPHA_G = 4.0 # 1/m — Gardner sorptive number\n", + "THETA_R = 0.05 # — residual water content\n", + "THETA_S = 0.40 # — saturated water content\n", + "PSI_DRY = -2.0 # m — initial (dry) pressure head\n", + "PSI_WET = -0.1 # m — wet boundary at top\n", + "DT = 0.005 # s — timestep (accuracy is time-dominated)\n", + "SNAPSHOTS = [0.05, 0.15, 0.30] # s — times to compare" + ] + }, + { + "cell_type": "markdown", + "id": "cell-6", + "metadata": {}, + "source": [ + "## Analytical Wetting Front\n", + "\n", + "Before running the solver, let's visualise what the\n", + "analytical solution predicts at the snapshot times." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "cell-7", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T11:10:36.726311Z", + "iopub.status.busy": "2026-02-23T11:10:36.726074Z", + "iopub.status.idle": "2026-02-23T11:10:37.126371Z", + "shell.execute_reply": "2026-02-23T11:10:37.124736Z", + "shell.execute_reply.started": "2026-02-23T11:10:36.726291Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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blfG2UuCsdq0EOfHV1H1iWB/Z3xL8GUgvat0TEE1l2Ify/T9ZdfHG1ulkpJdfelmlVsTJyMkF2Z9///13o9XQJciVz56hFkJzPo8SXErQK79Ltd8rqSPQVE39fZAieI2dIGzKd1e++3Kicu/evaq2gyXWvTGzZ89WtRsko0H2veGzayCfB0ORTVkf6Q2X7ZPx7HVPKslJMmt/H4mImoM93URkF6QXWYJqSSGUtNW6f1KMRwIeSXtsDjkglUC+boEqKejT1DmLpYquVKl+5ZVX1IGhVCOWCsZN6b1piKRmyzadbC5ZWW+pHFz7gFoO3s+kOrEE3fJ8cmArAaQhPV56tmV9JGiTZbULaEn1YQnQ5H0x9ILV/jMcuJ+sF/dMe3gbIoXxpIdVDrxrk55MKa5kafJ+S8Vm6WGsvR3SYywBkGQuSEDXXM353MjnQaankqEAdUlPo/QCy9RgdatIN8Twuar7vZDezaYyFNuT70Rt8p6cqqBZY6QnU3rKZRsb+rzVntKquSTobmpquexPCdykUFldMtRAelglGL/33nub/XmUfS/bWPvkoXwGGponvrHPR1N/H2RISWP7Uf7/qRgqgxtmJ2jOujeXpJBLxo30uMuQloZmKzCQ75qcNJRMHamqX/ckmJx8suV0hEREdbGnm4jsggTTcrAkgW3tKaQMpHdKUsSlp0MCwaaS1FMJJGUsoPR8yEGojEOW56ldAbopvd2SZi4Hnbfddlu9++XgTwIyqYouQboEtY0FCDLdmGyvrJdUL5f/K+mb0osuQZNU7ZZtlOeT15L0eqn0LNW2pReuobHtTSFjgWU/Si+SHNQaevAk6JbeU/mT8ZJ111WCcTnpIIGGBBdyQCupqX/88YfqYZKAU6Zrkp4oOeiX4F4OoA37W7ZPvP3226pXVYJ6eR75P6dL9q9UhpYqyrJ/JI1W9qEsk30k91vayy+/rFLyZd9JMCZBi1SVlpMSUr28Ob2uBrJvpPdQeiwloJbeQ8P+aoh8Nxo68SSVy6XitmQkSA+2nBiS6ZbkpIB8dgxBkWGfy2dMTqRI9ocE6fJ+yTCC2tW4T0WCI6kJIBXm5T2Vz5HsC5lmq6kp33XJ50U+cxL0yhRRhrmipQdZMjTk5Ie8x80lwaME8k0NumV/SjAn2yKfdfl8SZq4nCiTyuTyXFKB3TBHd3M+jzJ8Rr5nMuxFZj2QrAB5nYYq1zf2+bDG74O8d4aTJbJO8vzyeZBZGqRXvbnrfjrk8ym/g1KFXb5rv/76q/q+ybAe6bGXzAL5XMt3T8aWy/LaGUzCEKzL/yMishtWLdNGRNREEydOVFXCs7KyGn3MFVdcoSobZ2RkGKtcS2XsuupW0T569KhuypQpurCwMF1QUJDu/PPP1+3YsaNe1e+GqpcbVFRUqGq+8n8bIpWupeJuaGioqpxb++e1oareaWlpqoq5VDyW6sZxcXGqMnPtKun/+9//dO3atVOvm5iYqPvkk0+MlaSbW73cQCpNy/9/8cUXzZZ37txZLU9OTq73f6Qy+V133aWqnMu6SvXh/v376x5//HFVBd5gyZIlqnKyrG/d6tWPPvqo2kZ3d3ezfdxY9fKmvK/i448/1nXq1El9drp06aIqWV9yySVNquB8surlt99+e4P/Z8WKFboxY8ao/yeVq6Wi+W+//Wb2mNrVmGtr6PN1+PBh3bhx49TnUu47VdX1f/75Rz1Oqrk35L///tNdfvnlqpq6vFdS7bx79+66W2+9Vbdx40azx0r1fKlWL68t343LLrtMVQ+vu58Nnzn5HDT0vbj//vtVVXepVC37Y82aNfU+k83ZJ2L+/Pm6s88+W1Wyls+TPJ98v+Qzdqr3ryFPPPFEkyra1/XHH3/oLrjgAlWZW/ZnfHy87pprrjFW7a+rqZ9HWd61a1e1bR06dNC9/PLLus8++6xelf+TfT6a+vtwOtXLpXp/nz59dG+88YauvLz8tNZd1lVmdair7ne+oc+GfK7kN1s+UwsXLlS/i9dff72uW7du6j2XGRWSkpJ0b775ptksB0Len1NVqCciamlu8o+tA38iInsnvYBSeVnmSZYKu2SfpHdRUk8nTpyo5k12RjLOVqpWS1YFNY2kGsuwjtdff71Fd5krfB7tSWFhoRryItkIMoc8EZG9YNBNRHQSO3fuVAXGJL1cUlsl5fR00ojJ8mQMq6RTSxqpFLKS90kOtnfv3o2NGzcaK6w7G0m/lZRfSSM+VRV8ajmu+nm0J5LOL6n4knbe2LR1RES2wF8kIqKTkDGTMi2OTFEjhd4YcNsPGUcq423lPZLx6DJGXSqvyzhzZw5wZJyz1CiQKa0YdNsPV/082hOpJSAV+RlwE5G9YU83ERERERERkZVwyjAiIiIiIiIiK2HQTURERERERGQlDLqJiIiIiIiIrIRBNxEREREREZGVMOgmIiIiIiIishIG3URERERERERWwqCbiIiIiIiIyEoYdBMRERERERFZCYNuIiIiIiIiIith0E1ERERERERkJQy6iYiIiIiIiKyEQTcRERERERGRlTDoJiIiIiIiIrISBt1EREREREREVsKgm4iIiIiIiMhKGHQTERERERERWQmDbiIiIiIiIiIrYdBNREREREREZCUMuomIiIiIiIishEE3EVncc889h+7du0Or1Vpl7+p0OvUay5cvN1v+2WefIT4+HiUlJVZ5XSIiIksoLCzEAw88gNatW8PX1xeDBg3CmjVr7KI9ZVtKZHkMuonIoo4fP45XX31VNeLu7tb5idm7dy+efvpppKenmy2/7rrrEBAQoF6fiIjIHuXk5GD48OEq0H3rrbcwb948aDQaXHjhhThx4oTN21O2pUSWx6CbiCzq7bffRmhoKCZPnmy1Pbtp0yZ12b9/f7Plnp6emDFjhlqH0tJSq70+ERHR6br++utVD7ME3VOmTMH48ePx4YcfIi8vDwsWLLB5e8q2lMjyGHQT0SlJWltQUBAefvhhdXvPnj1wc3PDTz/9pG5//fXX6rYsl7S0q666qt5ZeTloSEhIqPfc1dXV6NOnD84999wmvRNyYDBt2jR1vUuXLup1Zd3kAEbIfZK298MPP/CdJSIiu/Lvv/9i4cKFeOONN+Dv729c3qFDB3V58OBBdVlZWdlge2qptvRU7SnbUiLLYtBNRKe0a9cuFBcXY8CAAer2xo0b1aXhtpwpDwkJQVZWFnJzc3H22WfXe46RI0fi2LFjOHLkiNlyOfDYvXs3Pvjggya9Ex9//LF63X79+qnxb/K3cuVKdbAgYmNj0a1bN3VQQ0REZE+kDWvXrp1qJyVQNvzJyWLh5eWlLtetW9dge2qptvRU7SnbUiLL8rTw8xGRE6obZMvtiIgItG/f3njb0GgLuV6XHCiI1atXo23btur6oUOH8Oyzz+Lxxx9H586dm3xmPjU1FVdccQWGDBnS4GPk9ZcsWXJa20pERGStrLG//voL+fn58Pb2bvAxhna1sfbUUm1pU9pTtqVElsOebiI6pYaCbMP4Lyn+snXrVhWQS9EXOUMeGRlZ7zkk7S04OBirVq0yLrv11ltV5VZD2npTpKWlqR71uuO5a4uOjlaPkd4DIiIieyBDsCTgfv7557FhwwazPyleJqSKuWisPbVUW9qU9pRtKZHlsKebiE5JDggMjbKcqZcg+6677lK3JZ1NipbJ/TJWTVLjPDw86j2HjEkbNmyYOjsvZs+erc74L126tNEz/s0polabTL8iY9LKy8sRGBjId5iIiGzu8OHD6nLw4MHGzDGDHTt2oGPHjmpstSgrK2uwPbVUW9qU9pRtKZHlsKebiE4pJSXF2Mtdd3z3okWL1OWIESPUGXkp/tLYPNmSFpecnKzS2e677z51Zn/06NHNPkiQ4jMybrsxUgHWx8eHATcREdmNqqoqdVk3kJYT2dK23XzzzcZlJ2tPLdGWNqU9ZVtKZDkMuonolKR3W9LQ6o7vlrQ0mdJkwoQJiIuLMzbcBw4caPB55EDBMBepXM6cObPZe18ONOR1GupNN5Dqr927d+c7S0REdsNQoXz79u3GZTIMSjLH5MT2HXfcYVx+svbUEm1pU9pTtqVElsOgm4hOSaYs+eOPP3DppZfim2++Ub3Is2bNQu/evVVv8kcffaQeZzjTvnbt2gafZ+DAgfDz81MHHK+99lqDY7+FjGNr7Ky9zFkqByEyl6m8Tt0KrnKCYP369Q1WUCciIrKVnj17qlTuF154QU1r+eeff+L888/Hzp07MW/ePLMpxE7WnlqiLT1Ve8q2lMiyGHQT0SlJgP3+++8jJycHy5cvV439vn378Morr6gz5fHx8epxUshF0sylAW/wB8fdHWFhYeox119/fYOPkdR10apVqwbvf/rpp1UhGZlDdOjQoZg7d67Z/cuWLUNBQYFx7lEiIiJ7IW2WBN433ngjrr76ajU1l2SQyUns2k7WnlqiLT1Ve8q2lMiy3HRSbYiIqAkkDS4oKAiPPPKIaqwbIo325Zdfrs6YG4JxA0mBkylNZPxaYmJig/9fetQlZW7btm3o1atXs9+Xa665RqXE1a7sSkRE5Ggaa0/ZlhI5HlYvJ6JmFVSTiuAnqxw+efJklfr28ssv47333lOVzSWAlgroEnC/+OKLjQbcQiqwypyhpxNwS5rcnDlzVBV1IiIiR1a7PX311VfZlhI5MPZ0E1GTff755yolTuYPPVnKmkx98uuvv6oecbmcNGmSSqG75ZZbGu0htwQJ2CXtvXYFWCIiIkdlaE+l4NmUKVPYlhI5KAbdRERERERERFbCQmpEREREREREVsKgm4iIiIiIiMhKGHQTERERERERWYnLVy/XarWqKJRMg+Tm5mat/UxERGRXZMbQoqIixMXFqXl/zxTbUyIicjW6JralLh90S8DdunXrFn1ziIiI7EVaWhoSEhLO+HnYnhIRkatKO0Vb6vJBt/RwG3ZUcHCwRXa6nO3Pzs5GVFSURXoP7IEzbpOzbpczbpOzbpczbpOzbpczblNhYaE66WxoB+2tPXXGfW4PuF+5bx0RP7fct47elrp80G1IKZcDBEsF3eXl5ViyZAluuOEG+Pr6wll+7GS7ZB8508GPM26XM26Ts26XM26Ts26XM26TgaWGVlm6PXXGttQeOPNn2da4b7lvHRE/ty3TlvLX1go8PDyQlJSkLomIiIhtKRERuS4G3VYgwXbHjh0ZdBMREbEtJSIiF8eg2woqKyvx448/qksiIiJiW0pERK6LQbcVeHp6YujQoeqSiIiI2JYSEZHrYtBtjZ3q7q6q2LFACREREdtSIiJybQy6raCiogLffvutuiQiIiK2pURE5LoYdFuBl5cXxo4dqy6JiIiIbSkREbkuBt3W2Knu7oiNjWV6OREREdtSIiJycQy6rUDSyj///HOmlxMREbEtJSIiF8eg2wokrXzixIlMLyciImJbSkRELo5BtzV2qrs7wsPDmV5ORETEtpSIiFwcg24rpZd/9NFHTC8nIiJiW0pERC6OQbcVeHt7Y9q0aeqSiIiI2JYSEZHrYtBtJQy4iYiI2JYSERHZVdA9a9YsJCUlITg4WP0NHToUf/7550n/z/Lly9G/f3/4+vqiQ4cO+PDDD2FrlZWV+OKLL9QlERERsS0lIiLXZVdBd0JCAv73v/9h48aN6m/MmDG45JJLkJKS0uDjDx06hAsuuAAjRozAli1b8Nhjj+Guu+7C3LlzYete7htuuIG93URERGxLiYjIxXnCjlx00UVmt1988UXV+7127Vr06NGj3uOlV7tNmzZ466231O3ExEQVrM+cORNTpkyBLbGXm4iILNamVGvh7gZ4etjVuXKrY1tKRESWotFq4F5RBDffEMDNDS3JbltvjUaDH374ASUlJSrNvCFr1qzBuHHjzJadd955KvCuqqqCLQ8SZs+ezYMFIiKyiLu+PAvTPx6Mp2ZfDOh0LrFX2ZYSEZElaLQ67DhWgBcWvIYJs8/CPR9OwYnyE3DZnm6xfft2FWSXl5cjMDAQ8+bNQ/fu3Rt8bEZGBmJiYsyWye3q6mrk5OSgVatWDU7nJX8GhYWF6lKr1ao/S/Dy8sLNN9+sLi31nLYm26HT6Zxme5x5u5xxm5x1u5xxm5x1u2y5TdmF5djiUYBSL3fklh5Aal4JEsL8z/h5z3RbrN2eOmNbag+c8ftpL7hvuW8dkTN+biuqNdh+rBAbDudh/aET2HTkBIZXrUZ5mx+Q5ueNNK99uGzLbAwdfNsZv1ZT95vdBd1du3bF1q1bkZ+fr8ZmX3fddapYWmOBt1ud1AD50DS03ODll1/Gs88+W295dna2CvQtQYL+o0ePqt56T0+728Wn/YEqKChQ+9fd3W4TJJrNGbfLGbfJWbfLGbfJWbfLltv0/qL1KK15TW/4wLuqGFlZxWf8vEVFRWf0/63dnjpjW2oPnPH7aS+4b7lvHZEzfG7LqjTYkV6CrceKseVYEVLSS1ChqYkJocXdnr/g4oBfcYlfnFoWp2pd90NWVlaLtaV214pJEbJOnTqp6wMGDMCGDRvw9ttv46OPPqr32NjYWNXbXZvsPGmcIyIiGnz+Rx99FPfdd5/ZmfnWrVsjKipKVUy3hLKyMnz99de4++674efnB2f5QsqJDNlPjvqFdJXtcsZtctbtcsZtctbtstU27c4owqH9m4HO+tvh/iGIjo62yHPLrB9nwtrtqTO2pfbAGb+f9oL7lvvWETna51an0+HoiTJsTs3H5tQT2JKaj10ZRSqFvK5gFGOm10cY57EJLwWFGZdfMfAuDE0a0qJtqd0F3Q3t2Nrpa7VJGvpvv/1mtuzvv/9WwbqkozXEx8dH/dUlHzJLfdDk4GD69Onq0hE+vE0lX0hL7id74Yzb5Yzb5Kzb5Yzb5Kzb1dLbJO3fi3/sQhuPNGyrWRYSEGGx1z/T57F2e+qsbak9cMbvp73gvuW+dUT2/Lktl17sYwUqRVyCbAm2s4sajg0NEsL8MCU2EzdlPI/AsmModnPDgqAAdZ+fpy8mJ05t8bbUroJumfJr/Pjx6ky5dNVLIbVly5Zh0aJFxrPqx44dU2e+xS233IL33ntPnWm/6aabVGG1zz77DN9//73NzxhJD3xkZKRdfniJiMj+zd96DKv252KI/3HjssAAy/RyOwK2pURErud4vvRin8DmI/nYlHoCO48XoKomVbwhMqK4S3QQ+rUNw5AO4RjYNgxxe78F/noM0OoLa/8WHmUcpjWhw4UI8QlBS7OroDszMxPXXHMN0tPTERISgqSkJBVwn3vuuep+WZ6ammp8fPv27fHHH3/g3nvvxfvvv4+4uDi88847Np8uTCqnL1myRI1P5zg0IiJqrrySSjz/+y51PcbDNIwqIFA/Hs0VsC0lInJuJRXV2H6sAMlH87EtrUAF2+kFJ68JEuTrib5twtCvTSj6tw1D79ahCPatyXAuOwH8diuwc77x8ZqEAfgu1AsoOaZuX9ntStiCXQXd0kt9Ml9++WW9ZaNGjcLmzZthTyTd7uqrr24w7Y6IiOhUXly4SwXeHtAg2isbgH4sWoBvqMvsPLalRETOo7Jaiz0ZRdh6NB/JafnYdjQf+7OK0cBQbDMdowLQr02YCrClN7tTVCDc3RsomH1gKTD/NqDIlB2GoXfg385n4fCKh9TNgbED0SWsC+DqQbczpcSlpaUxvZyIiJrtr5QMzN18VF1P8s1EqZvGeJ8tUuJshW0pEZFj0mp1OJhTUtODLQF2AXamF6rA+2T8vT3Qp7W+B1sC7b5tQhHq733yF6sqA5Y8C6ybZVrmGwJc8gF03Sbg04VXGBff2PNG2AqDbiuQaU5kfHmvXr2YXk5ERE2WVViOR+YmG28/0rscBw+6u2TQzbaUiMj+SdHP4wXl2H40H1vT9Kni248WoKii+qT/z8PdDd1ig5CUEIo+rUPUZefoQHh6NKMe1vEtwC8zgJw9pmXtRwETZwEh8VhzfDV25u5UixPDEzEsbhhshUG3laY9mzp1qrokIiJqas/AAz8n40SpvvDLuO4xGOSzDFtqHYCEeLtO0M22lIjI/tqp1LxS7DhegB3HCpGiLguM7dbJdIgMQFJCiBqDLQF2j7hg+Hp5nN6KSO/28leBVW8DuppsME9fYOyzwKCbpaS4WvTp9k+N/+XGXjeqKu22wqDbCjQaDQ4cOKDmCmf1ciIiaopPVhzEf3tl/DYQHeSD/01JgtsPj6HA3TV7utmWEhHZ8DdYUsSzi40BtgTXO48XnrIHW8QG+xoD7N4JoeiVEIIQv4anc262wyuBX+8C8g6YlrXqDUz+BIjqaly05vgabMjYoK63DW6LsW3GwpYYdFvpQCE5ORn9+/dvdL5wIiIig9X7c/DKot3G2zMv641wPw8gYzsKQ3yNy4N9gl1mp7EtJSJqGVUarQqod6YX1QTZBdiVXoSyKlNNkcZEBnqjZ3yI6rmWAFsC7ZhgU7tlMeUFwOKngE21Cmu7ewEjHwDOug/w9DZLeX9n8zvG27f2vhUe7qfZq24hDLqtlBI3adIkppcTEVGT5iS98/stxgqud43phJFdooDMFKCqFAUeAS6bXs62lIjIssqrNNidUaQCa0kPlym7pKr4yebCNogL8UWP+BD0jAtBz/hgFWxLZpZV07Z1OiBlHrDoUaDYNIUmEgYBF78LRHer91/+TfsXO3J3qOudwzpjfPvxsDUG3VY6O79r1y6mlxMR0SkPfm6dvRm5JZXq9qguUbh7bM10Jqlr1UXt9HJX6+lmW0pEdPqyispVj/Wu9ELj34HsEpU6fiptI/xVcN1Dgmu5jAtGRGALT4ecvQf44wHg0H+mZd6BwDlPAwP/zzh2uzaNVoP3trxnvH1X37vg7taM4mxWwqDbSgcKBw8exNChQ5leTkREjRakue/HrWo6FdE63A9vX9FHVXRtKOj29/SHl6TSuQi2pURETU8PP5BdXBNYm4LsnGL9Cd2TkU7qtmG+6N0mHL1UmngIuscFW24M9umoKAKWvwKsnQVoa40h73weMOF1ILR1o/917r652J+/X11PikrCqIRRsAcMuq2UEjdhwgSmlxMRUaNe+Ws3/tiuT5UL8PbAh1f3N5+PtCboLvTwcLkiaoJtKRFRffmllWrO69rB9b7MYlRqTj4HtvDycEOn6CD0jNOnhkuKeJfoQJQU5CE6Otr2BaB1OmD7z8DfT5inkoe2Ac5/Beg6Xn+WoBEFFQV4d8u7xtv397/fphXLa2PQbaW5RaWQ2ujRoxl4ExFRPbPXHcFHyw+q69Kx/d5V/VTvglHBUaAgFbpaPd2uFnSzLSUiVyYp4IdzS2qlhuuD7PSC8ib9//AAbyS2CkL3VsFIrPnrGBUIb0/zwFqr1aIEdiB1HfDXY8CxjaZlHj7AWfcCZ90DePmd8ik+3PYh8iv02WPj241Hv5h+sBcMuq1AKuZlZmaqSyIiotr+2J6OJ+frC7yI5y7pibO7RZvvpJpe7jI3N1TXnKQP9nad8dyCbSkRuYriimrsrgmupYK4XEpxs6ZUD5cTtx2iAmsC6yB1KYG21QucWUreQWDJM8DOBebLu4wHzn8ZCG/fpKc5mH8QP+z+QV339fDFfQPugz1h0G0FMk3Yueeey/HcRERkZunuLNz9g6lS+c0jO+DqIW3r76Ujq9VFroepRyLMN8yl9ibbUiJyNtUareq9lurhe2r+5HpqXmmT/n+QrycSY/XBtYy7lgC7S0wQfL1sOx3WaSk7Afw3E1j3EaCtMi2P6gaMewHofG6zTtK+sO4FVOv047+n95qO2IBY2BMG3VZKidu4cSPGjRvH9HIiIlLWHMjFLd9uMk7LMnVAAh45v/5UJ8rBpeoit9a8oxG+ES61J9mWEpGjkiBQ0sANQfXeTP3lgaymjb02VA/XB9imHuyEMD/H6L0+mcpSYMMnwMo39YG3QUAUcPZjQN9rAY/mhajz98/HhowN6np8YDyu73E97A2Dbit90UpKSpheTkREysbDefi/rzagolp/sDUhqRVenpwEd0Ol8tpOHNGn20nQHSNBea66HukX6VJ7k20pETmCgtIq7M4oxJ5MU++1XC8qr1V1+yT8vDzQNdaQFq7vwe4aG4xAHycL06orgS1fA8tfMy+S5ukLDL0dGH4P4Nv8YVQ5ZTmYuXGm8faTQ56En+epx3+3NCd7N+0nJW7UqFFMLyciIqw+kIP/+2ojSiv1Y/PGdIvGm1NrTQ3WSC+3yI3qDOTqg+4IP9fq6WZbSkT2pLxKg/1ZxWY913syCpFZWNGk/y+/+e0jA1SA3S0mCF3kMjYIrcP8Gz4B6yy0Gn1F8mUvAScO17rDDUi6HBjzxEmnADuVV9e/isLKQnV9QocJGB4/HPaIQbeVUuJWr16NCy+8kOnlREQubNmeLMz4ZpOxh3tklyh8MK1fveqxZg78a7yaGxxr6Oh2yfRytqVEZIuq4UdyS2oF1vo/GYttqMdxKnEhviq4NgTWXWOC0TE6AD6eDjj2+nRptcCehcDSl4Csneb3dbsQOPtxIKb7Gb3E0tSl+PPwn8YZPh4c8CDsFYNuIiIiK/g7JQN3fLfFOH5vbGI03p/W7+QHXdIjcHC5/rpvCHK9ao3pdrGebiIiaw9hySqqMCtoJoH2vqwilFc1bdx1iJ+XCq67xgTpe7Bjg9A5Jkgtd1kSbO9aoE8jz0oxv6/DaGDMU0BC/zN+mdyyXDyz5hnjbQm47bmdZNBtjZ3q6Ylhw4apSyIicj3fr0/F4/O2G3tFLugVi7cu73vyHm5xfAtQrp9jFO1HIa/CVGTG1Xq62ZYSkaUUlldhX52eaxl3nV9aq2r2Schvd+foQGNgLWOuJdCOCXaQablagpw0TpkH/PcakL3b/L6EgcCYJ4EOoyx2wkQC7rzyPHV7dOvRuLjjxbBnjAqtoKqqCsuXL8fEiRPh4+NjjZcgIiI7JAcCby7Zh3f+2WdcNrFPHGZe1huetab/atTuhabrnc9FbuY/xpvhfuFwJWxLiai5Kqu1OJBdbAyqDQH2sfyyJv1/iZ/bRQQYe64Nf7Ks0Tocrk5TDez4WR9s5+43vy9+ADDqIaDzOP3OtRCpVr4sbZm6Hu4bjmeGPmP3Jz8YdFuBvOkBAQF2/+YTEZFl5199fN4OzNmYZlx204j2eHR8YtOL5Oz5o+aKG9DlfOQe+VHdCvIKgo+Ha53EZVtKRI3RanU4eqJMVQ2vPfb6UE4Jqps48Do6yMfYcy1zXXeLDUan6ED4ebvQuOszoakCkufo59o+ccj8vtZD9MF2xzEWDbZFamEq/rf+fzB4eujTdp1WbsCg2xo71dMTAwYMYHo5EZGLKCirwh3fbcaKfTnGZU9MSMT/jejQ9CfJPWBKyWs9CAiMVmPWhCMcUFga21IiEjnFFdh1vACbD2TiWEkm9mQWq1Rxw4wQpyJTb3U1BtY1vdcxQQgLMNXMoGaoKAI2fQWs/QAoPGZ+X7sR+mBbLq3Q+VihqcD9y+9HaXWpuj2p0ySMaTMGjoBBt5VS4hYvXoypU6cyvZyIyMkdzC5WU4IdzClRt7093PH61N64qHdc857I2MsNoOsFKK0qRXFVscsG3WxLiVxLSUU19mVJanihsaiZ9F7nFFc26f97ebihY5R+3HXtHuz4UD9mn1pCUSaw/iNgw6dAeUH9AmkjJdi27nRdr214Dbvz9Cen2wW3w8ODHoajYNBtpZS4mJgYfsGJiJzcf3uzVQ93YXm1uh0e4I1Z0/phcIfTCJJ31wq6u01ARmmG8WZsQCxcDdtSIudUpdHicE6JqahZTXCdmqfvvWyK1uF+ahouFVjXBNgyB7ZXU2pnUPPk7AfWvAts/R7Q1JmTvMt44Kx7gTaDrb5XFx1ahDl75qjrMtxq5qiZCPAKgKNg0G2NnerpiaSkJKaXExE5ccG0z1Yewkt/7DJWKJd0xU+vG4DW4f7Nf8LiLCBtrf56RCcgsjMyj68x3h3r73pBN9tSIsf/nTxeUI69NdNxGXqwD2aXGKdSPJWIAG99anh0IFoFAAM7x6nK4QE+DGGs7uhGYNVbwK7f5d00LXf3ApIuB4bdCUR3s/56ADhccBhPr37aePvRQY+ia3hXOBJ+Yq2gsrISCxcuxLRp0+Dr62uNlyAiIhspKq/Cw3OT8cd2U0/02MQYvHVFHzV28LSkzAd0NQehifppTzJKTM8fExADV8O2lMhxFJRWqaJmtSuGy/WimiygU/Hz8lA91l1jJD28pgc7JghRQfoCklqtFllZWYiODoW7O3uzrVqJfM9CYO0sINV04lfxDgIG3AAMuRUIbubwqTNQVFmEu5beZRzHfWGHCzG582Q4GgbdVuDh4YEOHTqoSyIich7SS3P7d1tUhVyD28/uiPvP7dr0CuUNkelWDHpdqi4ySzNduqebbSmR/Smv0mC/GnetD6rV2OuMImQUljfp/8u0W5IGrsZcx5hSw1uH+Z/ZbyidEbeKAmD1D/rx2gWmGTiUwFh9oC0Bt29Ii+5pjVaDR1Y8gkMF+uronUI74ckhTzrkEF4G3VY6UEhMTGTQTUTkRP7YmYtXl6aivErfIx3k64k3pvbBud3PsBc6PxVIW6e/HpUIxPSo19PtimO62ZYS2Y5Gq1NjrCUlfE9GMfZk6lPDZSx2E2fkQlyIrz41vCawljHYHaMD4OPJTim7kb0XbutmIWrr93CvrjOXeWRXfQp50lTA0zZTVr675V38d/Q/dT3EJwTvnP0O/L1OYwiXHWDQbaWUuHnz5uGGG25gejkRkROkkz85fwfmbz1uXNYjLhizpvVHmwgLNP475tbr5Ra1C6m5ano521Ii64+7zi6uMKaEG6qGy5/hBOOpBPt6qjmuDVXDDdNzhfh58e2zR1otcOAffQr5gX8gfcZm/cadx+l7tjucbZVpv5rqz0N/4rMdn6nrHm4eqnBa6+DWcFQMuq10dl4KqTG9nIjIsW06cgL3zNmCtDxTD8CVg1rj6Yt6wNfLQr0122sF3T2nGK9mlujTy73dvRHmEwZXw7aUyLKKK6pVYG2YikuNwc4owonSqib9f29Pd3SODlRFI03TcgUjJtjHIdN9XY5M87VtDrD+YyB3n9ldWk9/uPWdBrfBtwCRnWBrW7O24slVTxpvPzjwQQxpNQSOjEG3lQ4UOnbsyKCbiMhBVWu0eH/pAbzz7z6VZikCvN3xwsRemNQvwXIvlJkCZG7XX48fAIS3rxd0Sy+3Kx7Qsi0lOrPU8F3phTV/+gD76Ik66cONkJ+btuH+NYG1qahZuwh/eHJKLseTsR3Y8BmQ/CNQZapHooS2gXbgzchOOA9RrTvBzQ6K1B0uOIw7/70TFTXTk03qNAlXdbsKjo5Bt5VS4n788UfcfPPNTC8nInIwUiTtgZ+2qV5ug/5tQvH4OQno09nCFVs3f2O6LlOw1CipKkFRVZHLjucWbEuJTq2wvAq7a4JqQ4AtvddlVZom7T6pDm4IqvU910HoHB0EP2+Ou3Zo1RXAzgX6wmiGmiG1tRsBSK921/EquVyXlQV7kFuWi1uX3Ir8inx1W3q3HbVwWl0Muq2xUz09MXToUM7TTUTkQLRaHb5cfRiv/rXbOJZRiunedU5n3DaqA/Jycyz7glXlQPIP+uuevkDSZca7zIqouWDlcsG2lOjkvddyeSy/ab3XAd4etQqaGYqbBSM8wJu72ZmcOAxs/ALY8g1Qmmt+n3eg/uTuwBuNBTuNY7ztQGlVqerhPlp8VN3uHNYZb4x+A14ezlEbgEG3Fcj8ga1bt+Y8gkREDuJIbgke/DkZ6w/lGZe1CffHG1N7Y0C7cDVHrMXt/h0oO2Gam9vPNG47rcg0ZUtCkAXT2R0I21JyVWfae902wl8F14mtJDU8GN1bBSMhzI9Tcjnz3Nr7lwAbPwP2LZbyeOb3R3fXB9oScPsEwR5Vaavw4H8PYnuOfrhVtH80PjjnAwTJ3OBOgkG3FVRUVODbb7/F7bffDj8/P2u8BBERWaj36Nu1R/C/P3ebHdBeP6wdHjq/K/y9rdhMbv7adL3ftWZ3MehmW0rOzxK9191UYK0PsOVPUsQDfXh47xJOHAG2fKv/KzLNrqG4ewHdLwEG/h/QZohNq5A3ZS7ux1Y8ZpwaLNArUAXczja0it9KK/Dy8sLYsWPVJRER2aedxwvx2Lzt2JqmHzsmpDfotUt7Y2jHCOu+eN4h4NBy/fXwDkC7s8zuPlqkT68TrYMcd4qUM8G2lJxJWaVG9VynHNf/SXDN3mtqtupKYM8fwOavgANL6/dqh7QG+l+vP5EbGO0QU9Y9v/Z5LDq8SN328fDBO2PeQdfwrnA2DLqtlBIXGxvL9HIiIjtUWlmNt5bsw2crDxkrk4trhrTFI+O7IaAleok2fWm63veaer0QZj3dga6bXs62lBxRfmkldmcU1wTYBeryQHYxav3cNIq919SgnH36QHvr90Bpnfoibu5A5/OA/tfp59h2d4wieDqdDq9vfB1z9+mnzfR081RjuAfGDoQzYtBtpfTyzz//HPfeey/Ty4mI7Mg/uzLx1IIUs/TNjlEBeHFSLwzpYOXebYPKUlPQLSmAfabVe4ihkIyvhy8i/SLhitiWkiMEDRmF5Ug5ZujBLkBy2glkFFU26f9z7DWdsq3Y9Suw6SsgdXX9+0PbAv2u0bchwRaeWaMFfLjtQ3y18yt13Q1ueGnESxiZMBLOikG3lVLiJk6cyPRyIiI7kVlYjmd/S8Ef201Vwb093XHn2Z1w86gO8PFswZ6B5DlAeU1Ke88pQFCM2d1anRbHio4Zi6g5w1Qpp4NtKdnb7AaHckuMwbUMT5HreSWnDrC9PNzUNFw94oL1f/Ehavw1x15Tg9KT9TU/ZF7tigLz++REbeKFQL/rgPajJCXIIXfiB1s/wKxts4y3nxz6JMa3l+nLnBeDbiulxIWHhzO9nIjIxsqrNPh81SG8/+9+lFSaCqUN7xSBFyb2QvvIgJZdIZ0OWPeR6faQW+o9JKs0C5XaSpdOLRdsS8lWqjRa7M0swo5jBWZjsEtr/YY0xt/LHYlxIeipAuwQdI8LVnNgy0k+okYVZwPbfwK2fgdk6it4m4nsqh+n3ftKIKCFsrKslB3ywbYPVC+3wYMDHsRlXUxTZjorBt1WSon76KOP8NBDDzG9nIjIBqRhX7wzEy8s3KWqAxtEBHjjyQu745I+cbbpQT64DMjepb/eeggQ17feQ1i5XI9tKbWEao0W+7OLkXy0ANvl71gBdqYXorL61NMEyu9J95rgWnqwE1sFwV9TjNiYGHa8UBM+fJXAvr/1gfa+vwBttfn9nn5Az8n6YLv1YLuuQN7Udvn9re/jo+SPzALua3uYz97hrBh0W4G3tzemTZumLomIqGVJReDnf9+JlftNxWbc3YArB7XBg+d1Rai/DX+b13140l7uupXLXXWObsG2lCxNCidKQTNDcJ18NF8F2OVVpw6wZWaDHrUCbLmMCfYxO3mn1WqRlVXCN45Onu2UkawPtKVnuzS3/mPiBwB9rgR6XQb4hjjF3tTpdHh3y7v4ZPsnxmUPD3wYV3e/Gq6CQbeVMOAmImr5isFvLt6Lb9elmlUlH9IhHE9f1EONobSp7D3A3r/014MTgG4XNfiwQwWHjNfbBreFK2NbSmcyBvtgTgm2H8tXvdiGVPGmpIjLsJNe8SHqr0d8MHq0CkGIP6eBpTNQnKUfo73teyBzR/37g1oBSZcDfa4CopxruiypU/LK+lfw3e7vjMseGfQIpiXWLyLqzBh0W0FlZSW++OILppcTEbWAimoNvllzBO8t3Y/80iqznqknJiTivB6x9lGMbOWbpjlVB88APDxPGXR3COkAV8W2lJpbLHFLaj62Hc3H1tR81ZNdXFEnXbeRCuI940OQJEF2gvRihyDEjwE2WSh9fO+imvTxvwFdnRM+Hj76omgSaHc422Gm+mqOam01nl79NH498Ktx2aODHsVViVfB1TDottKZ+RtuuIFn6ImIrEh6sxdsPYbX/95rNgWYn5cH7hjTCTee1R6+XnZyEHPisL6XQ/iGAgOmN/rQgwUH1aWfpx9iA2LhqtiWUmNKK6tVivjWtHzjX3pB+Sl3mJyIS0qQHuxQ1YvdMz7YtsNNyDnTx9O36ufTlvTxsrz6j0kYpE8f7zEZ8AuFs6rQVOCh5Q/h37R/1W13N3c8O+xZTOw0Ea6IQbcVz9ATEZF1xoYt25uNV/7cjd0ZRcbl0pk9sU88Hj6/G2JDfO1r169629TLMeRWwCew0YMUwxzd7YLbqYMUV8a2lOTk2v6sYmxNO6GCa+nNlsritUaQNKhViK8KsJMS9AG2/IUFMMAmK55YlSBbTq7m7K1/f1Ac0PsKfa92ZGenfxtKq0px1793YV3GOnXby90Lr418Dee0PQeuikG3lQ4SZs+ezfRyIiIL25aWj5f/3IW1B817D0Z1icJD53dVqaF2pzAd2PKt/rp3IDDo5kYfmlqYqsa/ifYh7eHK2Ja6Jpn3evORE9iUekKliUuxs9rT/TUkwNtDBdd92oSiT2v9X0ywnZ14I+dTmgek/AIk/wSkra1/v6cvkHiRfpqvDqOdMn28Idml2bj9n9uxK2+XMWvr7bPfxtC4oXBlDLqtwMfHBzNmzFCXRER05vZlFuGtJfuwcHu62XLpyXrk/G4Y1inSfnfzmvcATU3208AbAf/wU6aWu/p4bsG21DWyVqSa+KYjJ7DxsD7QPph98urfMhNB19hg9GkdUhNgh6FTdCA85A4ia6sqA/b8qe/R3r+4/jRfou1wIGkq0GOS01Qfb6oD+Qdw25LbcLzkuLod7B2MD8Z+gN5RveHqGHRbgUwZkZeXh8jISM7TSER0BiSt9J1/9uG35ONqqFzt4kcy/deEXq3so0haY4oygY2fm3o9ht5x0oebBd2hrh10sy11PmWVGtVzvfHICWNvdu3ihw2JC/FF75rea/mTYmf+3jx8pRak1QCH/tOnj+/8Fag0DWsyikrUB9q9LgVC27jk27MhYwPuXno3imr2T6uAVpg1dhY6hna09arZBf5qWUFVVRXmz5+Pe++9F56e3MVERM11MLsY7/67XxVKqz12MzLQG3ef0xlXDGoDLw8HGO/832tAVan+ev/rgcDokz68duXy9sGunV7OttTxZRWWqwDb0IudcqwA1ScZjO3l4aYqifdvE4YB7cLQt00Y08TJtvNpS4/29p+B4oyGp/mSIFum+orpqS8s4qIWHlyIJ1c9iSqt/iRaYngi3j/nfUT5R9l61ewGI0IrpcRNnz6d6eVERM10OKcE7/y7D/O3mAfb4QHemDGyA64Z2tZxermksM6mL/XXvQKAEfef8r8Ygm4PNw+Xn6ObbanjOZ5fhnWHcrHuYB7WHszF4dyaE06NCPP3Qv+24ejfVh9kS7Ezu5lxgFzTiSP6Hm35y95d/36fYCDxYn2vdruzXGac9smGiHy24zO8vflt47IR8SMwc9RM+Hv523Td7I2DHLk4XkpcRkYG08uJiJroSG4J3vt3P37ZckxVK659UH7zyI64dmhbBPg4WJO19GWg5qy/qlh+il5umc/UEHS3DmoNLw/XniuYban9S8srxbpD+gBbgu20PNPUfQ2RsdfSi92/XZgKtDtEBtj38BByDSW5wK4F+l7t1DX173f3Ajqfqw+0u5wPePnZYi3tTqWmEs+vfR7z9883Lru0y6V4fPDj8HR3sPa6BXCPWCklbsmSJejatSvTy4mITmJXeiFmLTuA35OPm/Vsh/hJsN0B1w1rh0BHC7ZF1i4geY5pXu5hd57yvxwpPKKmDBNdwrrA1bEttb8erVQJsmt6sSXYPpZfdtJUcRmDPaBdOAa0DUO/NmGcsovsR9kJYNfv+urjB5ebpnSsrc1QoNdl+oJoJymA6YpyynJwz9J7sC17m3HZ3f3uxo09b+SJtEY44JGMY6TEXX311UwvJyJqxMbDefhg2QH8uzvLbHmwryduGtEB1w9vhyBfB+7p/fcFCVP018+6F/ALPeV/2ZO3x3i9a3hXuDq2pfaRLr5qf476k2n6MgrLG32st6c7+rYOxeAOERjSPlyNx/bzdu3UW7Iz5YXAnj+AHb8AB/41ZSLVFtlFP0Zbgu2wtrZYS7u3M3enmoM7szRT3fb18MXzw5/H+e3Pt/Wq2TUG3VZKiUtLS2N6ORFRnZ6y5Xuz8cHSA1h/2HyebRmzfeNZ7dWY7WBHDrbFkdXA7t/11wNjTzovd217TtQKusMYdLMtbXkFZVWqF1uC7JX7c046fZePp7tKER/cPgKDO4SrXm2Oxya7U1min+IrZR6wbzFQk01kJqQN0GMi0HMK0Kq3SxdEO5VFhxapgmnlGv0JuBj/GLwz5h10j+hu61Wzewy6raC6uhpr1qxBr169mF5ORC5Pxmj/uSNdpZGnHC802x/xoX64aUR7XD6wjXP0isnUMn8+bLo9+hHA27/5QTd7utmWtoCKag02H8k3BtkynVdjxcX9vDxUsbPB7cNVb3ZSQgh8PJ3gO0vOOZf2vr/1Pdp7/wKqyxquPC5p4z0mAwkDGGifglanxXtb3sMn2z8xLusT1Qdvnv0mIv0iLf4WOiMG3Vbg7e2NqVOnqksiIldVUlGNX7Ycx+erDuFInSrGHaMCcOvoTrikT5xjTP3VVFtn66eZETG9gH7XNvm/7s3bqy6DvYNV74GrY1tqHUdPlOK3bdnYnJ6GNQdzUVrZwFhWqaDv7qbSxYd3isRZnSPROyFUpZAT2aXqCmD/P/ox2tKzXVlc/zEB0UD3S4Cek4HWQwB3fp6boqCiAI+vfBzLjy43LpvUaRKeGPIEvD0Y6zQVg24r0Gg0OHDgACIiIuDOLzQRuZj0gjJ8uPIoFuzYhsLyarP7pHfsttEdMa57LNzd3ZxvvOA/z5lun/9yk6eTySvPQ3ZZtrGXmxWd2ZZa7GNZpcH6Q3lqaMeyPVk4cJKU8S4xgfogu1MkBrUPd+y6CuT8NFXAwWX6Hu3dC4GKgvqP8QsHul+s79HmFF+nNX77vmX34VjxMXXb3c0dDw18CFd1u4rtVDMx6LZS0J2cnIz+/fvDy4sNFhG5hh3HCvDZykP4bdtxVNfJUZWD+BmjOqhLpw0oV8wESvSBs5rHtf2IJv9XsyJqHM+tsC09sxNfS3ZlYenuLKw5kIuyqoZ7syMDvTGycxRGdInEsI6RiAn2PYNXJWoB2mrg0Er9GO1dv+mrkNflGwIkXqRPH28/CnDx6RdPtwbL3H1z8fK6l1GprVTLQn1C8erIVzE0bqitV88hMei2UkrcpEmTmF5ORE5Pq9WpCuSfrjyoqhvX5u3hhkv6xGP6We2R2CoYTi33ALB2lv66hw8w7vlm/ffaQTenC9NjW9q8A+Sd6YVYsjMLi3dlYMcx89oJBpJcIlXF+8f5YUK/dugVH+p8GSfkfKRWxuFVCN44G26HlwClOfUf4x0EdJugTx3vcDbgybTn01VWXYYX1r6AXw/8alyWFJmE10e/jtiA2NN+XlfHoNtKZ+d37drF9HIiclpF5VWYu+kovl5zBAdzzNNVw/y9MLFnBG45pztiQvzg9HQ64M+HAI2+NwBDbwfC2jXrKVJyU4zXEyMSLb2GDolt6clVVmux7lAuluzMVL3ajc2ZHRXkg1FdojC6axRGdIpCkK8HsrKyEB0dwoCb7JdWCxxdr08d37kA7sUZqFeS0isA6Hq+PnW801jAi5kaZyq1MBX3LrsXe0/oa4wISSV/YMAD8GLGgPME3S+//DJ++eUX7N69G35+fhg2bBheeeUVdO3a+NQpy5Ytw9lnn11vuQS93bp1g60OFA4ePIihQ4cyvZyInMrezCJ8veYw5m0+hpI6BZg6RAWoab8m9o5DUX6uOth3CVK4Z/8SU0XcEfc1+ym252w3znfaKbSTpdfQIbEtbXh89op9Ofhje7oKtosqzGsmGPSMD8bYxBj1171VsFlwLVOxEdntCcxjm/W/qSnzgcKj9R/i6Qu3zuP0Pdqdz2vy7BB0an8f+RvPrnkWxVX6InR+nn54dtizGN9+PHefswXdy5cvx+23346BAweqqUIef/xxjBs3Djt37kRAQMBJ/++ePXsQHGxKX4yKioItU+ImTJjA9HIicgrVGi0W78xUvdpS7biuoR0icNPI9hjdJVod3MtBfRFcRFk+8OcjptsXvAb4BDXrKaSImqFIjcx16uluV02zzbAtNQXaUgRNAu1/dmWhuIFA28vDDUM7RuLcxGickxiDuFAXyDAh5wm0ZcYH6dGWcdr5R+o/xsMbuo7noKD1OQgeMBVufiG2WFOnTid/Y8cb+PPYn8Zl7UPa483Rb6JjaEebrpszsauWfdGiRWa3v/jiC0RHR2PTpk0YOXLkSf+vPC40NBT2QE4YSCG10aNHM/AmIoeVU1yBH9anYva6VKQXlJvd5+/tgcn94nHt0HboEtO8INOp/PMsUJKlv971AqDbhc1+ipQcU2p5j8gellw7h+bKbanMn710tyHQzqyXVSKCfDxxTmI0zu0ei5FdIllpnBxL5k59j7YE23kH6t8vJx9lbLb0aHe9ADqfYJRnZSG4mSc16dT1RB767yEcLDhoXCY9208PfRoBkr5Pzhl011VQoC/9Hx4efsrH9u3bF+Xl5ejevTueeOKJBlPOW7KgSWZmprokInIk8ru16cgJFWgvTE5HpcY8FbVDZACuGdoWU/onINjVpxNKXQds/Fx/XQ5OpJf7NCqz78jZYbzeK7KXJdfQoblaWypFCTceOYF5W45hYfLxetPtiSBfTzXd3oSkWDW1l49n06akI7ILOftqerR/AbJ317/fzQNoP1IfaMsJTP9ax/8cFmFR8rv6w54fMHPDTGN1chne9PiQx3FJx0ucd5YRG/K05w/Dfffdh7POOgs9e/Zs9HGtWrXCxx9/rKbnqqiowDfffINzzjlHjfVuqHdcHiN/BoWF+gqfkg5pqXFOHh4eGDt2rLp0lrFTsh3ynjjL9jjzdjnjNjnrdtnTNuWXVmLeluP4YUMa9mXpx3MZSNt7TrdoXDOkLYZ3jDCOD21sve1puyyl3jZpquD2+90wHJZoz34cCIo7rQNDw3hu0SO8R4vttzN9HWu3p87YljbkQFYx5m89jgXbjuPoifrF0IJ9PXFu9xhc0CsWwztGwtvT3Xjf6ewXZ/x+2gvu2wbkHQJ2zoNbyjy4ZZpOMBro5Fe07XDoZHovmWoxILL2DuW+tYL8inw8s/oZLD261LisY1BHzBw9Ex1CO6jfB1c52WkJTf0ttdug+4477lBpZStXrjzp46TIWu1Ca1K8LC0tDTNnzmww6JZibc8++2y95dnZ2aqn3BKqqqqwdu1aDBkyxGkKqckHSjIP5Evo7m5q8B2dM26XM26Ts26XrbdJXnfb8WLM356Df/edQKXGvJEN9vXAJT0jMalXFOJCpCiaFjk5NfNQ2/F2WUPdbQrc8C4Cs3ap+6qieiC33UQgqybNvBnk+bZn64PuYK9geJV6Iaus+c9zOoqKzmzkvbXbU2dsSw2KKzT4a3cefkvJwe6s0nr3+3q6Y3SnUIzrGo6BbYLg5aH/HuXnNTBVUjM54/fTXnDf6rkXHYPvgT/hd+APeGWbhs/UVhnbD+UdL0B5h/OgDYjWLyzRmobrcN9axZbcLXh1+6vIqTD9lkxsMxGXRV8G/3J/NbMBWacttcug+84778Svv/6K//77DwkJCc3+/9JAf/vttw3e9+ijj6oe9Npn5lu3bq0Kr9UuxHYm5My/VF2NjIyEj4+P0zQkkmoi+8mZGmln3C5n3CZn3S5bbdOJ0kr8svmY6tU+kG0+3ZcY0DYMVw5qjfE9Y+Hr1fz0Vad/rzK3w23Lh2q5zs0DHhPfR3Rsq9N6Ximgll+Zr673iuqFmJgYtBRf3zObXsfa7amztaVq6EZqPuZsSMPC7ekorzLvHZEEkhGdI3FJnzicmxiDAB/rHKI54/fTXrj0vi08rqb2Uj3axzY0+BBdXH99j3b3S+AZkoBAQP01hUvvWwsory7Hu1vexbe7TfFRqE8onhv2HEbEjVAnS7lvrduWetpbgyQB97x581R6ePv27U/rebZs2aLSzhsiDXdDjbd8gS31JZbnl8IvculMPwzyY2fJ/WQvnHG7nHGbnHW7Wmqb5Pd17cE8/LAhFX9uz6g3VjvU3wtT+iXgioGt0dkChdGc9r3SVsF9/q2AVj/e1m3kA3CL73vaz7kj15Ru2TOyZ4vurzN9LWu3p87SluaVyEmuo+ok1/46QzdEr/gQTOobjwt7t0J0UMvMM+yM30974VL7tjhLBdpqnHbqGpUsXk9skn6Mdo9JcAtrZxySczpcat9aUEpuCh5b8ZhZsbTBsYPx0oiXEO0fbTyhwX17epr6ebSroFumC/vuu++wYMECBAUFISMjQy0PCQlR83YbzqwfO3YMX3/9tbr91ltvoV27dujRowcqKytVD/fcuXPVny0rrq5evRoXXnihy1VcJSL7ciy/DHM3HcXPm44iNa9+Guvg9uG4anAbnNfj9Hq1XY3bspeB7F2mg8kRD5zR823K3GS83i+635munlNx9LZ05/FCfLn6kBqvXVmtrTdOWwLtywe2Qfc4y2TZEbWIklxg16/6YmiHVwK6BsazRvdQQbYKtiM45ZStVGur8en2T/HRto9QrdOfKPZ298Y9/e/BtMRpcHfjyYuWZFdB96xZs9SlnNmuO3XY9ddfr66np6cjNTXVeJ8E2g888IAKxCUwl+B74cKFuOCCC1p47YmI7Gde30U7MlSgvepAjpoGtbYwfy9c2j9BHfB3im5qch95ZWwB1ryr3xHuXsCkDwHPMwsGt2Rt0T+dmzuSopK4k51gTvsluzLxxarDWHcor979g9qH1wzdaMWTXOQ4yk4Auxfqe7QPLgN09aewQ2QXoIe+RxvR3WyxllTL4YLDeHzl40jOSTYuSwxPxMsjXubc2zZiV0F3Uyrlffnll2a3H3roIfVnTzw9PTFs2DB1SUTUUr+fW9Ly8dPGo/h923EUVVTXq0B+VqdIFWyf3zOWUw01V1UpQpY+AjdDr87ZjwIxZzandmFlIfad2Keudw3rikBvngBx1La0pKIa361LxZerD6vskrrTfE0d0FpllHSM4ntMDqK8ENjzp75He/8/gLaq/mPC2tekjk/W/x5ymimb0+q0+HHPj3hj0xsoqy4zntT9v17/h1uSboGXh3MVpXQk9t+SOSCpuLp8+XJMnDjRKYq/EJH9yiosxy9bjuGnjQ0XRWsb4Y9L+yVgcv8ExIfqh+lQ87n9/Tg8Cw7rb8QPAIbdfca7cWvWVuhqxkD2i2FquSO2pSdKKlWgLX8FZeZBSceoAFw/vD0m9423WlE0IouqLKkJtOcB+xYDGtOUgEYhbYAeE/XBdqs+DLTtSFphGp5a/RQ2Zm40LmsT1EaN3e4d1dum60YMuq1CihEEBARwYnkisorSymos3pmJeVuOYcW+HGi05llC/t4emNCrlerVlnRW+U2iMyDVeDfps6x0Xv5wk7RyjzMPojZnbjZe7xt9+sXYnJU9t6UZBeX4dMVBfLc+FaWV5qm2Y7pF4/ph7VRmiWFOeyK7VVUG7Ptbnzq+9y+gpnfUTFCcPtCWHu2EAQy07YxGq8F3u7/DO5vfQbnGNF3j5V0vx33974O/l79N14/0eOrVCiQVbsCAAQ6REkdEjjNWdPWBXMzfcgyLUjLqHegLCbAv65+AC3q1Ys+apZw4Avxq6tXWnf8/uEV2tshTG8ZzCxZRc4y2NKe4Au8v3Y/Za1PNZgDwcHdTU33dOqqjRar/E1lVdYU+ZVxSx6Vnu7J+VX3I3NndLwF6TgFaD5YSzXxT7NChgkN4atVT2Jq91bgsPjAezwx7BkNaDbHpupE5+2nJnCwlbvHixZg6dardpsQRkWOM0045Xqh6tH/ddhzZRfVT/SRlfHK/eNWr3TYiwCbr6bQ0VcDc/wMqCtTNsk4T4NPnaos8dYWmAttztqvrrYNaI8o/yiLP60zsqS0tLK/CJ/8dxGcrD5md8PLxdFfT7N00sgMSwtibRHb+eyZF0KRHW4qi1fyumfGPABIv1qeOtx0OuHNGC3uuTP71zq/x/pb3UamtNC6/stuVuKffPezdtkMMuq1AUuFiYmLsMiWOiOzf0ROlWLD1uAq2G5rXV6YbmpAUp6YcGtA2jCms1iLTgx1dr67qQtuicMSziLLQ7/qOnB2oqilMxF5u+21LK6o1+HLVYXyw7IDZmG1fL3dcN6wd/u+sDogK4sl1slOaauDISmDHXGDXb/oq5HX5hgCJF+lTx9uPBFhoy+5JAU7p3d6Ru8Ns7Pazw57FgNgBNl03ahyDbiuQVLikpCS7SokjIvuWW1yBP3dkqB7t9Q1MNeTt4Y6zu0WpQPvsbtGsPm5tB5cDK97QX3f3hG7KZ9B5WS5teH26PpgX/WP6W+x5nYkt21LJMvlnVxaeX7gTR3JN89t7ebjhykFtcMfZnRAd7Nvi60V0SlotkLZW36O9cz5Qkl3/Md5BQLcJ+h7tDmef8dSH1DLKq8vxUfJH+HLHl8Z5t93ghmu6X4M7+t4BP08WS7VnjAqtQOYOl7nCp02bBl9fNspE1DDpOfstJQf/LTyixmvXLYgmBrULx8S+8bigVyxC/Xlg1CIKjgFzb5TQS397zJNAfH8gK8tiL7E2fa3xOsfd2VdbKtklz/2+E//tNQUr0tkuJ7zuHdsFrcOZRk52RqbcPbZZP0Zbgu2i4/Uf4xUAdD1f36PdaSzgxeNTRyJtxnNrnkNaUZpxWfuQ9nhu2HPoE93HputGTcOg2wo8PDzQoUMHdUlEVFtxhVQez8Dv29Lx375sVGnqB9oy1dDkfgm4uHccD/BtUWDop+tMvUMdzwGG3WXRlyitKkVydrK63ja4LVoFtrLo8zuLlm5Ly6s0ePffffho+UFU1zoBNrh9OJ65uAcSWwW3yHoQNTnQztyhD7IlfTz/SP3HePgAXcbpi6F1Pg/w5gkjR5NXnoeZG2bit4O/GZd5unvixp434qakm+Aj7zE5BAbdViAHCImJiQy6iUgpq9Tg391Z+G3bcSzdk4WKalPVY4OEMD9cmBSHC5NaoUdcMGtC2MqiR4GjG/TXQ9sAUz7VV+2VlE0LkTlUDamB7OW2j7Z005ETeOjnbWZz3ceF+OKxCYlq+j3WaCG7kb23pkd7LpCzt/797l5Ap3P0PdpdxwO+PFnkiGSIy4IDC/D6xteRX5FvXC41QJ4a+hQ6hna06fpR8zHotlJK3Lx583DDDTcwvZzIRUkBpuV7svFbcjr+2ZXZ4BRfMcE+OLtjCKYO6Yi+bcJ4YG9rW78DNn6mv+7pC0z9BvAPt/jLMLXcftpSOSH22l978MXqQ6rj0DBu+5ZRHXHb6E7w82bGGtmBE4drerR/ATL1sx6YcXMH2o/Sj9HudqFVfreo5RwuOIzn1z6P9Rmm2h9B3kFqzu3JnSfDXd5vcjgMuq1AzspL8RemlxO5XqC9an8OFiZn4O+UDBRV6Hsza4sM9Mb4nq1wUe849GsdgpycbERHhzLgtrX0bcDv95puT3gDiLPOODlD0C0FcAbGDrTKazgDa7eluzMKccd3W8xmCOidEIJXL+2NrrGca5vsoLZEyjx9r/axTQ08wA1oOwzoMUk/n3ZgtA1WkiypUlOJL3Z8gY+TPzabBmx8u/F4aNBDiPSL5A53YAy6rUAOEDp27Migm8gFSE/Zsj1ZqvK4pJDLmO26Qvy8ML5nrAq0ZXyop4f+LLXWginLdAZK84A5VwPV5frbA6YDfadZZZfmlOWo6V5Ej4geCPEJscrrOANrtaWStjl7XSqe/32ncaiHzLd9/7gumD68vfH7SdTiirOAnQv0Pdqpqxt+TPwAfY9294lASHxLryFZyapjq/Dy+pdxpNA0Nj8+MB6PD34cIxJGcL87AQbdVkqJ+/HHH3HzzTczvZzICRWVV6kA+8/tGVi2NwvlVfWD50AfT4zrEYOLkuIwvFMkvD15IG+XqiuBH68F8lNNB7Tn/89qL1d7qrAhcUOs9jrOwBptaUlFNR76ORkLt6cbl0mBtHev7ItO0YEWeQ2iZp/0kzm0pUf70H+AroGTsbG99GO0JdgOa8cd7ETSi9Px6oZXsSR1iXGZh5sHru1+LW7pfQv8vVj8zlkw6LbGTvX0xNChQzlPN5ETOVFSicW7MrFoRwZW7stBpab+gVGwryfGdo/B+T1iMbJLFHy9OB7Urskg3j/uBw6v0N8OiAamfg14Wq8a7Krjq4zXB7cabLXXcQaWbkuPnijF/321EbsziozLrhvaFo9ekMjvKrWsyhJgz5/A9p+A/f8A2qr6j4nsoq86LsF2VBe+Q06YSv71zq9VKnlZdZlZobTHBj+GruFdbbp+ZHkMuq3A3d0drVu3VpdE5Liyisrxd4o+0F5zsOF5tCMCvFWP9vk9W2Fohwj2aDuSNe8Dm7/WX5dpV674zqrpmlqdFiuPrVTX/Tz91MEVtUxbuvFwHmZ8swm5JfpxkkE+npg5tTfO6xHLt4BahqYKOLhMH2jv+h2oMlXKN5JebNWjPQWI6aGfIJ6czupjq1Uq+eHCw8Zl4b7heGDAA7iww4Ws8eKkGHRbQUVFBb799lvcfvvt8PPzs8ZLEJGVpOWVYvFOfaC94UiesaJx3arj0pstgfag9uHwcOeBkcORXqa/nzDdnvgB0Nq6Rc1SclLUnKuGqcK8Pbyt+nqOzlJtqXyX7/p+izE7pV2EPz69biDTycn6pAGRKQiTf9QXRSvNqf+YoFb6IFtSx+P6MdB2YhklGSqVfPGRxcZlUon8ym5X4rY+tyHYm9O7OTMG3Vbg5eWFsWPHqksism9SVGnHsUIs3pmBv3dmmqWe1p1HW4qhSaDdt3Uo3BloO66MHcDc/5N3X3971MNAr0ut/rL/HfvPeH1kwkirv56js0RbOnfTUTw0N9mYpTK8UwTev6ofQv15woOsKHu3fh5t6dXONxXGMvIN0Vcc7zVVX4HcnUORXDGVvE9UHzwx5AmmkrsIBt1WIKlwsbGxTC8nslOV1VqsPZirerSX7MpEekFN1eo6OkYFqOm9zu8Zix5xwUz5cpbqwN9fAVTWTBMl0+2MeqRFXvq/o6age0Q8q9Fauy39es1hPLUgxXh7cr94vDIlCV6sTk7WmuJr+0+I2PID3HN31b/f0xfocj7Q6zKg87lWrR1B9nNSf2naUszcOBNpRWlmqeQy5/ZFHS/inNsuhEG3lVLiPv/8c9x7771MLyeyEwVlVWpqLwm0l+/JbnAObcM8ved2j1FjPTvHcK5ep1JRBMy+FCioOfiRVM6JsyS6s/pLZ5dmY2fuTnW9W3g3xATEWP01Xbkt/XFDmlnALQXTnr6oBzNUyAqVx38Fkn8CjqyCO3Qw+zVxcwfajwKSpgLdLgR8mT7sKmRqyFc2vIJ16evMUskv73o57uh7B1PJXRCDbiuQVLiJEycyvZzIxo7ll2HJzkwVaEvPdnUDhdC8PdwxrFOECrTHJsYgJtgyUxORHU4NNucaIH2b/nZwAnDl94BXy9TdMBRQE+zltm5b+sf2dDzyS7Lx9m2jO+LB87oyU4Uso6oM2LtIH2jv+7vByuO6uP5wS7pMXxQtiCfYXEl+eT7e3/o+ftz7oyqeaTAwdiAeHvgwU8ldGINuK5BUuPDwcKaXE9kglSvluIzP1gfaO9MLG3xciJ8XxnSLVoG2TO0lc2qTE9NqgQW3AweX6m/7hgJXzwWCWq5yde3Uco7ntl5buuZALu7+YQsM59emD2/PgJss8xuSugbY9j2wcwFQ0UDbEtEJ2p6XIbfVaER0GQQ3zmDjUqq0Vfhxz4/4YOsHKKw0fT7iA+Nx/4D7MbbNWJ74c3E80rRSStxHH32Ehx56iOnlRFZWWlmt5s1euicL/+7OQmZhRaOF0CTIlr+B7cI5rtOVLHka2P6jaVzlVXOA6G4t9vLl1eXG+bnDfMLQK7JXi722K7WlMvPAbbM3oUqjj7gv65+AJyYk8kCXTl/uAWDbD0DyD0B+av37A2P1lcelV7tVH1WtXJOVxT3uglOASVXyAwUHjMtkWsibet2Ea3tcCx+ZkpJcHoNuK/D29sa0adPUJRFZXmpuKf7dnYl/92SrtHEpjNaQXvH68dny1y02iAffrmjNB8Dqd0zjK6d8BrQZ0qKrsPr4amPF2tGtR8ODlYot3paWVFTjpq834kSpPtV3VJcovDy5F8dw0+mN05bpvSTYPrq+gQ9mkL7yuATa7UaYVx5vaI5JclpHCo9g5oaZWHZ0mdnyiztejLv73Y1o/2ibrRvZHwbdVsKAm8hyqjRabDiUi4VbjmJd6m7szy5p8HE+nu4Y1jFCpY6P7R6DViEtM16X7NT2n4G/HjXdnvA6kHhhi6/GP6n/GK+PbTu2xV/fFdrSp39NMU731yEyAO9c2ReerFJOzan5sH+JPn1cxmtrKs3vlxN2Hc4G+lwFdL0A8PbnvnVhBRUF+CT5E8zePRvVWlNR1qSoJDVuWy6J6mLQbQWVlZX44osvmF5OdAZyiyuwbE82/t2Thf/2ZqOovOFq43Ehvji7W7QKtId1jISfN+c7JQB7FgHzZph2hczFPWC6Tcb5yZQxIsArAENatWwvuyu0pb8nH8fPm46q61Kf4eNrB6i6DUQnJb3Sx7foe7R3/AyU5tZ/THR3oPeV+mm+gltxh7q4Kk0V5uyZgw+TP1SBt0G0XzTuHXAvLmh/AacAo0Yx6LbSmfkbbriBvd1EzSyCJoXPlu7Owj+7s7A1Lb/BTD13N6BfmzAVaJ+TGI2uMUwbpzoOLgN+vBYw9ED0uw4YXavHuwVtSN+AosoiYwE1bw8OO7JkW5pRUI7HftluvP3cJT3QKTrwDN81cvr5tJPn6IPtnD317w+IAnpNBXpfAcT2AtzcbLGWZGfHJ0tSl+DNTW+azbft7e6N63tejxt73gh/L2Y/0Mkx6LbiGXoiOrn80kqs3J+j5s1evjcbWUUNF0GTXquRnSPRP84HFw3oiIhATutFjUhdC3x/JaCp+SxJkaML37TZgbMcqBlI9VqybFv67G8pKKzJgrmodxwm9Y3nLqb6qiuA3QuBLd8AByTzpM4ZXSl01W2Cvle74xjAg4fHpJecnYyZG2diS9YWs11yUYeLcGffO9EqkBkQ1DT8VbHSQcLs2bOZXk5Uh0arw/ZjBTVBtr43u4GpsxXpwTakjfdrE6p6uLOyshDmz55CaoSkis6+DKgqrfkQTQAmfWRe6KgFabQa/Jv6r7ou1WvPij/LJuvhrG2pZMX8uSNDXY8I8Mbzl/RgsUQyl54MbPlWP3tB2Yn6e6fNMH2PthRG8wvl3iMj6dF+Z/M7WHR4kdlekfm2ZQqwHhE9uLeoWRh0W4GPjw9mzJihLolcXVZROVbszVE92Sv2ZRurC9fl5+WBIR3CVZAtwXZCmHmqllbmSSVqTOZO4JtJpvlzpbfqsi8AD9uN7d2avRW55fpxosPjhjP90IJtqcxY8MxvKcbbj09IRChPyJGh+rgUUZRe7Yzk+vsktA3QZxqQdDkQ3p77jMzIWO2Pkz/Gd7u/MyuS1j6kPe7rfx9GJYziyT06LQy6rUCCg7y8PERGRsLd3d0aL0Fk15XGNx85oYJs+Us5XhMENaBLTKCa2mdUl2gMaBcGXy8WQaPTkLMf+PoSU0+W9F5dPhvwtO2Jzz8P/Wm8zqrllm1L52xIxZFcfUbD4PbhTCt3dVqNvpaD9Grv/r1+9XFPX31vdt+rgbZnATw2owaKpP2w5wd8uO1DFFaajlvCfcNxW+/bMKXLFHi6M2yi08dPjxVUVVVh/vz5uPfee+HpyV1Mzu9YfpkxZXz1/lwUVTRcaTzIxxNndY5UgfbILlGIC+WUXnSGcvYBX14IlGTpb8f1Ba6aY/MpfaRq+V+H/zKmlo9pM8am6+NMbWlpZTXe/me/8fZjFySy58lV5R0Ctn6n/yvUV7A3E9cP6HcN0GMy08epQVqdFn8f/hvvbHnHrEia/G5f2/1aTO85HYHeLM5IZ44RoRVIKtz06dOZXk5Oq7xKgw2H84wF0PZlFTf62F7xIfre7K5R6NM6FF6cO5csJXuPecAd0xO4+hfAN9jm+3jt8bXIr8hX10e3Hq2mCyPLtKU/bkhDTrG+UN74nrHo3ZpjcV1uTm3pzd70JXBoef37/SP0BdEkhTymuy3WkBzEmuNrVEXyXXm7zJZf3PFiVSQtNiDWZutGzodBt5VS4jIyMpheTk5Dq9Vhd0YRVu6Xcdk5WH8oDxXVDY+xDvP3Ur3Yo7tG4axOUYgKYm0DsoKsXcBXFwEl2frbMrXPNQsA/3C72N1/HPrDeF3mbiXLtKVSjPGL1YeNj7l7bGfuWleRdxDY9BWwdbbpe2/g5g50OlefPt7lfMCTBTepcSm5KXhr01tYm77WbPmg2EGqSFr3CJ6sIctj0G2llLglS5aga9euTC8nhyXz30rhM5nSa9X+HOQUNzx1j1QV79smrGZsdhR6xofAQxYSWUtmCvDVxUBpjv52q97ANfPtJuAuqy4zVi0P8g5i1XILtqX/7Mo0juU+q1MkusXaPquBrNyrvWehvldbxmzXFd4B6HuNvmc7mFM30cmlFqbi3S3v1qtI3jWsK+7tfy+GxQ3jUBWyGgbdViCpcFdffTXTy8mhlFRUY92hXNWTvXJfzklTxluF+KoD3tFdo9VliL/tKkSTi8nYrg+4y/JMY7ivmQf4hcFeLD+6HKXV+sDw3LbnwtuDvW6Waku/rNXLfeMIVp52WjJWe/NX+sJodXu13b2AxAuB/jcA7UawKBqdUk5ZjiqQNnfvXFTrTDVn4gPjVRr5+Pbj4S7ZEkRWxKDbSilxaWlpTC8nh5gze4VM5bU/B1tST6BK0/Ck2QHeHhjaMUIF2Gd1jkLHqACeDaaWd3wr8M1EU5Xy+P76Mdx2Nr/uHweZWm6NtlQKNq4+oJ+CrX1kAEZ1jrLI65Cd0FQBe/4ANn4BHFxa//6wdkD/64E+VwOBfO/p1Iori/FFyhf4Zuc3KgOpdkXym5NuxtQuU+Flw2klybUw6LaC6upqrFmzBr169WJ6OdmV1NxSrNifrXqy5eC1oKzhObMlO1yKE43oFIkRXVgAjezAkdXAd5eb5uFOGAhcPRfwDYE9yS/Px8pjK9X1KL8oDIgZYOtVcpq29Netx433TeobD3cOY3EOBceATV8Am78GijPN75MpmrpJr/b1QPtR7NWmJqnUVGLOnjn4JPkTnKg4Yaqx5+mP63pcp/5Y3JJaGoNuK/D29sbUqVPVJZEtFZRWYc3BHPxXkzKemqdPeW1Iuwh/NZ2XFD+TXu0QP579JTux92/gx2uA6nL97dZDgGk/2UWV8roWHlqopgsTkrLo4c655y3Vls7fcsx438Q+8RZ4t8hmdDrgyCpg/cfArt8BnaZ+r3a/6/SF0QKjbbWW5GA0Wo36DX5/y/s4XmI6SSfza0uvtvRuR/hF2HQdyXUx6LYCjUaDAwcOICIiwlhxlagllFVqsP5QDpZsP4qt6fuRcrwA2oYzxlVQPbyTpIxHYUTnSLQOt+28xkQN2v4zMG8GoK0Zh9fxHODybwBv+5yCa8H+BcbrkzpNsum6OFNbeiSvDHsyi9Tyvm1C0SaCv1cOqaIYSJ4DrP8EyDafpgluHkC3CcCAG4D2o9mrTc2aa/uf1H/wwdYPsD9/v9l9MnvEHX3vQOug1tyjZFMMuq10oJCcnIz+/fvDy4u9hWQ9VRottqXlY9X+XKw6cPJx2V4ebujXJkwF2CM6s8o4OYCNnwO/3yfdYvrb3ScCkz+x2+mAduftNs732iuyFzqFdbL1KjlNW7psT81c7ADGdefcuQ4nZz+w4VP9dF+GISIGAdH6QFtSyIPjbLWG5IB0Op0qXPn+1vfV729tw+OG4+5+dyMxItFm60dUG4NuK5BUuEmTJjG9nKwyX/bO9EKsPqAfky3zZZdW1knLq6VbbJBKFR/ZOQqD2ocjwIdfeXIQK94A/nnWdLvftcCFbwF2nK49f/984/WJnSbadF2crS1dtsdUwfrsbiyi5RC0WmD/YmDdR8CBf+rfL8NEBt0EJF5styfSyH6D7dXHV6tge3vOdrP7kiKTcFe/uzC41WCbrR9RQ3gEbqWz87t27WJ6OVmkYTmYU6IC7NX7c7DmYC7ySxsufibahPtjWMcI9Ij0xLg+7RET4sd3gRxvrOeSp4FVb5uWDbsLOPc5wM3Nrgv3/H7wd3Xdx8MH57c/39ar5DRtaWBIKNYezDVOV9g1JsjWq0YnU1kCbP0OWPchkGue6gtPX6DXZfpgu1Vv7kdqtvUZ6/HBtg+wJWuL2fLE8ESVRj4ifgRnVyG7xKDbSgcKBw8exNChQ5leTs2WXlCm0sVVb/b+XGQU1hSPakBUkA+Gd4zAsI6RqkdbxmXLNDtZWVnqPiKHUl0J/HqHfsynwTlPAWfdZ9cBt1iWtgwFFQXq+jltzkGwt/0VeXPUttQvIREV1Vq1TH7r3Oz8s+DSVcilMNqmL4HyfPP7QtvqA+0+0wD/cFutITkwCbLf2vAWtuZtNVveOawzbu9zO8a0HsPfBrJrDLqtQFLhJkyYwPRyapK8kkrVi7Nqvz5l/FBOSaOPDfb1xJAOERjeKVL1aHeKDmQjQ86hvACYcw1waHnNAjdgwkxg4P/BETC13Hpt6a97Tb+J/dra15zsBODYJmDNB8DO+aaChwbtRgBDbgO6nGfXQ0PIfm3P3q7SyFcdX2W2vH1Ie9zW5zaMazsO7m4sWkz2j0G3leYWleIvo0ePZuBN9ZRUVKux2IYgW8ZoN8bXyx0D24Wr3h2pNN4jLgQenJuWnE3hcWD2ZUDmDlMK6pRPgcSL4AiOFx83zs3dKqAVxxJauC3dkmkKtKUYJNkBrQbYvRBY+wGQusb8PncvoNel+mC7VZKt1pAcnBRGk6m/lh1dZra8TVAb3NL7FlWVnFMykiNh0G2lcbiZmZnqkqiiWoMtqflqTPaqA7mq2nh1I/N4ebq7oU/rUAyr6cmWqXF8PNk7QE4saxfw7RSgsGYOZr8w4Mo5QBvHKYLz896foaupsD6l8xT2uli4LU1O098O8PZAF47ntq2qcmDb98Dqd4C8g+b3+UcAA6brs1OCWGGeTs/+E/vVmO3FRxabLY8LiMOV7a7EVX2ugjcL75EDYtBtBTJN2Lnnnsvx3C5Ko9Vhx7ECNYXXmgO52HA4D+VV+vGIdcnQxO6tglWALYG29GoHssI4uYpDK4AfpgE1Y6HVuM+r5wKRneEoqjRVmLtvrrru6eaJKV2m2HqVnKotHXjW2Xjyo23qds94ZvrYdPjHhs+AtbOAEtP0bUpUN2DIrUDS5YAXi3fS6TlUcAizts3CokOLjCcxRbR/NGYkzcAlHS7BidwT8HRn6EKOiZ9cK6XEbdy4EePGjWN6uYv0xuzLKjb2ZMv47KLyOuPaaukQGYBhnWqKn3WIQFgAp0ohF7T9Z2D+rYCmUn+7VR9g2k9AYDQcyT+p/yCvPE9dH9NmDCL9Im29Sk7Vlq5csw7u8IYW7ugay6rlLa4wXZ9CvvELoLLI/L72I4FhdwOdzrH7Qodkv9IK0/Bh8odq9getztRBEeEbgZuSbsKlXS5VM0JIkVgiR8ag20pBWElJCdPLnVhaXqlxrmz5yy6qaPSxscG+Ksge3jFSXbbiNF7kymTYzbL/Acv/Z1rW6Vzgsi8Bn0A4mh/2/GC8fnnXy226Ls7YluYWFMENEep252jH+3w4rJz9wOq3gW0/mE6MKZKedTEw/B4gvp8NV5AcXXpxOj5K/ggL9i9Atc7UURHmE4bpPafj8m6Xw8+TmRPkPBh0WyklbtSoUUwvdyISVMsc2fre7Byk5ZU1+tgwfy81fZf0ZEvaePvIAFYYJxJVZfre7ZR5pv3R71pgwpuAh6dDjj3clLnJWEl3YOxAW6+S07WluWE9oDmiT2fuFM2ebqvLTAGWvwrsXCCnPUzLPbyB3lcCw+4CIjtZfz3IaWWVZuGT5E/UsJwqbZVxuUyzeH2P63FV4lUI8Aqw6ToSWYPjHeU4SErc6tWrceGFFzK93EEVlldh/cE8FWDLXNl7Muuk1dXi7+2Bwe31FcalJzsxNhjurDBOZK4oA/j+SuD45poFbsC454GhdzhsauqPe3806+Xm/NGWb0vLU7fDA1HQwB0do3kgbjXpycB/rwK7fjNf7hOsL44mY7ZZHI3OQE5ZDj7f8Tl+3PMjKjSm7MBAr0Bc0/0a9RfkzRNr5LwYdBMBqKjSYEuaPshetT8X248VqIJoDfH2cFdVxQ1zZfduHQovD84RSdSo9G36gNtQodw7UD8lWNfxDrvTSqtK8dsBfYAiKZAXdXSM6c0cTWmlRl36eLojKtDH1qvjfI5v0fds7/nDfHlAFDD0dn3A7Rtiq7UjJ5Bfno/PUz7HD7t/QFm1KUtQfjenJU5TvdshPvyMkfNj0G2NnerpiWHDhqlLsk/VGq0KrFfuz8HyXelITi9BZXXDRTqk07pXfAiG1syVPaBtOPy8OY0XUZPs+h345SagqlR/O6Q1cOUPQGxPh96B8/bPQ3FVsbo+vv14lRpJluXh4YHVFQnQQIs2oX7MJLAgr8xkuP3zCbDvb/M7AmP047X7Xw94+1vyJcnFFFYW4quUr/Dtzm9RWl3z+y8n0Dx8cEXXKzC913SE+4bbdB2JWhKjQiuoqqrC8uXLMXHiRPj48My8vRTk2ZtZjFX79cXP1kmF8YrGK4x3ig7E8JppvIa0j0CIv1eLri+RUxRMW/km8O/zprGhCYOAK2Y7XIXyujRajTqQNJDeGrK8vKIy9MVBrEUbxIX6chdbwrHNcPv3BUQc+Md8eVAr4Kx79TUWOO0XnYHiymJ8u+tbfJ3yNYqqTEPzvNy9cFmXy/B/vf4PUf5R3Mfkchh0W4GM6wsIYPEse6kwLuniEmjnFDdeYVwO6KS6uCFlPDqYB3hEp62yGCGL74H7wUWmZb2mAhe/C3g5/ndr2dFlOFp8VF0f2moouoR1sfUqOaX0wnKU6LzUKZs4zvpwZrJ2A0tfUGO2zSooBCcAI+4F+lztFN9Nsu2Qm+93f48vUr5AQUWBcbmnmycmdZ6Em5NuRmxALN8iclkMuq2xUz09MWDAAKaXtzAJqtUUXjW92al5pnSmusIDvPUVxjuEo0so0K9za5XKSERnKPcA3OZMg1/WLtOyMU8AIx5w2IJpdUkPjoEU/yHryCquxtbqeHW9VSinDjotJw7rp+hLngPUmgNZExgPt1EPwL3vNMCTGXl0+sqry1VxtM92fIa88jzjcg83D1XrYkbSDCQEJXAXk8tj0G2l9PLFixdj6tSpTC+3ouKKapUmru/JzsHujMYrjAdIhfEOMo2XfiqvbrFBqsK4VqtFVlYWxwoSWcK+xcDcG+FWru/l0PkEwW3yJw5dMK2ulNwUbM7SV2DvENIBw+OH23qVnFZuUSlGex/Aisp2iAz0tvXqON5sAf/NBDZ9CdSalknGbGtHPIDshPMR3SoBcGcRUDo9lZpKNe3Xp8mfIqtMP62fcIMbJnSYgFt634K2wW25e4lqMOi2Unp5TEwMAzkLk2riyUfzsXJfDlbsy8Hm1BOoPkmF8X5tQ1WALcXPkhJYYZzIquO3V7wO/PuCcfx2dWgHuF/1A9yiuzrVjq89llt6ud3dGLRYS35pNbK1AdDBDWH+DLqbpCwfWPUWsPZDoFalaPiGAmfdAwyaAXj6AlmmIImoOWRu7QX7F+Dj5I+RXpJudt957c7Dbb1vQ4fQDtypRHUw6LZSenlSUhLTyy00LlsC7JX7s1WPdkFZrTP2tbjVVBg3BNmsME7UQiqKgPm3ms3vq+s6AbnDn0NUpHMdeGWXZ+PvI/pqz2E+Ybiww4W2XiWnll+uQUq1fgwog+5T0FQBGz8Hlr0MlJ0wLfcKAIbeBgy9A/AL1S/TNjxTB9HJVGursfDgQny47UNjTQuDMa3H4LY+t6FruHOdZCWyJAbdVlBZWYmFCxdi2rRp8PVlYZLmKCqvwpoDuSrQXrEvG4dzGx+X3T4yAGd1isRZnVlhnMgmcvYBc64GsnfXLHADxjwO3fB7ocvOcbo3Zf6R+ajW6Wc9mNp1Knylx5Cs5kRxGcZ578W/lR0RFsAZJBrNMtnzJ7D4SSB3v2m5hzcw4EZgxH0OP1sA2ZZWp8WiQ4swa9ssHC48bHbfiPgRuL3v7egR0cNm60fkKBh0W4EU5OrQoQMLczVxvuxtRwtUgC1p41vS8lUaeUNC/LxUL/aIzlEq2G4dzjlEiWxmx1zg17tUpXLFJwSY8inQZZxT9qRJNd7f0vS9+d7u3rii2xW2XiWnd6KsGoc0YdAyvbxh6duAvx4HDq8wXy4zBZzzJBDapiXeJnLiYPuf1H/wwdYPsD+/1gkdAENaDcHtfW5Hn+g+Nls/IkdjV0H3yy+/jF9++QW7d++Gn58fhg0bhldeeQVdu548XUXmxL7vvvuQkpKCuLg4PPTQQ7jllltgy6A7MTGRQXcjsgrLsWxvNpbvyVbBdmF5w/Nle7q7oV/bMIzsLL3ZUSp93MPdOaofEzms6gr9gf6GT0zLohL1829HdISz+n7P9yjT6MfIyvQ3kX6Rtl4lp5dfpsE+jX4+X6aX11J4XF8/Yet3xhoKSpuhwLgXgYT+Lf5ekfPQ6XRYfnQ53t/6PnbnGbKY9PrH9FfB9sDYgTZbPyJHZVdBtwTPt99+OwYOHIjq6mo8/vjjGDduHHbu3KnmvW7IoUOHcMEFF+Cmm27Ct99+i1WrVuG2225DVFQUpkyZAlull8+bNw833HAD08trerO3puVj2Z5sLN2ThZTjhY3uu45RAaone0TnSFVtPNDHrj6iRK7txBHgp+uA41tMy5KuAC58A/Bu+DfaWeaf/W7Xd8ZpcK7vcb2tV8kllFVUYILPLiyu7AJfLxasQ3UlsPZ9YPmrQFWtoVdh7YBznwMSL3aaafnINsH26uOrVbC9PWe72X1JUUm4o88dqodbigUTUfPZVUSzaNEis9tffPEFoqOjsWnTJowcObLB//Phhx+iTZs2eOutt9Rt6WHeuHEjZs6cabOgW3q6pZCaK8/7nF1Ugf/26oNsGZ/dWAE0SRmXMdmG3ux4zsVKZJ9k3Oi8GUDNdGDw8AEueBXod53TH+j/tPcnFFTqt3t8+/Gcc7aFlFZqkVIVAx9vTx7oH1wO/PEAkLPXtINkSMeoh4BBN3GubToj69PX472t72FLVq0TqgC6R3RXPdsydpvBNpETBd11FRToD3LCw8MbfcyaNWtUb3ht5513Hj777DM1X7aXl3nxlYqKCvVnUFio73WV+ZrlzxLkh0nGdMulpZ7T1mQ75CxoY9sj9+04Xoglu7JUj/b2YzUH5g3oGReMUV2iMLprFHonhMDTw9SD0dL761Tb5YiccZucdbscYps0VXBb+gLcVr9jXKQLaw/dZV8Bsb30hZzkz9G2qxlz0X6V8pXx9vXdr3eK7RJnuh3Wbk9LqnRI14YjysvLafZ5sxUeh9viJ+GW8otxkU6mqet/A3SjHwX8I/QLm7F/nOn7aW8cbd9KkC092xsyN5gt7xzaWU39dXbrs9WxrGyT/NmSo+1bR8J9e2aa+pm026BbvlgyTvuss85Cz549G31cRkaGmhO7Nrkt6ek5OTlo1apVvXHjzz77bL3nyc7ORnl5uUXWXQ5CZGz65MmT4ePjA2f5QMlJEHlf3N31QXKVRovNR4vx34F8rDiYj6zihnuzA709MLhtMIa2C8aQdiGINFahrUJebo7dbZejc8Ztctbtsvdtci/OQOg/98M7faNxWXn7cSgY/RJ07kGNzvVr79vVHH+k/YHssmx1fVDYIARVBCHLSeY4LioqOqP/b+32tLyiHBN9dmCLex+n2edNpqmC/45vELjxXbjVSiWvjOmDwrOeQnVUD6BYAxQ3f7840/fT3jjKvt2dvxtf7f8KG3NNv+2idUBrXNfpOoyIGQF3N3f1XbYXjrJvHRH3bcu0pXYbdN9xxx1ITk7GypUrT/nYuikvhrNxDaXCPProoyqYr31mvnXr1moMeHBwsEXWXQL+4cOHq4Bf5ux2li+k7E+fwFD8tz8XS3ZmqWJoxRUNF0FLbBWE0V2iVI92vzahZr3Z9rhd8v47y4+4M26Ts26XXW/T7oVw++1OuNXM+atz94Tu3OfhPWgGok6RTm7X29XMeWl/Xv2z8fY1Xa5RQ54ceZtqO9MpLa3dnpZWu2G9tjVCQn3UfncZaevh9vvdcDNOxQfo/COgO+cZePa5CuHS030GnOX7aY/sfd/uytulqpH/d+w/s+VtgtpgRtIMjG83Hh7u9jk00t73rSPjvm2ZttQuI8I777wTv/76K/777z8kJCSc9LGxsbGqt7s2OSMuwW5ERE3aVS3S89xQ77N8gS31JZbXlnHmcukMPwzH8suwOCUDC7elYcvRYlQ3MKWXt4c7hnWKwLndY3BOtxjEhjjO/LXyI27J998eOOM2Oet22d02VZUBfz8BbPjUtCw4AW6XfQm31gMdd7tOg8xNm1aUpq4PiR2CbqHdHH6bajvT7bBmeyoFOCuqdTiOELTy8XKafX5SFUXAP88D6z+uVZXcDRhwA9zGPAk3/8aH2jWXM3w/7ZU97tv9J/bjg20fYPGRxWbL4wLicEvvW3BRx4vg6W6XIYHd71tnwX17+pr6ebSrb5j0UEvALZW/ly1bhvbt25/y/wwdOhS//aafO9Xg77//xoABA+qN524pkl4uldSlErtMfeaogfYfyelYuD1dVR5vrAjamG7RKtAe2SWKlcaJHF3WLuDn6UDWTtMyqYh88TuAXxhcSZW2CrO2zjLevjnpZpuuj6sprdLAExpM9t2BdM+GC6k6lX2Lgd/vBQr0J3mUuL7AhDeA+H62XDNyYIcKDmHWtlnqBKKu1vRy0f7Rqmd7UqdJ8PKwzbEykauxq6BbgtTvvvsOCxYsQFBQkLEHOyQkxBi8SjrbsWPH8PXXX6vbMh/3e++9p1LcZNowKawmRdS+//57m22HBPtjx461WdB/uo5LoL1dH2hvSW040E4I81NBtvwNbBcOLztNGyeiZpAhORs/B/56DKiuGYvr6Quc/z+g//VOX528Ib8d+A1Hi4+q6zJNjsxP63Ljim2ovEoDDdyxtLIjens7VlvaLKV5wKJHgOQ5pmWefsCYJ4AhtwJ2mupL9i2tMA0fJn+I3w/+Dq3OVOQpwjcCNyXdhEu7XAofmYGCiFwz6J41S9+rMHr06HpTh11/vX5e1PT0dKSmphrvk97wP/74A/feey/ef/99xMXF4Z133rHZdGGGNANJe3eE9Jec4gr8tu24+tvcSKCd2CoY5/eIQb8YTwzr3talp0IjcsqD/t/uAnbVyhiK7gFc+hkQnQhXVKWpwkfbPjLelilzqGVVa6Rfzg3Z2kB4OUltlHr2/gX8eidQnGla1n4UcNHbQPipM/2I6jpefBwfJ3+MBfsXoFpnqrkT5hOG6T2n4/Jul8NPTuoQUYuzq5asKdMRfPnll/WWjRo1Cps3b4a9kPTyzz//XJ0IsMf0culBWLIrE/M2H1PF0DQNjNHuFhuECb1a4YKkVugYFaiKLEgvD+dpJHIih1cCv8wACvU9usrAm4BxzwNe9vfb1VLm7Z+H4yXH1fXh8cPRJ7oPp6mxQdDtBQ2m+m5Dkc58WlCnGLstWSWb9Rl7im8IcN5LQJ9pLplZQmcmsyQTn2z/BHP3zVUFIA2CvYNxfY/rcVXiVQjwCuBuJrIhuwq6nYWklU+cONGu0svlhMbGIyfwy+aj+D05HUXl9auOd40JwoSkVrigVyt0ig60yXoSUQuorgD+fR5Y/Z6pYJOM2b7kfaDbBJd+Cyo0Ffgo2dTLfUefO2y6Pq6qSqtFNdyxsCIRY7y84TQOrwLm3wrkHzEt6zwOuPhdICjWlmtGDiinLAefbf8MP+75EZXaSuPyQK9AXNv9Wlzd/WoEeQfZdB2JSI9BtxVIWnl4eLhdpJfnFlfg501H8d36VBzJNc31adAqxBcT+8ZjUt94dInhDzOR08vYAfxyM5CVYlrWbgQw+WMgOA6u7ue9PyOrVD92e3TCaPSM7GnrVXLp9PJ8nR88PW3flp4xTRWw9EVg5VumE13S83j+S0C/69i7Tc1yovwEvkj5Aj/s/gFl1WXG5ZI6Pi1xmurdDvEJ4V4lsiMMuq2UXv7RRx/hoYceskl6ufRqbzh8ArPXHcGf2zNQqTEV0RD+3h4Y37MVJveLx5AOEfBwZyobkdPTaoA17wH/vgBoanpEPLyBMU8CQ29nwSZAHbx+ut00VdptfW6z2dvl6qo0WpVefrXfFlToHLwH+MQRYO6NwNENpmVthgITZ3HsNjVLYWUhvkr5Ct/u/Bal1aaOFF8PX1zR7Qrc0PMGhPtabmo5IrIcBt1W4O3tjWnTpqnLllRSUa16tSXY3ptZXO/+4Z0icGn/BJzXIxb+3nzriVyGHPTPuwVIXW1aFtNT37sd08OWa2ZX5EBW0jXFOW3OQWKEaxaSswfVWh2q4I45ZUm4zJHTy1PmA7/eBVQU6G/LXMhyomvYnTzRRU1WUlWC2btm48uUL1FUWWRc7uXuhaldp+LGnjciyj+Ke5TIjjHyspKWDLiziyrw1erD+GbtERSUVZndF+bvhcsGtMaVg9qgfSSLaBC5FClOufU74M+HAeOBmhsw/C7g7McBT04ZY5BXnofPdnymrru7uePOvnfa6E0jUV2ToVUFD3h4OGA2VlU58Nej+qn4DMLaAVM+BxL623LNyIGUV5djzp45atz2iYoTxuWe7p6Y3Gmymv4rNsDBM0GIXASDbiuorKxU05xZO738UE4JPllxUPVuV1abp5APbBeGaYPb4vyesfD14hRfRC6nOBv4/R5g9++mZSFtgEkfAu2G23LN7JJMsyO9SWJSp0noGNrR1qvk0qpU9XKtSi/3QFs4lPxUYM41QPpW07Iek4GL3tJXKSc6hUpNpapE/knyJ8guyzYulxOCF3e8GDOSZiAhKIH7kciBMOi2Ui/3DTfcYLXe7v1ZRXhzyT78sT1ddWQZeHm44ZI+8fi/Ee3RLTbYKq9NRHZOfhRSfgEWPgCU5ZmWy1RE5/8P8OVvQ11pRWmqN8kwNpJjuW2vWqtV6eXflvXFTZ4OlF5+YCnw83TTd0/mRL7gVaDvNSyWRqdUpa3Cbwd+w4fbPkR6SbpxuRvcML79eNza+1a0C2nHPUnkgBh0W7G329JSc0vx1j97MX/LMdSeWjvQxxNXDW6DG4a3Q6sQ151bl8jlFWcBC+8Ddv1m2hX+EcBFbwOJF7n87mnMu5vfNc5te033axDtH819ZQdjuoUUU/N0hPRyOdm18k39VHy6msyzsPbA5d8CsayATyen0Wrw5+E/MWvrLKQWpZrdN7bNWHUisHNYZ+5GIgfGoNtKAffs2bMtll4u47Tf+WefGrdtOBARkYHeuPGsDirgDvGznznBicgGB/w75gJ/PGjeu939EuCC14FAFthpTEpOijrYFWE+YZjec3pLvGPUhCnDJL38cr9keKKrfe+vylL93Ns755uWdT5PX6jQL9SWa0Z2TqvT4p/Uf/D+lvdxoOCA2X0j4kfg9r63o0cEi10SOQMG3Vbg4+ODGTNmqMszodHqMGdDGmb+vQd5JaaecwmwbxnVEdcNa8sq5ESurrHe7QmvAz0m2XLN7J5Mr/jmpjeNt2f0noFA70CbrhPpaVR6uQe+KBuAh1t4JpBmKcoAvr8SOL65ZoEbMPpRYOSDgLsTzC9OVvvtWXFsBd7b8h525e0yu29w7GDc0fcO9Inuw71P5EQYdFuBVqtFXl4eIiMj4X6aje6+zCI8PDcZm1Pzjct8PN1x88gOuGlkBwT7smebyKUZe7dl7Lapqi26T9QH3AGRtlw7hyAHvesy1qnrrYNaY2qXqbZeJarFDTqEuJWb0rXtTcZ24LsrgMKj+ttywmbKZ0DX8229ZmTHwbb85ry75V0kZyeb3dcnqo8Ktge3Gmyz9SMi62HQbQVVVVWYP38+7r33Xnh6ejZ7mpQPlh3Au//uU9VbDS7qHYdHxndDfCjHbBO5POldW3i/eWVy/0hgwkz2bjf1d1pThdc2vGa8fVe/u+DlwZOZ9sQTWkzw2QWdxg7Ta/f+Bfx0A1BT8R4hrYGr5nDee2rU5szNeG/re9iQscFseWJ4opqi8Kz4s+Dm5gD1C4jotDDotgJJK58+fXqz08uPnijFPT9sxcYjpl4rmVv75cm9MKRDhBXWlIgcilYLbP4KWPw0UFFgWi5p5BfMZO92M3y3+zscLjysrveL7ofz2p5n8beLzoykl88u74dHPO3sZMiW2cCvdwI6jf52/ADgiu+AoBhbrxnZad2Id7e+i1XHVpkt7xTaCXf0uQNj2oxhsE3kAhh0Wym9PCMjo1np5Ut3Z+HuH7agsFxfQdfD3Q0zRnbAXed05jzbRATk7AN+uxs4sqpO77aM3Z7IPdQMOWU5akoew1Q8Dw96mAe9dppeHuleAp09pZevehtY/JT5cI5JHwJezEIjcwfyD6g0cimUVlvb4La4rfdtOK/defBw9+BuI3IRDLqtlF6+ZMkSdO3a9ZTp5TK+55MVB/Hyn7uNc25LCvk7V/ZF/7Zh1lg9InIk1ZXA6reB5a8BmgrzebfHvQD4h9ty7RySFC8qripW1yd3nozuEd1tvUrUAA9ocbb3Aeg0SfaRZbL4SWDNe6Zlg2YA5/+PBdPITGZZJt5d/S5+P/i7qk5uEBcQh1t634KLOl4ET3cefhO5Gn7rrUDSyq+++upTppdrtTo89esOfLvWNCfjeT1i8OqlvTkFGBEBRzfq01izdpr2Rmhb/bzbHc/mHjoNKbkp+GXfL+p6oFegGktJ9qkaHvixvLft08sl4P7tLmDLN6ZlY54ARjwAcAwu1cgty8UnyZ/gxz0/okpXZdwvUX5RuDnpZkzpPIV1I4hcGINuK6WXp6WlnTS9XAqm3f/TNizYety47J6xnXHXmM5wd2chDSKXVlEM/Ps8sO4jyYfRL3NzB4beoZ+OyNvf1mvokCSz6JX1r0BXs0+l1ynCj/Uy7Dm9vJV7oW3Ty7Ua/YmvrbNrVsoduPBNoP/1tlsnsivFlcX4audX+Drla5RWlxqXB3sH48ZeN+LKblfCz5PDD4hcHYNuK6iursaaNWvQq1evBtPLpYf7oZ+TjQG3jN9+/bLemNg33hqrQ0SOZM8i/TRgBWmmZbFJwMXvAnGct/VMLDq8CFuytqjr7YLb4apuV53pu0VWTi8f5JUGnbav7QLu+bcCyXP0t908gEs/4wwBpFRoKvDD7h/w6fZPkV9hmt7V18MXVydejRt63aACbyIiwaDbCry9vTF16lR12ZAX/9iFX7Yc0z/Wwx0fTOuHsd1Z9ZTIpeWnAYseMZ8GzNMXOPsxYMjtgAd/rs9ESVUJZm6Yabz94MAHmerpAOnl8yt64hFbTOUmAfe8GcD2n/S3ZQzupV8A3S9u+XUhu1KtrcaC/Qswa9ssZJZmGpd7unliSpcpmNxqMrq17tbkQrpE5Bp4FGcFGo0GBw4cQERERL0f3R83puGzlYfUdckil4JpDLiJXJimSl8R+b9XgSpTaiLajwIuegsI72DLtXOq4mlZZVnq+siEkeqP7JcUFnWDFm3d86GTMdUt/eK/31sr4PYCpn4FdJvQsutBdkWKoi0+slj9lhimGzTMgDChwwTc1uc2xAfEIytL/ztDRFQbg24rBd3Jycno378/vLxMZ+h3HCvAE/N2GG+/MLEXzu8Za41VICJHcGQ1In69B+4n9pmWBUQD570E9LqURZosZFfuLjUvt/Dx8MGjgx611FOTFXlAhx5e0pOobdmAW6qUb/7K1MN9+TdA1/Ettw5kd7Ug1hxfg7e3vI2dubWKWgIYnTAad/a7E13Cuhhr+hARNYRBtxVIWvmkSZPM0svLqzS478etqNTof5CvHtIGVw1uY42XJyJ7V5ID/P0k3Ld9B1MujBsw6Cbg7McBv1Cbrp6z9U69sPYF49Q9M5JmICEowdarRU1ML19YkYiklhxaseJ1YPW7NTfcgMkfM+B2YcnZyXh789tYn7HebHm/6H64t/+96BPNOhtE1DQMuq3U071r1y6z9PIPlh3A3kz9vLDdWwXjqQt7WOOlicieSS+I9KAteQYoNxXe0cX1hZtURI6zUcEoJ/bz3p+RnJOsrncI6YDre7DqtKNwhxYdPXKh03ZqmRfc/I1+1gAD+U72nNIyr012JbUwVQXbfx/522x5t/BuuKvvXTgr/iy4cbo4ImqpoLuqqgoZGRkoLS1FVFQUwsPDz+TpnCroPnjwIIYOHarSy9MLyvDxfwfUfV4ebnjj8t7w9mSBDSKXkr4N+P0+4NhG4yKdTzAKB96DoNF3wc3WcxE7oZyyHLy1+S3j7SeGPMHiaQ7EHTq09zih0nut7sBS4Pd7TLfHPgsMuMH6r0t2N9f2R8kf4ac9P6FaV21c3iaoDe7oewfOa3ce3GXaOCIiawfdxcXFmD17Nr7//nusX78eFRUVxvsSEhIwbtw43HzzzRg4cCBclaSVT5gwwZhe/tpfe1BepU9tvHZoO3SL5RQSRC6j7ASw7H/A+o+B2vMNJ10O3dhnUVbqhiB3D1uuodN6Y+MbKKosUtcv6nARBsa6brvkqOnlf1d2QX9rp5dn7QJ+vBbQ1gRZg28BzqoVgJPTK6suwzc7v8HnOz5XMx0YhPuG47bet2Fyl8nwkoJ6RESnqVkt2ZtvvokXX3wR7dq1w8UXX4xHHnkE8fHx8PPzQ15eHnbs2IEVK1bg3HPPxZAhQ/Duu++ic+fOcMV5uqWQ2ujRo5FeVIV5NdODhfp74a4xrrc/iFySTDm05Vvgn2eB0lzT8sguwITXgfYj9enmpax0aw3r09fjt4O/qetB3kG4f8D9Vnkdsm56eaJnlnXTy6W+wuypQEWh/naX8fpChuQy03/9euBXvL/lfePsBsLP008NRbmux3UI8Aqw6ToSkQsG3atXr8bSpUvRq1evBu8fNGgQpk+fjlmzZuHzzz/H8uXLXTLollS4zMxMdfnFqsOqGKq4aUQHhPjzTCmR00tbD/zxIJC+1bTM0w8Y+QAw7C7A01RkkazTa/XMmmeMt+/pdw8i/CK4qx2MG3SIci/RVxS3Bk018NP1QEGq/nar3sCUTwFmnjg9OT5bcWwF3tz0Jvbn7zcu93DzwJTOU3Brn1sR6Rdp03UkIhcOun/6qWbOylPw9fXFbbfdBlcl47ilt79C64afNqapZb5e7rhqEKuVEzm1ogxg8dNA8g/my3tMBsY9D4SwanZL+GDrB0gr0v/29onqg0u7XNoir0uWpYEHllV2xFBrpZcveRo4vEJ/PTAWuHIO4BNondciu7EjZwde3/g6Nmaa6muIMa3H4O7+d6uCi0RElnZGLVl5eblKo87Kyqo3N6Gkn7sqSS/fuHEjymN6oqRSo5ZN7BOPsAD2bhE5pepKYN0sYPmrQKV+lgIlugdwwatAu7NsuXYud0D99c6v1XVvd288O/xZFj5y4PTyJM9066SXb/8ZWPNezQt5AVO/BoJbWf51yG6kFabhnS3vYNHhRWbLk6KScH//+9Evpp/N1o2InN9pB92LFi3Ctddei5ycnHr3yTQKUsHbldOWSkpKsHh7hnHZxL7xNl0nIrKSfYuBRY8AuaYURfiGAmOeAPrfALTkHMMurkpThSdXPWmck1tSRNlr5ZgkodwNQIBbleXTy3P2A7/eZbp9/stAm8GWfQ2yGwUVBfhw24f4Yc8Pagx37Yrk9/S/B2PbjOX0X0Rkdad9NHjHHXfgsssuw1NPPYWYmBjLrpUTpJcPHjYCT36oH88ZHeSDge04nRqRU8k9APz1GLC3dq+Jm36aobOfAAI4hrilfbr9U+P4zMTwRFUEiRyXBu5YVdUOozy8LJuVMvdGwFChuveVwMD/s9zzk92o0lZhzu45mLVtFgorC80qkt/S+xY17IQVyYnI7oNuSSm/7777GHA3kl7+57//QaORipfuGNMtGh7ucs6eiBxeeQGw4nVg7SxAU2la3mYoMP4VfTEmanH7TuzDx9s/NhZDenbYszygdnAe0KKf1zHoNBYsyPrvc6YChxGd9TMJuLF9drZsw+VHl6tx24cLDxuX+3r4qhNxUpU80Jtj94nIQYLuSy+9FMuWLUPHjh0tu0ZOIqtIDsb100wM7cgeLyKHJ5WON38JLH3JfAqwoFbAuc8DvS7lwbut3hqtBk+tesqYOjq953QkRiTaanXIXh1cBqx+V3/dwxu49DPAm9NBOZM9eXvw2sbXsC59ndnyiztejLv63oWYAGZmEpGDBd3vvfeeSi+XebllCjFJqa7trrtqjZdyMZ6entiiawsN9AWVBrdn0E3k8OO2/3ocyNljWubhAwy9DRjxACse25gUTtuRu0Ndbx/SHjN6z7D1KpGF0ss3VLXGuR4eZ/5kFcXAgjtNt8c+w6wUJ5JTloP3tryHefvnGWs6iH7R/fDQwIfQI7KHTdePiOi0g+7vvvsOf/31F/z8/FSPtxRPM5Drrhx0V1RUIjgnBR5ojVZhAYgN8bX1KhHR6cjcCfz9BHDgH/PlPacA5zwNhLXlfrWDtPJ3t+h7L93gptLKfeSECDlFevkQr1ToNBaoXv7Pc6b5uNuNAAbfeubPSTZXoanANzu/UfUcSgzj9AHEB8bjvv734dy257JIGhE5dtD9xBNP4LnnnsMjjzwCd3d3y66Vg0svLEehxlNVX+0WG2zr1SGi5irO0qeRb/4KqNVrgoSBwHkvAa0HcZ/aSbXyx1Y+pgomCRmv2Te6r61XiyxE2tASndeZD9tIXQus14/3h6cfcPE7AI9bHH7c9l+H/8Kbm97E8ZLjxuUBXgG4OelmTEucxpNvROQcQXdlZSUuv/xyBtwNOJBThq3V+inCusayWAeRw6gqB9Z+AKx4A6gsMi0Paa1PR5UebhZdshtSlXh33m51vVNoJ9zR9w5brxJZkBbuqi29wN3jzL7TC+RzUTPtmEzlF97BYutILS8lNwWvrH8FW7K2GJe5u7nj0s6X4rY+tyHCj0P6iMiJgu7rrrsOc+bMwWOPPWbZNXIC+zIKMNr7AFZUtkOXmCBbrw4RnYrMA7xjLrDkWVMKqvAOAkbcBwy5FfDy4360I9uyt+GzHZ+p655unnjprJfYs+VkPKDBCO/DZ5ZevuY9IHef/nr8AP13mRxSXnke3tn8Dn7Z9wt0hpMoAIbFDcMDAx5A5zALVrknIrKXoFuj0eDVV19V47qTkpLqFVJ744034KrSC8qRrQ2ADm5ICPO39eoQ0ckcXgksfgo4tsm0zM0d6HcdcPZjQGA095+dKa0qxWMrHjMWTLq1z62sVu6EpA2VtvS0s0sKj+uzVgzfaZVWboGibNSiZFaCOXvm4P2t76OoVgZSu+B2eHDggxgRP4LjtonIeYPu7du3o29f/di5HTv0VWMNahdVc0UZRVVIqY5V1+NCWUSNyC5lpuh7tvf9Zb684xhg3ItATHdbrRmdwhub3kBqkT4jISkySU0RRs6XfCLp5dKWXnK6gfKSZwBDca0BNwIxrGDtaNanr8fL61/G/vz9ZuO2b+19K67qdhW8PMw7fIiInC7oXrp0qWXXxIlk5pdgnPdeLK/uhOggBt1EdqXgqL5I2tbvTOM8RXR3YOyzQOdzOW7bjq06tkr1eglfD1+8eNaL8HQ/7aaM7JgnNBjjfQBa7Wmkl6etB5L1nxP4huqzVshhpBenY+bGmfj7yN9myy/peAnu6X8PIv0ibbZuRESng0cqVnC8oAJlmjBEBPrCw921e/2J7EbZCX2q6bqPAE2FaXlwPHD240DvK5h6audOlJ/Ak6ueNN6+b8B9aBfSzqbrRNajhRsOacLQv7nZc9JNLlP9Gcj32z/c4utHlldeXY4vUr7A59s/R7mm3Li8Z0RPPDr4USRFJXG3E5HzB92pqalo06ZNkx9/7NgxxMfrq3i70jQWJ8o1yNFGoWcge7mJbE6qF8t0QSteB8rzTct9Q4AR9wODbmaRNAf5bZWAO7ssW90e2mooLu96ua1Xi6xI0sv3aaLg1tz08v1LgLR1+uuRXYEBHH7gCJalLcP/1v8Px4qPGZeF+4bjnn734JJOl6gK5UREjqpZv2ADBw7ETTfdhPXr1zf6mIKCAnzyySfo2bMnfvnlF7ia0koN3LTVmOCzC8He7OUmshmtRp9C/m5/YPGTpoDbwwcYdidw11Zg+N0MuB3Ed7u/w/Kjy40H4pJWzoNw508vl7ZUq6luXi/30hdNt89+FPBgUp89kyD7zn/vVH+GgNvDzQNXJ16N3yb9hkmdJ/G7TkQOr1kt0a5du/DSSy/h/PPPV9XKBwwYgLi4OPj6+uLEiRPYuXMnUlJS1PLXXnsN48ePh6spLK+CBm5IqYpBV39vW68OkeuRg+59i/VFlLJSat3hBvS+Uj+2M7S1DVeQmmtP3h68sdE0I8bzw59HlH8Ud6STM7SlSc3p4dzzB3C8Zv7mmF5A4iVWWz86M1WaKny18yt8tO0js1TywbGDVSp5x9CO3MVE5JpBd3h4OGbOnIkXXngBf/zxB1asWIHDhw+jrKwMkZGRmDZtGs477zzVy+2qCsuqoYM7DmvDMdDPx9arQ+RajqwG/nkeSF1tvrzzOOCcp4FY1/1tcuTpwR7870FUaivVben9Gpkw0tarRS3A0Ja6ubs3/YTbspdNt+UEW1P/L7V4VfIX1r2AQwWHjMukONpDAx/C+e3Od/lZcIjI+ZxWzpX0bE+ePFn9Uf2ebkmJu9BnF4K8E7h7iFqC9Gz9+4J+LGdtcf2Ac58D2o/g++CgXt3wqvHAvFt4N9zb/15brxK1EENbqq1uYo/nwaVAxnb99bi+QFfXy7azdzllOXh94+v4/eDvxmUyTOTKblfi9j63I8g7yKbrR0RkLRzoZGFFKr3cHeurWuMyP6aXE1lV9h79+M2dC8yXR3QGxjwOdJ/I6b8c2N+H/8bcfXPVdT9PP7w68lV4e/B31VUY2tLEphZSW/2e6frwe/jdtyMarQY/7f0J72x+B0VVRcblSZFJeGLIE0iMSLTp+hERWRuDbgsrq9RCBzcc14YgwIcHh0RWceIwsOwVIPkHQKc1LQ9pDYx+FEi6nMWTHNzx4uN4Zs0zxtuPDnoU7UPa23SdqGUZ2tImpZdnpgAH/tFfD20LJF5k9fWjptmVuwvPrnkWKbmmGhvB3sFqvu0pnaewSBoRuQQG3RZWpdGqlLjJvjvgic6Wfnoil+ZekgW3P18DNn0FaKtMdwREAyMfBPpfB3iyloIzFFh6YPkDKKrU94iNbzceEztNtPVqUQvSQWdsS5uUXr7mfdP1IbcBzZ1mjCyurLoMs7bNwtcpX0Oj0xiXX9LxEtw34D41CwERkas47aA7LS0NrVuzAnBdldValRK3tLIjkrx4ToPIIkrz4LbyLUSt/whu1eXmc21LGungGYB3AHe2k5i5cSa25+jH5iYEJuDJoU+ysJILMrSlnU4VQJfmAdt/Nv0m9L26RdaPGrc2fS2eW/Mc0orSjMs6hXZSqeT9Y/pz1xGRyzntqLBbt26477778MgjjyAggAe7BpUafXp5tjYQPt4MuonOSHkhsO5DYPW7cKsoNC33CgCG3gYMvQPwC+VOdiKLDi9Sc3ILb3dvvDH6DRZXclGGtvSU6eXJPwKaCv31PtMAn8AWWT+qr6CiQJ00m79/vnGZl7sXZiTNwPSe0+Hl4cXdRkQu6bTn0li8eDH+/vtvdO7cGV988YVl18rBe7q9oME0381w11bbenWIHFNFEbDideDtJH2htJqAW+fuBd3gW4G7twFjnmDA7WSkSvnTq5423n5k8CMssOTCDG2ptlo/XVyj04Rt/sp0u991LbJuVPdt0OHPQ3/i4vkXmwXc/aL74eeLf8aM3jMYcBORSzvtrthhw4Zh3bp1+Prrr/H444/jnXfewZtvvonRo0fD1cd0V8MdCysSMYyF1Iiap6IY2PAJsOodoCzPtNzNA7q+VyO7+w2I7NC76fP2kkON/7xv2X0orS5Vty/qcBEu7XyprVeLbMjQlt7mcZJDlaMbgayd+uutBwPR3Vps/UgvvThdzbn939H/jLsk0CtQTe93aZdLWSiNiOhMeroNrr32WuzduxcXXXQRJkyYgEmTJmH//v0u3dMtKXH5Oj94c0w3URO/OCXAqrf1PdtLnjEF3G7uQNIVwB0boLvwLWgDW3GPOmkv2QtrX8D+/P1mYz/d3NxsvWpkQ4a21E1+Bxqz9VvTdfZytyitTovvd3+PiQsmmgXcY9uMxYKJCzC161QG3ERENTwtdcA0btw4FBUVqR7vP//8E7fffjueeeYZBAUFwdV6uiUl7mq/LXDX9rb16hDZt8pSYONn+oC7JLvWHW5Ar8uAUQ8BkTWzAGhrTQ1GTmXe/nn49cCvxvm4Xx/9Ovy9/G29WmRjhrZUW92h4QdoqoCdC2oe7A/0YIX7lnK06CieXv001mesNy6L8ovC44Mfxzltz2mx9SAicvqg+8MPP8SGDRvU365du+Dh4YGkpCQVbPfp0wezZ89G9+7dMW/ePAwYMACuokKjRRXcMacsCecyvZyoYVVlwMbPgZVvASVZte5wA3pOAUY9DER14d5zATtzd+LFtS8abz877Fl0CGkkyCKXYmhL72ms+NaBpUDZCf31ruM5g0EL9W7/tOcnvL7pdTUkxEDSyCWdXObfJiIiCwbdL774IoYMGYLrrrtOXUpg7eNjmh93+vTpeOmll3D99ddjx44dcBXVGp26rIIHPD047pSoXrC96Utg5ZtAcWatO9yAHpP0wTbHZLqMvPI83LP0HlRq9YWyLu96Oca3H2/r1SI7Im1po3bMNV3vyfH/1na8+DieWv0U1qWvMy5rFdAKzw1/DkNaDbH66xMRuew83ady44034sknn4Sr8YJWpcRpqgfaelWI7ENVub7C8Io3gOIM8/u6TwRGPwJEJ9pq7cgGqrRVePD/27sP8Kaq9w/g3yRNJy277L33HmUjMhURB46/uEDFAQKiMhQBWS4EQaYDtyg4fg4URNl7I3sjs8yWlo40uf/nPSHpoJSOpMlNvp/nKeTerHPvTXLue897zlnxMs7En1HL9YvXxyvNXuGxoBvqUs1aLZMPUCKw7zf77aCCQFWmNLuLdCFceHAh3t30rnOgQ0fr9ktNXkKBQE7RRkR0K26dSDoyMhJ///03/DEl7suERuhh5nyU5OekZXvrF/aW7aun099X6y57sF2ijqdKRx40ZfMUZ3/QYiHF8H6H9xFoCuQxIedMYI669OXM0suPrwaSr9pv1+wBBKRm2pFrRyaXvtvrzqxzrisZVhJjo8aiVZlW3NVERNnk1vxnGXm2ffv22X78ypUr1SjopUuXVs/96afUuR4zs3z5cvW4jH/79u2DNwwAQ+TXU3+tnQ5MawAsfjl9wF3zTmDAauCBLxhw+6lfDv+CL/faR50OMAaogDsyNNLTxSIvJHVppoPYH1iSert6t/wskt+0bst8273/1ztdwH1vtXvxw10/MOAmIvKmlu6cio+PR4MGDfDEE0/g3nvvzfbz9u/fj4iI1ME7ihcvDk+nxD0QshMpFvZxIj+TGAtsnAus+zD9PNuixh32lu1S9T1VOvICuy/uxth1Y53LI1uMRMPIhh4tE3knR12qWWve2Ax+4A/7bWMAUKWjR8rnq64kXsG49eOw9PhS57oSoSUwptUYtCnTxqNlIyLSK68Kurt3767+cpPGXqhQIXjTwC+fJjTFHYFMlSQ/ce0SsGEOsGEWkBiT5g4DUPsuoO0wBtuEiwkX1cBpSdYktTfur36/+iPKqi59LSBDXXrhAHDluP12hVZAcEHuQBdZe2otXlvzGs4npE7h2KtKL7za/FWEB/rXFLBERF4RdJ84cQLlypVT6dwZU5JkkLXy5csjvzRq1AiJiYlqirLXXnsNHTt69qq3ARoKGhKhcV5h8nXxF4B1M4CNH6X2rxQGo3004bYvcTRycg6cNmzFMJyNtw+k17B4Q4xoPoJ7h25dl2q29Hcc+DP1drWu3IMukJiSiGlbpzm7fYhCQYUwJmoM590mIvJk0F2pUiWcOXNGtTKndenSJXWf1er+Ps2lSpXC3Llz0aRJEyQlJeGLL75Ap06dVF/vdu3aZfoceZz8OcTGxqr/bTab+ssruegQABvuCNqL5ORWLnlNbyDbIdvmK9vjy9uVL9t09SwMEmxv+RQGS+potpqketZ/AFrrIUDRKo4CueQteaz0I+OxktuTN07G5nOb1XLxkOJ4t927MBlMuvnu+ernLy/cWZ+mrUttKXXSvZ7h6ArJobG/V5VOLvuN8RcZP8v7L+3HiNUjcDjmsPMxrUq3wriocSgeWtynPvPu5ou/E96C+5b71ltl9/ue66BbflQytnKLuLg4BAcHIz/UqFFD/TlERUWpVvZ33333pkH3pEmTMHZsan9Ch/Pnz6vW8ry6du2aSon7KrEx2sXHIzo6Gr7ygYqJiVHH3Wj0nfnHfXG73LlNxrgzCNs2D6H7vofBap9bWWhGMxJq3ov4hk/BGlEWahxBF3/2eaz0I+Ox+un4T/juwHfqPrPBjNfqvwYtTkN0nH5+H33x83f1aprslFxwZ30q+9pRl76YkJRal9pSEHl8rQq6raHFcd5WyOW/Nb7O8Vm22qz48b8f8emBT2HRLOq+QGMgnqr+FHqV76W776g38MXfCW/Bfct9q/e6NMdB99ChQ9X/EnDLHNyhoaHO+6R1e8OGDWjY0HOD4rRs2RJffpmaHpXRiBEjnNvguDIvafIy+FrawdhyKyT0okqJK2aMR6FCBREZWQy+8mMnx1z2ky9VJL64XW7ZpsvHYJBpv3Z8A4PNfnImtIBgoPFj0FoNRHBEGbjzchuPlX6kPVYy8vGs/bOc973R6g10qNwBeuOLn7+8XiB3Z31a8KzVWZeGhYWmZtWd2grj9ewaY6U2iCxRIk/v47fBiyUG4/eMx5rTa5zraxSugYltJqJqoaoeLZ+e+eLvhLfgvuW+1XtdmuOge9u2bep/uYq3a9cuBKYZLExuy+jjw4YNg6dI+STt/GaCgoLUX0by4+iKH0gDDDDBho6BhwFbO5/60ZWKxFX7yZv44na5bJvO7QHWTAV2LQS0NF1GzGFAs34wRL0AhJdwpnq6G4+VfsixOhp7FK+segW2631y+9frj15Ve0GvfO3zl9ftcGd9KvvaWZdqDVJf70RqkGio2AYGHzkW+WnT2U14dd2ruJh00Xne8nidx/FCoxcQaOIAsHnla78T3oT7lvvWG2X3u57joPuff/5R/8u0XtOmTXNJ63Da1PRDhw45l48ePYrt27ejSJEiamA2uap+6tQpfP755+r+qVOnomLFiqhTpw6Sk5NVC/eiRYvUnyelwITvEhvgATMrL9Kp/zYCq6YABxanXx8UATR/Gmj5HBBW1FOlIx24knwFg9cMRpwlTi3fXv52DGw00NPFIh1x1KWvBZhTVx5LDbpRsa1HyqVXkk4+e+dszNkxBxo0ta5IcBFMajtJ9eEmIiL3yXWf7k8//dS1JQGwefPmdCOPO9LWHnvsMcyfP18N3CajpjtIoC2t6hKIh4SEqOD7t99+Q48ePeBJkhJXyhjLgTRIX2Tu28PLgFXvA8dXp78vpLA90JaAO8R7pucj75RsTcbYbWNxKu6UWq5VpBYmtJkAo4xqT5QNWpq61DkTiPxGndxovx1aDChWnfsym87Fn8Orq17FlnNbnOtalmyJSe0moViIb3SDIyLy2Xm6ly1bpv5kgJOMI7d98sknOX69Dh06qLT1m5HAO61XXnlF/XkbSYlrbv4PNmuKp4tCdGs2K7D3f4D02T6zI/19EWUASSFv8hgQGMa9Sbckv+Fvrn8T/1751zlS+fTbpiPUnDr+B1FO6lLYmthXXD4KJFy23y7TRHJNuSOzYeXJlRi1ehSuJF2x71eDCY9WfRSDWgxCgClPp4FERJRNuf61lRFLx40bh6ZNm6o+1JmNZO7PKXE/JdVFX6aXkzdLSQJ2LgDWTAMupnbrUIpWBVoPVtN/IYDdJCj7Pv73Y/zvyP/U7WBTsAq4S4RxsCvKfV1az5Fefmpr6p1lGnOXZiOdfNaOWZizc45zXcmwkpjUZhLKoiwzT4iI9BB0z549W7U89+3b17Ul8gEG2FDBeAU2aUEk8jZJccCW+cC6D4Grp9PfV6oB0GYoUKsnYDR5qoSkU4uPLsa0rdOcy+Nbj0edYnU8WibSf13qTC8/bR/IVSnNoDsrlxMvY/iq4Vh7eq1zXYdyHdR3Mtwc7jPTmRIR+XzQLf2pW7XiwBuZMUFDHfM52KzZmyydKF9cuwRsmANsnJOaopl2QKK2Q4HKHZmySbkeEVlSWB0er/o4OlfozL1Jea5LNcfMCWzpzpZ/L/yLocuH4kz8GbUsYykMbjxYjVAuWYkZuwMSEZEXB939+/fH119/rebqplQyIqikxP2WVAtPmtOMuErkKTGn7K3a0rptiU9/X407gDZDgHLNPFU68gGHrxzGi/+8CMv1OdzvqXoPHq78sKeLRTrnqEsbm8z2QdTO7rLfUbAcEMbBvzIbT2HhwYWYtGGS87soo5O/2/5dNCvJ33giIt0E3Y7RxIVcKZ07dy7++usv1K9fH+YMAeaUKVPgr4ywoYrpYmpKHJEnXDgIrJsO7PgWuH4CphhMQL37gTaDgchaPDaUJ9HXovHsX8/iavJVtdymTBuMajEKly5c4p4lF9Wl1YGYk8D1zxgia3PPZpCYkojx68fj58M/O9c1LN5QBdwcU4GISGdB97ZtafpTyQ96w4bq/3//tY9S6+Dvg6oZoaGS6TJTuMgz/tuAQv+8C8OxZdcn3rkuIBho/CjQaiBQqDyPDuVZvCUezy973pnGKlODvdf+PQQYOSIyua4u1TQbcH5f6h2RNbl7M0wHJpkmuy/udq77v1r/h5eavASzZAkQEZHH5ejM6J9//nFfSXwsJW5JcnUMYHo55RfJqjjwhxqJ3PjfegSnvS+oINC8P9DiWaBAcR4TcglJX31p+UvYd8keDJUOK42Zt89UU4Oxzyi5si5tIYFj9J7UO4ozQ8dh5/mdKuC+kHBBLYcEhGBM1Bj0qNyDH0IiIi/C5gg3pcTVCoiG1crRyymfpv1aOx24cCDdXVp4KRhaPgs0eRwILshDQa6di3vdm1hzeo1ajgiMwKzbZ6FYCPvZkuvrUpVefoEt3Rn9cvgXjFk7Bsm2ZOeFrw9u+wA1itTgx5CIyFeC7rT9uzOmlgcHB6Nq1aro1asXihQpAn9jgIbixnh7ShyRO8jo45s/sY9GHncu3V1a8ZqIrfMYwls/CYM5XZs3kUvI3L8/HvpR3Q40BqoT/cqFKnPvkksv7KTWpRpwfu/1ewxAMf8OKmX+bZma79PdnzrXNSnRBFM6TFEDpxERkQ8F3dK/e+vWrao1t0aNGqpSPHjwIEwmE2rWrImZM2fipZdewurVq1G7tn8NemKFCcuTq2BQAPtSkYvJYELrZ9lHIk+OS39fhTZA60HQqnRCwvkLCDcFcveTy32771sVdDtMaDtBnfATuasubWcyARcO2VfKeBSBoX67s2XAwldWvoLVp1Y7191f/X6MaD6C/beJiHwx6Ha0Yn/66aeIiIhQ62JjY9GvXz+0adMGTz31FB5++GEMGTIEf/75J/wtJa5+wBmml5PrnP3XnkL+70LAlpLmDgNQqyfQ+kWgbFP7Ko6aT26y+OhiTNww0bn8ctOX0a1iN+5vcmtdGphUPHXk8iL+m1FxOu40nvvrORyOOayWTQYThjcfjgdqPOD3A9gSEfls0P3OO+9g6dKlzoBbyO0xY8agS5cuePHFFzF69Gh1259IFpyM3R5msNgXiPLyYTq2Sg2OhkN/pb9PRiJv+DAQ9QJQtAr3MbndmlNrMHLVSGjXR8TvX68/Hq3zKPc8uY2jLi2QcDp1ZeGKfrnHZWTyF5a94BwwrWBQQTVTQItSLTxdNCIicmfQHRMTg+jo6BtSx8+fP69avEWhQoWQnGwf4MOfWGHEGktFDAvgOHWUmw9QCrD3Z2DNB8CZ7envCykMNHsKaP40RyKnfLPj/A4MWT4EKZo9y+LeavdiUKNBPAKUL3Vp/6Tjfh10r/hvBV5e+TISUhLUcoWICpjZaSbKR3DqRyIiv0gvf/LJJ/Hee++hWbNmKrVp48aNGDZsGO6++271GFmuXr06/I0JNjQ2n4I1pZmni0J6knwN2P6VPY38SpqTTEc/RmnVbvQIEBjmqRKSHzp85bCai9txwt+5Qme83vJ1prNSvtWlofGn/DboXrBvASZunAjb9YFZG0U2wgcdP0Ch4EKeLhoREeVH0D1nzhzVX/vBBx9ESoq99SMgIACPPfYY3n//fbUsA6p99NFHuX0LIv8QfwHYOA/YOBdIuJT+vlINgFaDgNp3AyZmTlD+9yF9eunTiEmKUcstSrbA5LaTYTKaeCgo34Qn+l96uQTZ7295H/N3z3eu61qxKya0mYAgU5BHy0ZERDmX67P4AgUKYN68eSrAPnLkiBq9vEqVKmq9Q8OGDeGvKXGbLOVgYno5ZUVG413/IbD9ayAlMf19VTqpkchRqb3Mw8f9SPnuUuIlPLP0GURfi1bLtYvWxrTbpiGQo+JTPtelhRIX+VXQbbFaMGrNKDVwocMTdZ/A4MaDYTQYPVo2IiLKnTw3nUmQXb9+/by+jM+lxLU0n2B6OWU+ONp/G+wp5Pt+kxWp9xlMQN177cF2yXrce+QxscmxGLB0AI7FHlPLFSMqYtbtsxBmZtcGyv+6NCjhnH1FUEEgxLfTqqUbh4yfIAMXCgmyR7UYhT41+ni6aERElF9B99ChQ/Hmm28iLCxM3c7KlClT4K8kjIrXzGyhpFQ2K7DvV3uwfXJT+j0TWABo/CjQ8ll7320iD7pmuaamJdp7aa9ajgyNxJzOc1AkuAiPC3mkLg1NOm9fEV7Sp4+AdOOQEcq3n7cPoClp5O+2fxcdynXwdNGIiCg/g+5t27bBYrE4b9+MDKrmz2wwYntKGZhM7Pfo95LjgW1f2dPIL9tbDZ3CSwEtBgBNHvf51hvSh8SURAz8e6AarVxIoD2v8zyULlDa00UjP61LD6UURkjANZ8Pus9fO49n/noGBy8fVMsFzAUw/bbpaFqyqaeLRkRE+R10//PPP5nepvRMsKJt4DGkpLCy9FtXz9kHRtv0EZB4Jf19JeraRyKXVPKAQE+VkCidZGsyBi8fjI1nN6rliMAIzO08F5ULVeaeIo/VpR0Cj8CCAJiR4rNB939X/8PTS57GybiTzotdkl1Ss0hNTxeNiIi8oU/3qlWr1CjmMpDa999/jzJlyuCLL75ApUqV0KZNG/grDQact4XBwAFP/E/0PmDdDGDnAsCaYY76KrcBrQYClTuy6wF5lRRbCl5Z+YqzH6n03Z59+2zUKFLD00UjPyZ1qU1LgcEx9oUPBt0yJd9TS57C+QR7Cn3psNKY22WumoubiIh8R66HwVy0aBG6du2KkJAQbN26FUlJSWr91atXMXHiRPh7StzulJIwBTC93G8GRzu6EvjqfmBmC2DbF6kBtzEAaPAQMGA10PdHe+Dt590vyLtYbVaMWj0Ky04sU8vBpmB82OlD1CvOwfzI83Wp2RqHAFjtKwr4VtAtqeRP/vmkM+CuUrAKPu/+OQNuIiIflOuge/z48Zg9e7aaNsxsNjvXt2rVSgXh/kxOELoEHkDK9f7v5KOsFmDXQmBue+CznsDBJan3ySi7rV8EXtwJ9J7N0cjJa+cCHrd+HH4/+rtaDjQG4oPbPkCTEk08XTQiVZcWNRuQ7EjKCy/hM3vlwOUD6PdnPzU1n6hVpBbmd5uPEmG+s41EROSC9PL9+/ejXbt2N6yPiIjAlSsZ+rD6GRsMOGotDKOR82n6pMRYYOvnwIbZQMx/6e8rWA5o+RzQuC8QFO6pEhLdkqZpeGvjW/jh4A9qOcAQgCkdpiCqdBT3HnlNXRphuwSTyZY6+KQP2H9pP/ov6Y8rSfZzpbpF62J259koKBdriYjIJ+U66C5VqhQOHTqEihUrplu/evVqVK7s3wPvSErcQWtxGDl6uW+JOWUPtLfMB5Ji099XqgHQahBQ+27AlKehEojyJeB+Z/M7+Hrf1865gCe3m4z25dpz75NX1aXl8J+ar1sJLQa923txL55a+pSaHkzUL1ZfBdzhgbxIS0Tky3IdHTzzzDN48cUX8cknn6gpwk6fPo1169Zh2LBhGD16NPw9Ja5rkKSXc/Ryn3B2F7B2BvDvQsCWkv6+al3tg6NVbMO+2qSrgPuLPV+oZQMMeLP1m+hasauni0Z0Q1163FQDyViPQBm9PLSI7gNuaeGOTbZftG1QvIEasLBAYAFPF42IiLw16H7llVcQExODjh07IjExUaWaBwUFqaD7hRdegD+zwoDdlhIwmpheruvB0Q4vswfbRzJMj2cKBBo8aJ/2qzhHdyZ9B9xjW43FXVXu8nTRiDKtS6vZDsJkvN7SHVxI16OUP7P0GWfA3SiyEWbdPkvNFEBERL4vT3mwEyZMwKhRo7Bnzx7YbDbUrl0bBQrwiq0GI47ZisBo5OjlupOSbG/RlmA7enf6+0IKA836A82e8qkBfci/A+7e1Xp7umhEN61La+OgPb08KEK3XXcc83BfTrqslhlwExH5nxzXYLGxGfqyAqhevbr6XwJvx/0yoJo/p8TdGbQXKRaOAKwbiTHA1vnAhjnA1TPp7ytc0d6q3fBhIJCtEqTPgPvdze8y4CZdJRtJXfqbsRsG4EsEhuizlftc/Dk1D3d0QrRzlHKZko8t3ERE/iXHQXehQoVUH+6sTu7kfqv1+ryafka23wojNlrKoa9Or8r7lSsnEL7mPRj2/wAkx6W/r2wz++BoNe8AmLVAOg+4P9/zuVpmCzfpKb28q7YcAYYUIER//bllOrCnlz6NU3GnnPNwz+k8h4OmERH5oRxHhf/880+6k7kePXrgo48+QpkyZVxdNt3SYMBpW0GYGKh5r1NbgbXTYdjzE8K06/0FFYM9yJZgu3wLDxaQyPUBt2BKOelFGBJRw3A0tXuPjlxNvooBSwfgSMwRtVy2QFnM7TIXhYP1tR1EROShoLt9+/RTyphMJrRs2dLvpwlLv1OtuCf4X1g4erl3sdmAg0tUsI3jq9UqR86GFhAMQ8P/A6KeB4pW8WgxidzRh1sw4CY9KWqIxRQ8hecxH0E6CrotVguG/DMEey/tVcuRoZGY12We+p+IiPwT85/dQNLL/0muggeZXu4dUpKAnd8Baz8ALhxId5cWWgxxdR5GWPtBMBQo7rEiErmSTbNh4oaJWLB/QbqA+55q93BHk24UwDXcj19hlunCggtCLxe7Rq8djQ1nN6jlQkGFVMBdNrysp4tGREQexKDbTenl520FYDRyyjCPD462ZT6wftaNg6MVrQa0egFa3fsRf/kqwkKLeqqURC5ltVkxZt0Y/HToJ2cf7jGtxjDgJt0JQxLK4fpvd1A49GD6tun49civ6naQKQjTb5uOygUre7pYRETkC0F3VgOr+SMzrOgTvAOWZI5e7hFXzwLrZwKbPwWSMoy2X74V0HoQUK0rIBdFJOUcVz1TTiIXs9gsGLVqFBYfW6yWjQYjxrcej55VenJfk+6EGRIwCc9jKOYhKND7pyP9bv93mLdrnvNi11vt3kLDyIaeLhYREekx6L7nnvTpiYmJiRgwYADCwtJPpfTDDz/AX6XAiN+SauG+ALOni+JfLhwE1kwDdi4ArMk3Do7W+kWgXHMPFpDIfZKtyXhl5StYdmKZWg4wBKiT/i4Vu3C3ky6FIhn98C3MsHj9dI0r/luBCRsmOJeHNx+OTuU7ebRMRESk46C7YMH0/aoeeeQRV5bHZ9LLr2ghMDC9PH/8t9EebO/7Te19J1Mg0OBB+0jkxarlU2GI8l9iSiKGLB+C1afsAwSajWa83+F9tC+XfuBLIj0JNSQiEhftC14cdB+4fAAvr3xZjaUgnqjzBB6u9bCni0VERHoOuj/99FP3lMRHaNfTyx8J2cb08vwYiVyC7RNr098XFAE0fRJoMQCIKOXWYhB52jXLNQz6e5Bz4KZgUzCm3TYNrUq38nTRiPLcp3usYSiGazO8Nr38cuJl9f1LSElQy90qdsPgJoM9XSwiIvIyHEjNDSwwYkFCffQKDHTHy/u3lGTg34XAmg+A8/bpWJzCSwEtnwWaPAEER3iqhET5Ji45Ds8tew7borep5dCAUHzY6UM0LdmUR4F0TYOGECTgWW0uApHslS3dMobCSytewqm4U2q5TtE6eLP1m2osBSIiorQYdLuJBSZ3vbR/SroKbPnMPkBarP0Ex6lYdXt/7Xr3AwFBniohUb63sD3717PYfXG3Wg4PDMfs22ejfvH6PBLkE8IMiQiSgFsEhsLbvLXxLWw6u0ndLhZSDFM7TkVwQLCni0VERF6IQbcbmGFT6eUpFg7alWfXLgEb59qn/Uq8kv6+ci2A1oOB6t3sI5ET+Ymz8Wfx9NKncTTmqHMu4Lmd56JW0VqeLhqRy4TAgsmGF7wyvfz7A99jwf4FzjEUJOAuGVbS08UiIiIvxaDbTenlXyY0Qi8z08tzLS4aWDcD2PQxkByX/r7q3YE2g4HyLfN8rIj0RgJtCbgl8BaRIZGY03kOqhau6umiEblUGBJUwO1t6eU7z+/ExA0TnctvRL2BBsUbeLRMRETk3Rh0u4kMpka5cOU/YO0HwNbPgZTE1PUGE1C/j71lO7Imdy35pT0X96iU8kuJl9Ry+fDymNtlLsoUKOPpohG5Jb08CYFeFXRfSbyCYSuGIcWWopb71u6LXlV7ebpYRETk5Rh0uym9/IGQnUixRLnj5X3ThUPA6veBnd8C109mnNN+NXrE3me7cEVPlpDIo6Tv6MC/ByLeEq+WaxSugdmdZ6u+pES+KAgWvG942p5ebvZ80C1Tgo1aMwpn4s+o5caRjTGkyRBPF4uIiHSAQbebBlH7NKEp7g7koF63dPZfYNV7wJ6fgOtznCrmUPu0X1EvcNov8nvL/1uuWteSrElqXzSKbIQZnWYgIpCj9JPvCkMi3tCm2Be8YJDM+bvnY+XJlep24aDCeLvd26o/NxER0a0w6HYDAzQUNCRCk7mkKXMntwAr3wEOLE6/Pqgg0OJpoMWzQFhR7j3ye78c/gWvr3kdVs3eZaVtmbZ4r8N7CAkI8ft9Q77NbLAgGkVRDJdg9HDQveXcFnyw9QN12wADJredjBJhJTxaJiIi0g8G3S6mabJTbbgjaC9SUtq4+uV9I9hePgk4tDT9+tBiQNRzQLP+QHBBT5WOyKt8tfcrTN442bnco1IPjG8znq1r5BcMAD7GgxiCjxBs9NzpSkxSDF5Z8YrzwtfT9Z9GqzKtPFYeIiLSHwbdbkov/yqxMR5genmqU1uB5ZOBg3+m31kRZYBWg4DGj3rlPKxEnqBpGj7Y9gE+2vWRc92DNR7EiBYjYDRwejzyDwWQiBH4ECnGIMAgIbhnvovj1o1DdEK0Wm5esjmebfCsR8pCRET6xaDbTenlxYzxsDG9HDi9zR5sH/gj/U4qWA5o+xLQ8GGv6KtH5C0sNgvGrB2D/x3+n3PdM/WfwfMNn4fBQ4EHkWeyxlLwH0qhuCHOYycrvx75FUuOL1G3ZQyFiW0mwmQ0eag0RESkVwy63cAEGzoGHobV2gF+68wOe7C9//f06yPKAu0k2H4ECOA85kRpycjkLy1/CWtOr3H2HR3efDgervUwdxT5HRM0fI878aThJwR74P1Px51ONx/36KjR7MdNRES5wqDbDVJgwneJDfCI2Q+DyrO77MH2vl9vTCOXlm2Z/ost20Q3uJBwAc8ve17NxS0CjYGY3G4yOlfozL1FfinMkIChmId4U/4PWGa1WTFy9UjEWeLUcs/KPdG1Ytd8LwcREfkGBt1uSi8vZYz1r/Tyi4eBv8cDu39Ivz68NNB2qL3PNoNtokwdjz2O55Y9h5NxJ+1fm8BwTL9tOpqUaMI9Rn7LBCsOoQKKGbR8f+8v936pRiwXpcNKq/EUiIiIcotBt5vSy5ub/4PNmgKfF3sGWPEWsPVz4PrIrkp4KaDN9WDb7InEQCJ92HdlH0ZvH43LSZfVconQEph9+2xULVzV00Uj8igjNCxBe9xnXJev73si9gSmb5vu7OIxoc0EdSGMiIgotxh0uym9/KekunjSl9PLEy4Dq6cCG+YAKQnpp/5qNwxo8gSDbaJbWHlyJV7e/DISrYlquWqhqph1+yyUDCvJfUd+rwAS8Bw+x0VTzXwfrTzJmqSWZTyFpiWb+v2xICKivGHQ7WIaNBhgQwXjFdhsaVp+fYXlGrBpHrD6fSAxJnW9tAK0GmifazuILQJEt/LDwR/Uyb1j7t+mJZpi2m3T1AjJRH5Ps8Fk0LAb1VDUkH8XsH869BM2nN3gTCsf1GiQ3x8KIiLKOwbdbhpxtY75HDRf6tNtsyJk30IYtswArp5JXW8KBJo9Ze+3HVbMkyUk0gWbZsOMbTMwb9c857ouFbpgYtuJCDJx+jwiYbSlwAoj1qMJuhgP58tOOX/tPN7Z/I5z+fWo1xFqDuUBISKiPGPQ7ab08t+SamGA2QyfcHQVDH+OQEEZmdzBYAQaPAx0GA4UKufJ0hHphqSsvr76dSw+tti57u7yd+ONtm8gwMSfYyIHoy0ZgUhBP3yL06aW+bJjJm+cjKvJV9XtOyvfiTZl2vCAEBGRS/Aszw2MsKGK6SJsVp2nl186Aix5XU3/ZUi7vsYdQKfXgchanisbkc5cTryMF/95EduitzkHaHq56cvoXLQzjHIRi4icjDaLaunegdooAvenl687vQ5Lji9RtwsHFcYrzV7h0SAiIpdh0O2mEVcrmS7rd8ow6au98h1g/WzAZnGuthStBdMdb8NYuZ1Hi0ekyynB/noOJ66eUMshASF4q+1baF+2PaKjoz1dPCLvo1lV0L0H1RFluOLWt7LYLKqV22Fo06EoHFzYre9JRET+hUG3m9LLlyRXx0C9pZfLwG9bP7PPt33tYur6AiVg6/gaLpbqhMiSpTxZQiLd2XpuKwb9MwgxSfaBB4uFFMOMTjNQp2gd/V6YI3Izg2ZT6eWP4AccN97m1vf6Zu83OBJzRN2uX7w+7qpyl1vfj4iI/I9X5TSuXLkSPXv2ROnSpWEwGPDTTz/d8jkrVqxAkyZNEBwcjMqVK2P27NnwhvTyOgFnYdXTPN2ntgIfdQJ+HZIacAcEA22HAQO3AI0eAYwmT5eSSFd+P/I7+i/p7wy4ZUqwr3t8rQJuIro5g2ZVF7DXobH6310uJFzArB2z7O8JA0Y2H8nuHkRE5NtBd3x8PBo0aIAZM2Zk6/FHjx5Fjx490LZtW2zbtg0jR47EoEGDsGjRIniSARqKG+PVfJ+6mG/716HAvNuA0/a+pkrde4EXNtn7bnMKMKIcke/+3J1z8eqqV1XqqogqFYXPu3+OUgWYLUKUnZZumYDzJErDZnBf0D11y1TEWeLU7Xuq3YM6xXhBjIiIfDy9vHv37uovu6RVu3z58pg6daparlWrFjZv3ox3330X9957LzzFChOWJ1fBSwFenF4uFwR2fGMfKO3ahdT1xWsBd7wHVGztydIR6VayNVnNv/3z4Z+d6+6tdi9GtRwFs9GLfxOIvKyl24wU3I9fccSQ/fOCnNh/aT/+d/h/6na4ORwDGw10y/sQERF5VdCdU+vWrUOXLl3SrevatSs+/vhjWCwWmD3Qp1piWUkvrx9wxnvTy2VU8v8NAo6tSl1nDgM6jgBaDABMDAyIcuNiwkUMXT4UW6O3OtcNbjwYT9Z9UnWZIaLst3RLWvlqNEdpN52qTN06FRrsGWnPNHgGRUOK8vAQEZFb6DroPnv2LEqUKJFunSynpKTgwoULKFXqxjTOpKQk9ecQGxur/pcBjVwxqJGklcqpdZjBAs2meddASTJQ2sY5MPw9HoaUBOdqrVYvaF0nABFlrj/uxjLLdsi2edX2uIAvbpcvbpMetuvg5YNqwLTT8afVcpApCONbj0eXCl1UuTPrbuLt25RbvrhdvrpNeeHW+tSWotLLY1EAJQ1Gl+/3jWc3YvWp1ep2qbBS6FO9j08dW3/7LHsL7lvuWz3i5zZvsvtbquugW2RsPXKc2N6sVWnSpEkYO3bsDevPnz+PxMTEPJcnISFBTXOyxlIRT8XGIjraOyo10+XDKLh8JALPbXeusxYog5h2Y5Bcvh0gm54YneUHKiYmRu1fo9GrhgLIE1/cLl/cJm/frrXRazF552QkWO0Xs4oGFcXYRmNRI6RGllOCefM25YUvbpcvbtPVq1fz9Hx31qfxcbEqvfwuLMXulDtcOrWeHMN3N7zrXO5bqS9iLtoHO/QHvvhZ9hbct9y3esTPbf7UpboOukuWLKlau9OSijkgIABFi2aeJjZixAgMHTo03ZX5cuXKoXjx4oiIiMhzmUJComGCDY3Np1AwohkiI4vB463baz+AYcVkGKzJztVas6dg6DQahQILZO9lbDZ1IUP2ky9V0r64Xb64Td66XXLSOn/PfEzbNs2Zpiojk0/tMBWRoZG63CZX8MXt8sVtklk/8sKd9Wl4WKhKL1+GNihvDkZk5K2/T9m19PhS7I/dr25XK1QNDzZ4ECY/mp3DFz/L3oL7lvtWj/i5zZ+6VNdBd1RUFH755Zd065YsWYKmTZvetD93UFCQ+stIKh5XVD5pW9iNBte8Zq5dOQH88AxwYm3quiJVgF4zYKjQSqXB53TbXLWfvIkvbpcvbpO3bZcMmDZ23VjnQEyiW8VuGNd6HEICQnS5Ta7ki9vla9uU1+1wZ30qs4A4aC6sS602K2bumOlcHtxkMMzePOipm/jaZ9mbcN9y3+oRP7e5l93fUa/6tY2Li8P27dvVn2NKMLl94sQJ51X1Rx991Pn4AQMG4Pjx4+pK+969e/HJJ5+oQdSGDRsGT5L08k2WcjAFePCaxq6FwKw2qQG3wQi0GgQ8uwao0Mpz5SLyATK375N/Ppku4H6+4fN4u93bOQq4iejmo5cHwIquWOHSwHDpiaU4EnNE3W4U2Qhty7TlISAiIrfzqpZume6rY8eOzmVH2tpjjz2G+fPn48yZM84AXFSqVAm///47hgwZgg8//BClS5fGBx984NHpwoSkl7c0n4A1pUX+v3liDPD7y8DOBanrCpYH7pkLVIjK//IQ+RiZZmjg3wNxJv6MWg42BWNCmwnoUjH9TApElLfRyy0IwGJ0RCXNNanfNs2GuTvnOpcH1B/AWQWIiMj/gu4OHTpkOsKvgwTeGbVv3x5bt6ZOz+MNZAviNbPkx+Wvs/8CCx4BLh9NXVevD3DHu0BwwXwuDJHvWXZiGUasGoGE66P/S7/t6bdNR+2itT1dNCKfa+mWFPMIxAHG9LOU5NY/J/5RswyIesXqIao0L0QTEZEfBt2+QAJuG4zYnlIGJlM+7t4dC4BfXgQcU4EFRQB3TAHq359/ZSDyUdJCNmfHnHR9QesWrYsPbvsAxUOLe7RsRL7a0i3p5R2wDruN1fP8enJBf87OOc7lAQ3Yyk1ERPmHQbcbmGBF28BjsFqbw+1SkoE/RwCbPkpdV6oh0OczoHBF978/kY+LS47DyNUj8c9//zjXda/UHeNajUNwQN5Gfyaim7d0S3r5T+iGalre+3SvOb0Gey/tVbdrFanFvtxERJSvGHS7gQYDztvC3N9XLC4a+PZh4OSm1HWNHwW6vwOYGQwQ5dWxmGMY9M8gHI2xd9kwwIAXG7+IJ+s+yb6gRG5u6Zb08rI4DRhL5vn1Pt/9ufP2U/Wf4veXiIjyFYNuN5D08t0pJd2bXh69D/j6fvu0YMIUZO+7LUE3EeXZiv9WYPiq4YizxKnl8MBwvNPuHbQu05p7lyifRi+PwlbsNDTN02sduHwA686sU7fLFiiL28rd5qJSEhERZQ+DbjeQE4XbAg8jxeKm9PIjK4AFfYGkGPtyRBngwa+A0o3c835EftZ/e97Oefhw+4fQrs8VXLVQVUzrOA3lI8p7unhEfsKGZATgO9yFWnlML/9yz5fO24/UfgQmo2tGQyciIsouBt1uIElxR62FXTq3qNP2r4H/DQRsKfblkvWBh78DIkq5/r2I/Ey8JR6jVo9So5Q7dK7QGeNbj0eoOdSjZSPyt/RymX6zNg7kKb38QsIF/HrkV3U73ByO3lV7u7CURERE2cOg203p5QetxWE0ufhq+toZwJJRqcvVugL3fQIEFXDt+xD5oeOxx/Hi3y/icMxhZ//tgY0Gon+9/uz/SeSB9HIJuhvjX2wzdsz163y//3tYbBZ1+74a9/HiGREReQSDbrfsVCu6Bh1wXXq5zF2+8h3gnwmp65r1B7q9BeTntGREPmrVyVV4deWruGq56mwRm9xuMtqVbefpohH5J5tVpZd/gftQz5a7rLEUWwoWHliobhsNRjxc82EXF5KIiCh7GLG5gRUG7LaUgNFkdE3AvWwcsHpK6roOI4H2rwDuHh2dyA/6b3+06yPM2DbD2X+7csHKav7tChEVPF08Ir8lI5dLS3dLbEGC8c5cvcbKkysRnRCtbssFtJJheR8FnYiIKDcYdLuYxMgajDhmKwKjKwZrWfF2+oC7y3ig1cC8vy6Rn4tJisFrq1/D8pPLnetkVOOJbScizBzm0bIREVTQXQcHsTWX15e/P/C983af6n24S4mIyGMYdLtlp1pxZ9BepFia5e2F1k4Hlk9MXe7xLtD8qTyXj8jf7bu0D0P+GYKTcSed/befa/gcnq7/tEpDJSLPS4YZH+EhNLXl/Lmn4k5hzak16nbpsNJoVbqV6wtIRESUTTy7dAMrjNhoKQdjXvpbyyjlS15LXe46kQE3kQv8dOgnPPL7I86Au2BQQcy8fSYGNBjAgJvIiwQgBV2wAsZctHT/cPAHZ5eRe6vfy2nCiIjIo9jS7QYaDDhtK5j7KcNkHm6ZFsyh4ygg6nmXlY/IHyVZkzBpwyQsOrjIua5O0TqY0mEKShco7dGyEdGNjNBQFcdznF4uYzX8etg+TZjJYOI0YURE5HEMut2yU624J/hfWJJzkV5+fj+woG/qPNzNngLavezyMhL5E0k1Hbp8KPZc3ONcd3/1+zG8+XAEmgI9WjYiylwSzPgQj6O1LWdR97bobTgdf1rdjiodheKhxbmLiYjIo5he7qb08n+Sq8AUkMNrGomxwLcPA0kx9uXq3YDub3GUcqI8WH1qNR749QFnwB1kCsL41uMxOmo0A24iL2ZGCu7HrzlOL//l8C/O23dWzt3I50RERK7Elm43pZeftxXIWXq5DHv+07PAxUP25RL1gHs/BlwxAjqRH5IU0zk75mDWjlnOvp3lwsvh/Q7vo0aRGp4uHhFlI728HM4g2pCzbiRLji1Rt0MCQtCxXEfuZyIi8jgG3W5ghhV9gnfAktw0+09a9yGwz94HDcEFgQe+AIIKuKN4RD7vSuIVDF893Dl6sehQrgMmtJmAiMAIj5aNiLInCYGYgqfQ0Zr9Pbbq5CpctVxVt28vfztCzaHc3URE5HFML3c5DSkw4rekWggIMGfvKWd3AcvGpi7f8xFQpJLri0bkB3ac34E+v/ZxBtwyBdjgxoMxreM0BtxEeqFpMMOCfvgWATk4U/n1yK+pqeVVmFpORETegS3dbkovv6KFwGjKRmq4JRFY9BRgTbYvtxoEVO/ijmIR+TRN0/D5ns8xdctUpGj2gQiLBBfB2+3eRotSLTxdPCLKRXp5JC7iv2wG3dcs19QYDqJocFG0KMnvPREReQcG3W5KL38kZFv2Ri9f9S5wfm9qP+7b0szNTUTZEpMUg9dWv4blJ5c71zWObIy32r2FkmEluReJdJpePtnwArpmM718zek1qk+36FS+E+fmJiIir8H0cjewwIgFCfURYL7FVEQXDgKrp14/EmbgnjlAQJA7ikTk0+nk9/9yf7qAu3+9/vi468cMuIl0LBDJGKLNzXZ6+bITy5y3JegmIiLyFmzpdhMLTLcerfy3lwCbxb7caiBQoo67ikPkF+nkhYIKYVLbSWhTpo2ni0dELhCE612vbsFitWDFfyvU7fDAcDQrmY1MMyIionzCoNsNzLCp9PIUS8ubP2j3j8BR+wkCCpUH2r3sjqIQ+SSmkxP5Og3JjvRy260fveHsBsRZ4tTt9mXbw2zK5kCmRERE+YDp5W5KL/8yodHN08utFuDvN1OXu78NBHJaE6Ls2Hl+J9PJifwkvXy4NiNb6eV/n/jbeVumCiMiIvImbOl242BqN7X9a+DSEfvtim2BGt3dVQwin0on//7Y9/jkwCdMJyfyo8HUsvPbsOrUKnU70BiIqNJR+VAyIiKi7GNLt5vSyx8I2YkUS3LmU4SteCt1udNodxSByKdcSbyCF5e/iLn75zoDbhmd/Pue37P/NpGPkvTy9w1PI+UW6eVHYo7gbPxZdVv6coeamTlGRETehUG3i8n4aDKI2qcJTWEOzGQk8h3fALGn7LerdwPKNXd1EYh8yqazm3DvL/dixcnrYyAA6Fe3H0cnJ/KDQdTe0KbAbDJk+TjH3NyiVelW+VAyIiKinGF6uRsYoKGgIRGazXZjRL5+Vupy+1fd8fZEPiHFloJZO2Zh3s550KCpdRHmCDU6ebty7TxdPCJyJ02DDQZcQBGVPp6VNafWOG9z5gIiIvJGDLrdslNtuCNoL6wpGQKDw8uAC/vtt8u3Aso0dsfbE+neqbhTGL5yOLaf3+5c16xEMwytORS1y9T2aNmIKH9YYMbHeBAdtZsn5SWkJGDLuS3qdqmwUqhUsBIPDxEReR2ml7uBpJd/ldj4xvTyDXNSb7d81h1vTaR7fx77E/f/735nwG0ymPBi4xcx5/Y5KBZczNPFI6J8TC8fgQ+zTC/ffHYzkm328VNal2kNgyHrVHQiIiJPYEu3m9LLixnjYUubXh57Bjj0l/12wXJAzTvc8dZEunXNcg1vb3obiw4ucq4rU6AM3mr3FhoUb5D++0REPk/Sy0+hJGxZpJfLmA8OUaU4ajkREXknBt1uYIINHQMPw5piH2VZ2fU9oF0PGho8BBhN7nhrIl3af2k/Xl75Mo7GHHWu61axG0ZHjUZ4YLhHy0ZEnrl4bUEAvsedaJ1Fl25HarloWrJp/hSOiIgoh5he7gYpMOG7xAYwB16fX1Su0suo5Q4NHnTH2xLpjgyQ9NXer/DQbw85A+6QgBCMazUOb7d7mwE3kR8LggVDMQ8BRsNNs2P2XNyjblcuWBlFgovkcwmJiIiyhy3dbrpCX8oYm5oOe34/EG0/MUDZ5kDRKu54WyJduZx4GaPXjMbyk8ud62oWqamCbQ6GRESSXn4E5W+aXr7j/A6kaPaMsiYlmnCHERGR12LQ7ab08ubm/2C1Xk8v3/976p11ervjLYl0ZeOZjRixagSiE6Kd6x6p9QiGNBmCQNP1DBEi8mspCMAStEcT7dap5Qy6iYjImzG93MXkgrykl/+UVBdm8/XgYf/i1AfU6O7qtyTSjWRrMqZsmYL+S/o7A+7CQYXxYacP8WrzVxlwE5FTICx4Dp/fNL2cQTcREekFW7rdwAAbKhivQNOsQNx54OT10VUjawNFOIco+afDVw5j+Krh2Hdpn3Ndi1ItMKnNJBQPLe7RshGRt9FghRH7UCXT9HK5gLfz/E51u2yBsigZVtIDZSQiIsoeBt1uYIKGOuZzsFltwPHV6uRBqdbZHW9H5PWDpX2z7xvVwp1kTVLrAowBGNhoIB6v8ziMBibcEFGG3w1ABd3r0QR1cWNL94HLB5zzczeMbMjdR0REXo1nu24g6eW/JdVCgNkMHFuTekfFtu54OyKvdSHhAp5d9iwmbZzkDLhllOFv7vgGT9Z9kgE3Ed1UIFLQD99mml7+74V/nbfrFqvLvUhERF6NLd1uYIQNVUwXYbVagePXg25pzSvXwh1vR+SV/j7xN8asHYPLSZed6x6u+bAaLC04INijZSMi7yct3TtQO9P08l0XdjlvM+gmIiJvx6DbDYzQUMl0Gcb4C6lThZVqCARHuOPtiLyKzJ379qa3sejgIue6YiHF8GbrN9GmTBuPlo2I9BV070F1VMtk9PLdF3ar/wMMAWqqQSIiIm/G9HI3pZcvSa6OAlfsJwVKhVbueCsiryIDG93/y/3pAu7byt2GRXctYsBNRNlm0DSVXv4IfrghvTzeEo8jMUfU7WqFqyHIFMQ9S0REXo0t3W5KL68VEA1z9OnUlaUbueOtiLxCii0F83bNw5wdc2CVUfsBhASEYHjz4ehdtTcMhsyn/CEiuunvCkzYhAYw2dKv33NxD7TrA5QytZyIiPSAQbeLyYmAARqKG+NhvnA9tVyUrO/qtyLyCv/F/ocRq0dgx/kdznX1i9XHpLaTUD6ivEfLRkT6JbXpSZRGBdwYdDsw6CYiIj1gerkbWGHC8uQqCL90faAXcyhQtIo73orIY2QqsB8P/oj7frnPGXCbDCY82+BZfNb9MwbcRJQnZqTgfvwKU4b0cpkuzIH9uYmISA/Y0u2m9PKmAf/BePV6enmJuoDR5I63IvLYVGAyMvmKkyuc68oWKKtatzlnLhG5Kr18NZoj1JZ+JLWDlw+q/40Go5qCkIiIyNsx6HYDuSZf3BCrUuOU4tXd8TZEHvHnsT8xfv14XEm64lwn/bZfbf4qwsxhPCpE5LLOWrEogNA0a602Kw5fOaxulw8vz+kHiYhIFxh0u2maE4M1DmZTin1FEaaWk/7FJMVgwoYJWHx0sXNd0eCiGNNqDDqU6+DRshGRj9Hs6eV3YSk2G5s4V5+4egLJtmTnyOVERER6wKDbDUywoVRAokqNC4CV/blJ91adXIU31r6B8wnnnes6V+iM11u+jsLBhT1aNiLyTVKHLkMbFNK0G1LLRbVCDLqJiEgfGHS7SUFDfOoCW7pJp65ZruGdze9g4YGFznXhgeEY1WIUelTqwanAiChfHbpyyHmbLd1ERKQXDLrdlF7eUtuMAIN9vmIU4UAvpD9bzm3BqNWjcCrulHNd69KtMbbVWJQIK+HRshGR75NMsa5Ygc3GqMxbupleTkREOsGg203p5QeNNdAAR2AOLQgEph0Ghsi7JVmTMGPbDHy2+zM1lJEICQjBsKbDcH/1+9m6TUT5QIMFAViMjiiRZvRyR0t3kClIzZhARESkBwy6Xcze9cyGSFyEQQKW8NKufgsit9l9cTdGrRqFwzH20YFF48jGGN96PMpFlOOeJ6J8I3VoBOKuzwkCpNhScDLupLpdPqI8TJyKk4iIdIJBtxsUQjw6Ya19IbykO96CyKUsNgs+2vUR5u6YixTNPuq+2WjGoEaD0Ld2X57cEpFH0ss7YB02G+2zI5yJP6MCb1EhvAKPCBER6QaDbjcoZbiE73En7sYfMEeUcsdbELnMkStHMHL1SNXK7VCrSC1MaDOBfSaJyGMkvfwndEP56+nlJ2JPOO+Tlm4iIiK9YNDtBsUNl1EWp6+nlzPoJu8kLUbSb3vm9pnOeW9NBhP61+uPZ+o/A7PJ7OkiEpHf0lQdKnUpUFetOR573HlvhQi2dBMRkX4w6HaDSEMMorDVvlCAozyT9zl85TBeX/M6dl3Y5VxXMaIiJrWdhLrF7Ce4RESeTi+XunSzsZtaPnE1TUt3OFu6iYhIP4yeLoAvKoQ4fIl7kCzXNMKKebo4ROlat6Xv9v2/3O8MuI0GIx6v8zi+7/k9A24i8hpSh0pdmnI9vZwt3UREpFds6XaDgoY41MZRNXUYggu54y2IctW6/drq1/DvxX/TtW6/2fpNNIxsyD1KRF5F6tDaOIAUQ410fbpDA0JRLIQXtImISD8YdLtp9PLGuB7YhDDoJs+3bs/fPV/13ZZRyh2t24/VfgzPNXwOwQHBPERE5JVBt9Slmw13wWqz4nSc9O8GyoaXhcFgn0aMiIhIDxh0u5gkwYUZEvAxHkRfLEQgW7rJgw5dPqT6bmds3R7fZjwaFG/AY0NEXp1e/gXuQx2bhgsJF5zTGZYuUNrTRSMiItJ3n+6ZM2eiUqVKCA4ORpMmTbBq1aqbPnb58uXqanfGv3379sHTfbpbYos9vTyksEfLQv5JWoU+3vUx+vzaxxlwS+v2E3WfUH23GXATkbeTOlTqUqPRPke3Q6kwzgpCRET64lUt3QsWLMDgwYNV4N26dWvMmTMH3bt3x549e1C+/M1HKt2/fz8iIiKcy8WLF4cnFTbEoQ6OQjOYgKBwj5aF/M+hK4cwYsMIHIg94FxXqWAl1XebwTZll9VqhcVi746QUzabTT03MTERRomYfIAet8lsNsNkMkHPQXcdHMRmgwFn48861zPoJiJ/qU/zgx7rNz3WpV4VdE+ZMgX9+vVD//791fLUqVPx559/YtasWZg0adJNnxcZGYlChbyn73QokjATj+KJwMUIYb8zyse+25/++ylm7ZiVvu92ncfwfMPnEWQK4rGgW9I0DWfPnsWVK1fy9BpSiV+9etVn+t7qdZukbixZsqSuyuyQDDM+wkNobNPY0k1Eflmf5ge91m96q0u9JuhOTk7Gli1bMHz48HTru3TpgrVr12b53EaNGqmrM7Vr18Zrr72Gjh073vSxSUlJ6s8hNjZW/S8fNvlzxQe3kOEqumAFDIFhLnlNbyDb4fhS+hJf2a6Dlw9i9NrR2HNpj3NdpYhKGNdqHOoXr6+W9b6NvnKsvH2b5AQhJiZGZQyFhobmuoKRq+ZyddiX6Gmb5HN17do1nD9/Xt2Wk4WM8vq5c2d9KmUOQIqqSy/iYecgaqJEaAmv+s7ojTf+7vgK7lvuW3fUp/lBT/WbXutSrwm6L1y4oNIvSpQokW69LMuHNjOlSpXC3LlzVd9vqfi/+OILdOrUSfX1bteuXabPkRbzsWPH3rBedqYE7nklrxGGJBTDccQbqyE6Ohq+QD5Q8sMhHzhfSj3R+3ZJ6/Z3x77Dl4e+hEW73roNI3qW6on+tfojWAvmZ9CLedvnT8pz8eJF9btbsGDBXL+ObI+QdCxvPsnw9W2SYyjH9Ny5c2o542dMWjXywp31aWLCNRihoSqO42xSEo5fOuW8z5xg9pnfNU/wtt8dX8J9y33r6vo0P+ixftNjXeo1QbdDxoMtH4SbfQBq1Kih/hyioqLw33//4d13371p0D1ixAgMHTo03ZX5cuXKqatQafuF51Zw0BkYDRqm4Ck8ad6mUt99gXzY5DjIfvKlSlrP27X30l6MWTcG+y6lDhxYuWBljGk5BiW1krrcJl89VnrZJgmUJA2uQIECCAjIe/Xgi1fN9bZNcizlorakxskApWllXM4pd9anR0NCkAQzPsTjiDIH41LKJbU+wBCAGmVrwGTUb191T/O23x1fwn3Lfeuu+jQ/6K1+01td6jWfgmLFiqkrLBlbteVqdsbW76y0bNkSX3755U3vDwoKUn8ZScXjisrHDAvMSMH9+BUB5oo+VaFJJe2q/eRN9LZdSdYkzNkxB5/8+wmsmtXZd/vxOo+rebfNBnsrkJ62yVePld62ScrgKE9ernanvVjqK1fN9bpNaY9pxs9YXj9z7q1PDc669IzpCZy9Zj83iAyNhDmAJ4a+9Lvja7hvuW9dWZ/mB73Wb3qrS73m1zYwMFCliS9dujTdellu1apVtl9n27ZtKu3cUwJtiSolrhzOwGAO8Vg5yDdtj96O+3+5H/N2zXMG3FULVcWX3b/EkCZDOFgaEfkMR11qNWiISYpxBt1ERER64zVBt5A0tY8++giffPIJ9u7diyFDhuDEiRMYMGCAM5Xt0UcfdT5eRjf/6aefcPDgQezevVvdv2jRIrzwwgse24YAWxKSEIhJeB4JxlCPlYN8yzXLNUzaMAmPLn4UR2OOqnUBxgDVsv3dnd+hXvF6ni4ikVeQaSfvvvtul7+uTGVZvXp1hISEqAvEq1atytZzKlWqpFLPMnvOmDFj1JXztH+ZDdLirxx16aWUBOe6oiFFPVomIiJ/4M66tFIW9aIv16VeFXQ/8MADKpAeN24cGjZsiJUrV+L3339HhQoV1P1nzpxRQXjaEc+HDRuG+vXro23btli9ejV+++033HPPPR7bBrNNeqFZ0A/fIsDMKZoo79aeXoveP/fG1/u+hgb7YBf1itVTwfazDZ6F2cRUSyKHTZs2oXnz5i7dIQsWLFAXgWV2ja1bt6r6pnv37unqo8yeIycto0aNUhlYN3tOnTp1VN3m+Nu1axcPptA0Z10aZ0gdlK1YSDHuHyIindalg7NRL/pqXepVQbd47rnncOzYMTUauUwhlnZAtPnz56uRyR1eeeUVHDp0CAkJCbh06ZK68tGjRw94kllLUilxkbgIgzlvg9SQf5N0ytfXvI5nlj6D0/H26XKCTcEY1nQYvuj+BaoVrubpIhJ51XQn0k1JppiUylmudLdo0cIlrz1lyhQ8+eST6q9WrVrq4rAMGDZr1qwsn9OvXz/0798/y+fIADtyRd7xJ4NbZWXhwoWoV6+eanEvWrQobr/9dsTHx8MXOerSq0gNutnSTUSk37q0XzbqRV+tS70u6NY76dMtKXFjDUORaGDQTbmz7Pgy3P3z3fjp0E/Odc1LNscPd/2Ax+o8xpF7iTKQgTgl20ls375dXen+888/0z1m4sSJagTSrP4ypq1JRpVcAO7SpUu69bIsJyWZyclzpHtU6dKlVercgw8+iCNHjtz02Mo2PfTQQyr4ly5YchFaMrsc0734GkddeiUlTdAdzPRyIiJ3YV3qPl4zermvkJbuQCRjiDYXFvNjni4O6cyFhAuYuGEilh5PHVCwgLkAXmr6Eu6tdi9HlSS6CRk99PTp0+qKdYMGDTJ9jIwP0qdPnyz3YZkyZdJ/Jy9cgNVqvWEWDVnOONtGTp8jrQeff/656isu83+OHz9eDRwqY5TIdmQWdKekpKhA29HtSq7U+ypHXfqu4TbnOqaXExG5D+tS92HQ7WJmW7L6PwjJSA5gn27KHmmp+uXIL3hr41uITY51rm9ftj1ea/kaSoZ534AQ5D96Tl+N81eTcvQcGX/AgLxNPVI8PAi/DGyT7cdLf6+bBdyiSJEi6i83Mk6jknaKldw+R/qlOUjwHBUVhSpVquCzzz5LN/+1g2xbp06d1GO7du2qWs7vu+8+FC5cGL5K6tJYjX26icg/61JXYF3qHXUpg24XM2kpSEYgJhtewFMIdPXLkw86E3cGY9ePxZpTa5zrCgcVxvDmw9G9Une2bpPHyUnC2djUwMdbSVp5VkG3pJfLX1YWL16sBmpxKFasmEq3y9iqHR0dfUNLdl6eI8LCwtRJgKScZ0ZeU6bRlBT1JUuWYPr06arP3YYNG1R6um/RnHVprG2Lcy37dBORXrEuNfl1Xcqg28WMsKqUuOHaDMQGvOzqlycfYtNs+G7/d3h/y/u4lnLNuV4CbQm4iwTnrkWOyB1XyXPKVS3dOSGjlfbu3fum9+cmvVwGlJEpSqSC7tmzp3O9LPfq1SvT10j7nLTlyeo5QgYQlb7aaYP+jKSlvHXr1upv9OjRKs38xx9/zLRlXO8cdelDqO9cxz7dRORPdakn3tfddWnvbNaLvlaXMuh2MYOWov6Xnt2akbuXMncs5hjeWPsGtkZvda6LDInE61Gvo0O5Dtxt5FVykuLtSKOWvscymuitUrBdyWazYefOnapvt1zpLliwoEvSy6US7tu3Lxo3bqwq6Hnz5qnpSuTEw2HGjBmqwl62bFm65zRt2lSljc+dO/eG58iUlxLIly9fXl25lz7dsbGxeOyxzMcDkavw8vqSChcZGamWz58/r0Z09VVSl169nl4eZg5DcAAHKCUi/6hLPcXddWnTLOpFX65LGRW6Kb38fcPT6K9x91J6KbYUfL7nc8zcPhNJ1tR+PTJImgyWFh4Yzl1GlEtS0b766qt4//33VUX93nvvuWRfPvDAA2pwtAkTJqjBzOrWrYvff//dOZiZkPsPHz6c7jkXL17EuHHjbvqckydPqtHI5bkyvUnLli2xfv36dI9JKyIiAitXrlRTpsgJhTxOtjFt33Bf4qhLE21/qLlWCgamP/EjIiJ91aUXb1Ev+nJdatB8da6RbJKdLVdwYmJi1EHIq2/mTsRDp99St6PbT0Zkx2fhC+Sql1w9kitCMrKhr8jP7dp/aT9Grx2NPRf3ONeVLVAWY1qNQYtSrpkDUfBY6Ye3HavExEQcPXpU9WkKDs59i6KnWrrdSa/blNUxdXX958rXW7doGqJ2jYacoDSqVAFWaKhVpBa+6/ldnsvp77ztd8eXcN9y37q6Ps0Peq3f9FaXsinWxUyaFTYYcAFFYOU06CTpkdYkzN05F5/s+gQp17sfGA1GPFLrEbzQ6AWEBIRwPxERZSB16X+GorBK24ABiAjK+4UBIiIiT2DQ7WJGzQoLzPgYD+IRppf7va3ntmLMujE4GnPUuS+qFKyCca3HoX7x1MGBiIgoPalLv8IDCNAWI8WQwvRyIiLSLQbdbhi9XOYVHYEPcTZwuqtfnnQiLjkOU7dOxYL9C5zrAowB6F+vP56q9xQCTZxOjogoK1KX9jbPxTfGUmq5YBD7dBMRkT4x6HZDS7ekxJ1CSZhgcvXLkw6sPLkS49aNw7lr55zr6hWrh7GtxqJa4WoeLRsRkV5IXXocpWDQDNAMGiICmV5ORET6xKDbDX26LQjA97gT92ocjMCfXEq8hMkbJ2Px0cXOddJfe2CjgXi45sMwGXkRhogoWzRN1aXbLN1g0v6yp5ezpZuIiHSKQbdb0sstGIp5OB34iatfnrx01Mdfj/yKtze9jStJV5zro0pFYXTUaJQNL+vR8hER6ZHUpVULfIUUY1G1zKCbiIj0ikG3ixlt9vTyIyiPYI5e7vNOx53GuPXjsObUGuc6SYF8pdkruKvKXZx6gYgol6QuPWcrD4N2TaWXc55uIiLSKwbdLmZCClIQgCVojzs0zn/pq6w2K77d/y2mbZ2GhJQE5/quFbtiePPhKBZSzKPlIyLSO6lLLye2hFFbDqvByinDiIhItxh0u2EgtUBY8Bw+x+nAO1z98uQFDl85jNFrR2Pn+Z3OdZEhkXit5WvoWL6jR8tGROQrpC61Fv4ZVmMBtcyB1IiISK8YdLuYETZYYcQ+VEGE5upXJ0+yWC34aNdHmLtrLlJsKc71far3weAmgxEeGO7R8hER+Q5N1aVJyRVh0C6q9PIwc5inC0VERJQrzH92Nc1+orAeTWBl0O0zdpzfgT6/9sHMHTOdAXeFiAr4pOsneD3qdQbcRF5i8ODBuPvuu13+ujNnzkT16tUREhKCJk2aYNWqVVk+fuXKlejZsydKly6txnb46aefbnjMmDFj1H1p/0qWLOnysuuV1KWmhDowXu+qFWoO9XSRiIj8gjvr0kqVKiE4ONjv6lIG3W4QiBT0w7cwBzCRQO+uWa7hrY1voe/vfXHoyiG1zmQwoX+9/ljYcyGalWzm6SISURqbNm1C8+bNXbpPFixYgCFDhmD48OHYunUr2rZti+7du+PEiRM3fU58fDwaNGiAGTNmZPnaderUwZkzZ5x/u3btcmnZ9V6Xnir6J6xGq1pmSzcRkb7r0sGDB2PUqFHYtm2b39WlDLpdzHD96vxW1IXVZnP1y1M+khHJe//cG1/u/RIa7GkLtYrUwrd3fosXG7+I4IBgHg8iL2GxWBAYGIi1a9eqCl2udLdo0cIlrz1lyhQ8+eST6q9WrVqYOnUqypUrh1mzZt30OXIiMX78eNxzzz1ZvnZAQIC6Iu/4K168eJaPX7hwIerVq6da3IsWLYrbb79dnZT4IqlLzYnVYNAMCDAEINAY6OkiERH5NHfXpf369UP//v39si5l0O1y9vTyPagOG9PLdelK4hWMXDUSA/4agNPxp9W6IFMQhjYZiq/v+Bo1i9T0dBGJKAOTyYTVq1er29u3b1dXuv/88890j5k4cSIKFCiQ5V/GVLfk5GRs2bIFXbp0SbdeluWkJK8OHjyo0uYk3e7BBx/EkSNHbvpY2aaHHnpIBf979+7F8uXL1YmIpvlmZSN1aYHE8iq9PMQcwikYiYjcjHWp+zD/2U0pcY/gB5wK6OuOlyc3kRPXP479gckbJ+NS4iXn+uYlm+ONqDdQPqI89z35pzntgbjoHD0lQGWHSO5PHhSIBJ5Zka2HGo1GnD59Wl2xllS0zAwYMAB9+vTJ8nXKlCmTbvnChQuwWq0oUaJEuvWyfPbsWeSFtB58/vnnqq/4uXPn1NX8Vq1aYffu3Wo7Mgu6U1JSVKBdoUIFtU6u1Psig6apunR78RWwGgOYWk5EflmXugTrUq+oSxl0u5yGFJiwCQ1QhunlunEu/hwmbJyAFSdTT/DDzeF4qelLuKfaPWxhIf8mJwlX7Vkf2ZHHUDvXpI/YzQJuUaRIEfWXG5Jil/EiXcZ1OSVpcw5S4UdFRaFKlSr47LPPMHTo0BseL9vWqVMn9diuXbuq1vb77rsPhQsXhi+SujQyriYuFjyC0AAOokZE/lWXegrrUvdg0O0GGgw4idIo7ZsZfz7Fptnwy4lf8PGhjxFvSe3L0al8J4xsMRKRoZEeLR+RV5Cr5Dlg/+mzt3Qb8vF9Ja08q6Bb0svlLyuLFy9Wg7s4FCtWTKXbZWzVjo6OvqH1O6/CwsJUQC0p55mRcixdulSltS9ZsgTTp09Xfe42bNig0tN9jRUGhCcXhUE7ypZuItK/HNZpnnpf1qXuwaDbxQzQYEYK7sevOBXQ39UvTy50NOYoxqwdg63RW53rioUUU8F25wqdua+JHLKZ4u2kaSp1SwY2QR5bg3NCRivt3bv3Te/PTXq5DCgj05pIsCvTljjIcq9eveBKSUlJqq922qA/I2ldb926tfobPXq0So378ccfM20Z1zO5ZGM1WLE+coNa5nRhROR3damHuLsu7Z3mtf2pLmXQ7WKG6ylxq9EclTmSmley2CyY/+98zN4xG8m2ZOf63lV7q3TygkEFPVo+Isodm82GnTt3qr7d0mpcsGBBl6SXSyXct29fNG7cWFXQ8+bNU1OcyImHg0xnIhX2smXL1HJcXBwOHbJPMyiOHj2qWg/k/cuXt48PMWzYMBXIy7K0nEuf7tjYWDz22GOZlkNatOX1Ja08MjJSLZ8/f16NAuuLrhoCUPtybewrtI/p5UREPlKXNm3aVHWnmjt3rl/VpQy63ZReHosCzmmmyHvsvrAbo9eOxoHLB5zrSoWUwtjWYxFVJsqjZSOivJGK9tVXX8X777+vKvf33nvPJbv0gQceUAOqTZgwQQ3AUrduXfz+++/OAViE3H/48GHn8ubNm9GxY0fnsuPquZwEzJ8/X90+efKkGo1cnivTm7Rs2RLr169P97ppRUREYOXKlWqaFTmhkMfJNqbtG+47NMQZjAixhqhmb87RTUSk/7r04sWLGDdunF/WpQbNV+caySbZ2XIFJyYmRh2EvFoxrR/aX16obp+692eUqdcBvnLVS64eyRUhGSVYbxJTEjFzx0x8tvsz1Y9bGA1G9K3VF/eVvg/lS5XX5Xb54rHyp+3ytm1KTExUV5Glf3BwcO7nodfSpJfndbAxb6HXbcrqmLq6/nPl6637/j0UPDgJD5QppZYfqPEAXmv5Wp7LSN73u+NLuG+5b11dn+YHvdZveqtL2dLthj7dkl6+DG1Q02oP7siztp7bijfWvoFjscec66oXro5xrcahVpFa6uSDiIi8SxzMqH+pPv4t9C9CAkI8XRwiIqJcY9DtTrxa5FHXLNcwbes0fLPvG2eqv9loxoAGA/BE3SfUbbkqTURE3icpTR0aZAryaFmIiIjygkG3y2kIgBVdsQKnTMNc//KULevPrFcjk5+KO+VcV79YfYxrPQ5VClXhXiQi8nJWow07i+xUtxl0ExGRnjHodjVNgwUBWIyOaMD08nx3NfkqpmyZgoUH7P3qHSdrAxsNxCO1HoHJaMr/QhERUY5IG3cCTGhyoQm2FdmGQFMg9yAREekWg2439euOQBwMBg5Qkp9WnlyJcevG4dy1c851TUo0wdhWY1EhIvMRDImIyDslG4EEU4KKwNnSTUREesag2w0Bt6SXd8A6nDIx6M4PMUkxeHvT2/jf4f8518mgO0ObDEWfGn3UKOVERKQvyUYNewrvUbcZdBMRkZ4x6HYDSS//Cd3QPIWDdLnbsuPL8Ob6N3Ex8aJzXVSpKLzR6g2UKVDG7e9PRERuoGlIRABaRrfEpmKbmF5ORES6xqDbTa3dZXEaBs5/6TYXEy5i4oaJWHJ8iXNduDkcLzd7GXdXvZvzDBIR6ZqGZANwMegiNIOGYJN3z3NLRESUFQbdbkovj8JWppe7gaZp+OPYHyrgvpJ0xbm+Q9kOeD3qdUSGRrrjbYmIyAPp5QcLHlS3OZAaERHpGYNuN0hGAL7DXWiTYnXHy/utS4mXMH79eCw9vtS5rlBQIYxoPgLdK3Vn6zYRkQ9JghltzrbBush17NNNRES6xhGm3NDSbYINtXEARqaXu8xfx/9C7597pwu4u1Togp96/YQelXsw4CYiZfDgwbj77rtdvjdmzpyJ6tWrIyQkBE2aNMGqVauyfPysWbNQv359REREqL+oqCgsXryYRykHEg0aToadhM1gY0s3EZGP1KWVKlVCcHCw39WlDLpdzh50N8a/nBPaRSOTv7LyFQxZPkS1dDtat99p/w7e6/AeioYUdcXbEJGP2LRpE5o3b+7S11ywYAGGDBmC4cOHY+vWrWjbti26d++OEydO3PQ5ZcuWxeTJk7F582b1d9ttt6FXr17YvXu3S8vmyyxGDcfCj6k+3Ry9nIhI/3Xp4MGDMWrUKGzbts3v6lIG3W5KL/8YD8JiY3p5Xqz4bwXu/vluLD6aekXrtnK34cdeP6JbxW4uOFJE5CssFgsCAwOxdu1aVaEbDAa0aNHCJa89ZcoUPPnkk+qvVq1amDp1KsqVK6euwN9Mz5490aNHD9U6Ln8TJkxAgQIFsH79+ps+Z+HChahXr55qTS9atChuv/12xMfHwz9pKr2845mOMNlMCAoI8nSBiIh8nrvr0n79+qF///5+WZcy6HYDaeluiS0wMb08V64mX8Vrq1/DC3+/gAsJF9S68MBwTGwzEVM7TkWxkGKuPWBEpHsmkwmrV69Wt7dv344zZ87gzz//TPeYiRMnqso6q7+MqW7JycnYsmULunTpkm69LMtJSXZYrVZ8++23qtKX1LjMSHkfeughFdjv3bsXy5cvxz333KMGj/RXyQYbDkQcUOnlbOkmInI/1qXuw4HUXMyg2dPL6+AgThlNrn55n7f21FqMXjsa566dc65rU6YNxkSNQYmwEh4tG5G/euDXB5wXwLJNYkVD3t5XLrAtuHNBth4rY2icPn1aXdVu0KBBpo8ZMGAA+vTpk+XrlClTJt3yhQsXVNBcokT63x9ZPnv2bJavtWvXLhVkJyYmqoD+xx9/RO3atW8adKekpKhAu0KFCmqdXKn3Z4lG4FTYKXWbQTcR+WVd6gKsS+vBGzDodoNkmPERHkIPC9PLsyveEo93N7+LhQcWOteFmcPwSrNX0Ltqbw6URuRBcpIQfS3a64+B9BG7WcAtihQpov5yQ1Ls0pIW6IzrMqpRo4Zqdb9y5QoWLVqExx57DCtWrMg08JZyd+rUSQXaXbt2VS3p9913HwoXLgx/ZdHM6HyqM/4u9TfMRrOni0NElCesS+HXdSmDbpeTebpT0AUrYDI94vqX90Fbzm3BqNWjcCrO3qIhWpZqiXGtxqFUgVIeLRsR2a+S55iLWrpzQirlrIJuSS+Xv6zIqKgyuIuzDMWKqXS7jK3a0dHRN7R+ZyT94qpWrapuN23aVA1MM23aNMyZM+eGx8p7LF26VKWsL1myBNOnT1f96TZs2KBGevVHFqMNB4vsVOnlDLqJSO881T2Sdekor6hLGXS7YcowIzRUxXGcMjG9PCsWqwUzd8zEx7s+hqbO0IGQgBC81OQl9KnRh63bRF4iuyneaa9cS6p0QEBAvn6PJZ27d+/eN70/N+nlEjjLtCYSEMuALg6yLCOo5nS/JCUl3fR+2VetW7dWf6NHj1Zp5pKSPnToUPgdzT56+blge1cjBt1E5G91qae4uy7tnea1/akuZdDtBjLi6od4HL2ZXn5TR2KOYPjK4dh7aa9zXaPIRpjQZgLKhZdzx2EhIh9ns9mwc+dO1bc7LCwMBQsWdEl6uVTUffv2RePGjVUlPm/ePDXFiZx4OMyYMUNV6suWLVPLI0eOVFOhyMisV69eVQOpyeBof/zxR6bvIVfh5bmSChcZGamWz58/r0Z49Vc2mxk9/uuBJWWWcApOIiIfqUubNm2qxjuZO3euX9WlDLrdwIwU3I9fAdMD7nh5XZOrU9/u/xZTNk9BojVRrQswBOD5Rs/jiTpP8MSKiHJt/PjxePXVV/H++++ryv29995zyd584IEH1IBqMlWJDHhWt25d/HwEQ4kAACaJSURBVP77784Bz4Tcf/jwYefyuXPn1MmFPF5OWOrXr69OEjp37pzpe0RERGDlypVqCpXY2Fj12lJ+OdnwVxajFeuLr1fp5UYDJ1shItJ7XXrx4kWMGzfOL+tSg+bP85EA6oDIQYyJiVEHKq/Wvf8QomJ+V7dPP/wPSldvDF+56iV9GOWqkYwSnNsBJF5f8zpWn7JP6yMqFayESW0noU7ROtDrdnkbX9wmX90ub9smGWX76NGjqt9TcHBwrl/HU+nl7qTXbcrqmLq6/nPl661f8DbejfkY+4MCEQATtj22Pc/lI+/83fEl3Lfct66uT/ODXus3vdWl/LV1w5RhSQjEJDyPZIvF1S+vW8uOL0Pvn3unC7gfrPGg6t/iqYCbiIi8l00LQK/jvRBsC/R0UYiIiPKE6eUup8EMC/rhWySZ7oO/k6nA3t70Nn44+EO6URRlZPK2ZVNHCCYiIko7KKnFYMM/pf6BzcDpN4mISN8YdLuBjF4eiYs4ZfLvRILdF3fjlRWv4MTVE851t5W7DWNajUHhYM/Pl0dERN7LYgRizbEIN3h3aiYREdGt+HdU6Kar85JePtYw1G/Ty6VvyBd7vsAjvz/iDLhDA0JV6/bUjlMZcBMRUTbqkgDcd+w+BDK9nIiIdI4t3W4QiGQM0eYiNuAu+JvLiZfVYGkrTq5wrqtbtC7ebvc2ykVwKjAiIsqeZIMVv5X9DaEGE3cZERHpGoNuNwlCsmr39iebzm5Sc29HJ0Q71z1e53EMajQIZpPZo2UjIiL9kHlVUgySYm6BycD6g4iI9I3p5W5IL09GICYbXoAlJQX+wGqzYtb2Wei/pL8z4C4cVBgzO83ES01fYsBNREQ5pKlhSe8+cTcCNQbdRESkb2zpdjlNpZcP12bgvPlu+Lpz8ecwfNVwbD632bmuecnmau7tyNBIj5aNiIj0K9mQgp/K/4QShrzPIU5ERORJDLrdRAZT8/UJ5teeXqvSyS8nXVbLRoMRzzV4Dv3r9YfJyD54RESUexaDAWabGaYAJuUREZG+sSZzMYNmTy9/3/A0LBbfTC+3aTbM2TEHA5YOcAbcJUJL4NOun+KZBs8w4CaifNehQwcMHjw4W489duyYuii6fft2l72mWL58uXrdK1euZPs5dPNZMAAz7jh5B8xMLyciyhesS/0o6J45cyYqVaqE4OBgNGnSBKtWrcry8StWrFCPk8dXrlwZs2fPhjcMovaGNgWBQYHwNTFJMXhh2QuYsX2G6nEn2pVth4U9F6JxicaeLh4R+akffvgBb775ZrYeW65cOZw5cwZ169bNMljOyWuSq9mQYkzBwooLYTDa6xoiInIv1qV+EnQvWLBAtSqMGjUK27ZtQ9u2bdG9e3ecOGGf6zmjo0ePokePHupx8viRI0di0KBBWLRoETzJBgOiURQ2m2+dKByIOYAHf3sQq07ZL4QYYMDARgMx/bbpKBRcyNPFIyI/VqRIEYSHh2frsSaTCSVLlkRAQIDLXpNcyyoXdTUgIjkCJu86VSEi8lmsS93Hq2qyKVOmoF+/fujfvz9q1aqFqVOnqhaJWbNmZfp4adUuX768epw8Xp735JNP4t1334UnRy+3wIyP8SAsKVb4SprfDwd/wOCNg3E6/rRzdPLZnWfj6fpPq77cRETekhJXsWJFTJw4UdUHEjRLPTF37txM08vldseOHdX6woULq/WPP/74Da8pvvrqKzRr1ky9pgTtDz/8MKKjU6dIJNexwoYALQAdz3RkejkRkQ/VpV9++SWaNm3qd3Wp1wyklpycjC1btmD48OHp1nfp0gVr167N9Dnr1q1T96fVtWtXfPzxx7BYLDCbb5xmJCkpSf05xMbGqv9tNpv6yztNpZePwIc4af4/F72m5ySmJGLixon4+fDPznX1i9XHO+3eQcmwkrrfPim/XFTQ+3b4+jb56nZ52zY5yuP4ywvH8/P6Ojl9T8f7vffeexg3bhxGjBiBhQsX4tlnn1VZUTVr1kxXtrJly6r777vvPuzbtw8REREICQlJ9xjHbamn5DVr1KihThCGDh2qTip+++23G7Y5P7c7K46yZFbH5fVz5876NEWzp5f/XOFn1DOW95rviC/wtt8dX8J9y32b8bPgTfVBVtKW0d11aVJSkl/WpV4TdF+4cAFWqxUlSpRIt16Wz549m+lzZH1mj09JSVGvV6pUqRueM2nSJIwdO/aG9efPn0diYmKet8NmlevzBpxCSVy6eBEBYfq+cnMy/iSWHFviXO5VrheeqfkMjPFGRMfre9scX5SYmBj1RTIafaPF3he3yVe3y9u2SS5WSpnkN1T+0pJlKadczHTcJ+nZ8hy5op32tqRvJyQkqN90WS/BqqyTP7kt62R7peKV18vsdmBgzmaAcFSIjrJ169YNTz/9tLr90ksvqYyov//+G1WrVnU+xrFNBQsWdKbVFSpUKN19jteU//v27au2QcolV/wlO6tVq1aqL3iBAgXU9jqem3H/eYqUQ47pxYsXb7gQffXq1Ty9tjvr04TkBNWFqXBSYWjBml+0gvjr744v4b7lvr1VfZqTujSz+tMddamUx1F/ubsuFY8++igc/Kku9Zqg2yHjB0MOUlYflswen9l6B7lSI1dU0l6ZlxT24sWLq6syeXU0sg62n47HUktzPFysJCIj9T1XdSQiMc44DqPXjsbgWoPRp34fn6qk5QsknxU5/r6yXb64Tb66Xd62TRIoSeUhFXnG/s6rV69W9/Xs2RPLli1zZhYtXrxYpYhJ+tiPP/6ornZHRUXh22+/RZ06ddC4cWN89tlnal3t2rUxb948dO7cWVXY06dPV1fF5TdYugVJCpv8Zko6m6Si5eQ3Wfaj4yRFNGjQIN02SAqbXIxNu22O23ICk3b5Zq8pKXQTJkxQ/1+6dMl5dfv06dNq2272Op7kOCkrWrSoGnA0rYzLOeXO+jSiZFU0OBqMCheiYKwdr/u61Jt42++OL+G+5b69VX2am7pU6pf8qEslmMyPunTbtm3qgq2/1aXesSUAihUrpnZyxlZtubqdsTU77YHP7PGyY2SnZCYoKEj9ZSQ70hWVT9Tjk9SHp3R0tPrA+0KF1q1SNzSJbALrVavL9pM3kR8CX9suX9wmX90ub9omKYOjcsx44VLSyRwXQW+//Xa1Tm7LYJeOx/fu3dv5vHvvvVf91sqyXNV2tBDL2BvyGy23n3/+eWclL8Gb47Z0M8ppS7ejPI7nZHy+3HaU37E+47Zmtt2OdXFxcbjjjjtUlybpjyYBiwzyKSdLjlaJrF7HUxxlyewzltfPnDvr03bdnkIbWz9Vp/tKXepNvOl3x9dw33LfZlWf5qQulb8HHnjAWX+6qy7N2MDpzro0Pj5e1Zv+WJd6za+tHFSZ+mvp0qXp1suypBxkRq72ZHz8kiVLVOf8zPpz5xcJuv/77z+f6i9VNCTzixhE5B+kcnf8rqa9+izrMrstv+mOq9UZbzsqKAnYbnY7PytaKZNwpLRlRvqoydV9Sal29GdjyrN7+WJdSkT+jXXpPlWXTp482e/qUq8JuoVcnfnoo4/wySefYO/evRgyZIi6+jFgwABnKlvafgCy/vjx4+p58nh5ngyiNmzYMI/n/csgb97SD4GIiG6uQoUKKsj/9ddfVX9kadXOSPqdSXAuaXxHjhzB//73P87h7WasS4mI9IN1qY6CbkmhkA76MqJdw4YNsXLlSvz+++/qIIozZ86km7O7UqVK6v7ly5erx7/55pv44IMPVFqjJ8mJWZ8+fZytJ0RE5L3KlCmj+pdJKp50Z3rhhRdueIykwMlFYRmdVfqcyVV6T05P6Q9YlxIR+V5dOn/+fHz//fd+V5caNG8Zi91DZOAXGW1PRvJ0xUBqQvokbNy4Ec2bN/domrsrSXqfL/at88Xt8sVt8tXt8rZtkoFfjh49qi5o5mWQLccopY7+Zr5Ar9uU1TF1df3n6tfzxbrUG3jb744v4b7lvnV1fZof9Fq/6a0u5a+tG0i/wJ07d2bZP5CIiIhYlxIRke9j0O2mlDgZeZDp5URERKxLiYjIvzHodgNp4ZaB3djSTURExLqUiIj8G4NuN5BgW0a3ZdBNRETEupSIiPwbg243kLTyO+64g+nlRERErEuJiMjPMeh2AxkBUAZS4zzdRKRHfj6phU/R87FkXUpEeqfn32By7XFk0O2mA3Pu3Dl+0YhIVxzTMl27ds3TRSEXcRxLPU65xbqUiPSK9alvueaCujTAheWh6+SAdO7cWZcnOUTkv0wmEwoVKqTm8BWhoaG5mrPTF+f81Ns2SXnlJEGOpRxTObZ6w7qUiPy9Ps0Peqvf9FqXMuh2A/ngbt68GV26dGG/biLSlZIlS6r/HScKua2kbDYbjEajz1Tget0mOUlwHFO9YV1KRP5en+YHvdZveqtLGXS76cMbHx/P9HIi0h2pcEuVKoXIyEhYLJZcvYZU3hcvXkTRokVVJe4L9LhN0lKsxxZuB9alROTv9Wl+0GP9pse6lEG3mw5O+/btmV5ORLolFUxuKxmpwOV3MDg42GcqcF/cJm/HupSI/L0+zQ+s3/IHzxzclBK3du1ajl5ORETEupSIiPwcg24iIiIiIiIiN2HQ7QYy+l+rVq3U/0RERMS6lIiI/JffR4WOyc5jY2NdtlOTkpKwePFi3HnnnQgKCoIvkP4eV69e9bn+jL64Xb64Tb66Xb64Tb66Xb64TY56z1EPelt96ot1qTfwxc+yt+C+5b7VI35u86cu9fugWyoeUa5cuTzuciIiIn3WgwULFnTJ6wjWp0RE5G+u3qIuNWiuusSt46s7p0+fRnh4uMvmppMrHnLS8d9//yEiIgK+wBe3yVe3yxe3yVe3yxe3yVe3yxe3Sap/OUkoXbq0S1o8XV2f+uI+9wbcr9y3esTPLfet3utSv2/plp1TtmxZtxwEOUnwtRMFX9wmX90uX9wmX90uX9wmX90uX9smV7Rwu7s+9bV97i24X7lv9YifW+5bvdal7MxDRERERERE5CYMuomIiIiIiIjchEG3G8goq2+88YZPjbbqi9vkq9vli9vkq9vli9vkq9vli9vk7bjPuV/1hp9Z7ls94uc2f/j9QGpERERERERE7sKWbiIiIiIiIiI3YdBNRERERERE5CYMuomIiIiIiIjchEF3Dh07dgz9+vVDpUqVEBISgipVqqjBdZKTk285cfqYMWPUxOnyvA4dOmD37t3pHpOUlISBAweiWLFiCAsLw1133YWTJ08iP0yYMAGtWrVCaGgoChUqlK3nGAyGTP/eeecd52NkOzPe/+CDDyK/5Ga7Hn/88RvK3LJlS90eK4vFgldffRX16tVTZZXP4KOPPorTp0+ne5wej5W3f68uX76Mvn37qvkb5U9uX7lyRfffq9xsl7d/r3KzXXr5bnmLmTNnqrozODgYTZo0wapVq7J8/IoVK9Tj5PGVK1fG7Nmz090/f/78TL8riYmJ8Dc52bdnzpzBww8/jBo1aqi51QcPHpzp4xYtWoTatWurQZbk/x9//BH+yNX7lp/bnO/XH374AZ07d0bx4sXVPN1RUVH4888/b3gcP7Pu2bf8zLoGg+4c2rdvH2w2G+bMmaNO7t9//311IjBy5Mgsn/f2229jypQpmDFjBjZt2oSSJUuqD/nVq1edj5EfZ6nUvv32W6xevRpxcXG48847YbVa4W5y0eD+++/Hs88+m+3nSOWS9u+TTz5RJzz33ntvusc99dRT6R4n+y6/5Ga7RLdu3dKV+ffff093v56O1bVr17B161a8/vrr6n/5gT1w4IAKaDLS27Hy9u+VnHxt374df/zxh/qT2xLI6f17lZvt8vbvVW62Sy/fLW+wYMECdXxHjRqFbdu2oW3btujevTtOnDiR6eOPHj2KHj16qMfJ46WOHTRokDqpTktOEjN+Z+RE05/kdN/KxS05wZbHN2jQINPHrFu3Dg888ID6/O/YsUP936dPH2zYsAH+xB37Vvj75zan+3XlypWqbpc6Y8uWLejYsSN69uypnuvAz6z79q3w98+sS2iUZ2+//bZWqVKlm95vs9m0kiVLapMnT3auS0xM1AoWLKjNnj1bLV+5ckUzm83at99+63zMqVOnNKPRqP3xxx/5dpQ+/fRTVa7c6NWrl3bbbbelW9e+fXvtxRdf1DwtJ9v12GOPqW25GV84Vhs3btTk63/8+HHdHitv/17t2bNH7eP169c7161bt06t27dvn26/V7ndLm//XrnqeHnzd8uTmjdvrg0YMCDdupo1a2rDhw/P9PGvvPKKuj+tZ555RmvZsqVLfgP9ed+mdbPPZp8+fbRu3bqlW9e1a1ftwQcf1PyJO/YtP7d5268OtWvX1saOHetc5mfWffuWn1nXYEu3C8TExKBIkSI3vV+u2J89exZdunRxrpN0rfbt22Pt2rVqWa4uSapi2sdIqmLdunWdj/Fm586dw2+//aZS7zP66quvVLponTp1MGzYsHStkN5q+fLliIyMRPXq1VULVXR0tPM+vR8rx2dWWk8zpnHr6Vh5+/dKrrpLinKLFi2c6ySdWtZl97298XuVl+3y5u+VK46Xr3y33JHFIsc37bEVsnyzfSvHI+Pju3btis2bN6vPiYNkQ1SoUAFly5ZVWREZW2d8XW72bXbcbP/rpY7z5n3r759bV+xXyTiV39C05978zLpv3/r7Z9ZVAlz2Sn7q8OHDmD59Ot57772bPkYCA1GiRIl062X5+PHjzscEBgaicOHCNzzG8Xxv9tlnnyE8PBz33HNPuvX/93//p/qVSNrvv//+ixEjRqhUtaVLl8JbSRqOpDnLj4sEdpI6etttt6kfMgnq9H6spL/j8OHDVSqtpAvp9Vh5+/dKXl8CzIxkXXbf2xu/V7ndLm//XrniePnKd8vVLly4oLoIZPZdvdm+lfWZPT4lJUW9XqlSpVCzZk3V11D61MfGxmLatGlo3bq12rfVqlWDP8jNvs2Om+1/PdRx3r5v/f1z64r9Kufc8fHxqsuDAz+z7tu3/v6ZdRW2dF8ngzHdbAAjx59cYU9LBsuRPopyItm/f/9b7mx5jYyDQGVcl1F2HuPKbcot6XcqJ5YZ+3dIa9btt9+uWqtk4KCFCxfir7/+Uv0fc8vd2yX92O644w5VZunXsnjxYtVPU1oc9X6spIVIjoNcyZSBNvR+rLz9e5XZe+Tkvb31e5Wb7fLE9yo/tstT3y09yul3NbPHp10vmQiPPPKI6jsr/Ra/++47lUUhF8L9TW5+Bz3xmnrk6v3Az23e9us333yjftel73LGC6X8zLpn3/Iz6xps6b7uhRdeuOVoshUrVkwXcMtgAzLK39y5c7N8nrRuCLnKJFfnHSS10nE1Sh4jaSEyem7alh55jIzonB/blFsyKuL+/fvVl/RWGjduDLPZjIMHD6rb3rxdDnLMpHVOyqznYyVBgVy5lFbGv//+O11LnB6Plbd/r3bu3KnSwzM6f/78DVeh9fS9yut25ef3Kr+2yxPfLT2RtHqTyXRDS0va72pG8nnI7PEBAQEoWrRops+R0aKbNWvm/Ez5g9zs2+y42f7Py2vqjbv2rb9/bvOyX6U+lO5W33//vbqQmRY/s+7bt/7+mXUZF/UN9ysnT57UqlWrpgYUSUlJyfaAT2+99ZZzXVJSUqYDPi1YsMD5mNOnT+ticC4ZIKlJkybZeuyuXbvUIEMrVqzQ8lNeBoG4cOGCFhQUpH322We6PVbJycna3XffrdWpU0eLjo72iWPl7d8rx8BcGzZscK6TQbqyOzCXt36v8rpd3vq9yu126em75enBfZ599tl062rVqpXlQGpyf1oyOFDagdQy+01o2rSp9sQTT2j+JKf7NrsDqXXv3j3dOhlYzR8HUnP1vs3IHz+3udmvX3/9tRYcHKz9+OOPmd7Pz6z79m1G/viZdQUG3Tkko+lWrVpVjSYswfeZM2ecf2nVqFFD++GHH5zLMsKyBAOyTk64HnroIa1UqVJabGxsuhOKsmXLan/99Ze2detW9R4NGjTIVmCfVzLS7rZt29RohQUKFFC35e/q1as33SYRExOjhYaGarNmzbrhNQ8dOqReb9OmTdrRo0e13377TY2g2KhRo3zZptxsl6x/6aWXtLVr16oy//PPP1pUVJRWpkwZ3R4ri8Wi3XXXXaq827dvT/eZlSBVr8dKD98rOUmtX7++GgVb/urVq6fdeeed6R6jx+9VTrdLD9+r3GyXXr5b3kBGpZeLKh9//LG6wDF48GAtLCxMO3bsmLpfTgj79u3rfPyRI0fUd2DIkCHq8fI8ef7ChQudjxkzZoy6IHP48GH1WyEngAEBAekunPiDnO5b4fh9lQt7Dz/8sLq9e/du5/1r1qzRTCaT+o3du3ev+l/2bdrR/f2BO/YtP7c5368SFMrn78MPP0z3OysXax34mXXfvuVn1jUYdOeiFU5aKDL7S7djAfXYtFeF3njjDdUyJ6077dq1U0FCWgkJCdoLL7ygFSlSRAsJCVEneydOnNDyg7SqZbZNcnJ8s20Sc+bMUWVN++V0kLLLdsr2BAYGalWqVNEGDRqkXbx4UcsvOd2ua9euaV26dNGKFy+ufrTKly+vXiPjcdDTsZIT/Zt9Zh3P0eOx0sP3Svbf//3f/2nh4eHqT25fvnw53WP0+L3K6Xbp4XuVm+3Sy3fLW8hJXYUKFdR+aNy4cbqWfvk8SMtgWsuXL1cXJ+TxFStWvOEilJxMymdJ7pfPlnzG5MKOP8rpvs3sMyvPT+v7779XF5nkOysXihYtWqT5I1fvW35uc75f5XZm+1UelxY/s+7Zt/zMuoZB/nFdsjoREREREREROXD0ciIiIiIiIiI3YdBNRERERERE5CYMuomIiIiIiIjchEE3ERERERERkZsw6CYiIiIiIiJyEwbdRERERERERG7CoJuIiIiIiIjITRh0ExEREREREbkJg24iIiIiIiIiN2HQTUREREREHjdt2jRUqlQJoaGhuPvuuxETE+PpIhG5BINuIso3HTp0wODBg33uvS9evIjIyEgcO3YsT69z3333YcqUKS4rFxER2c2ePRvh4eFISUlx7pK4uDiYzWa0bds23W5atWoVDAYDDhw44PV1m6u4cxuy+9ojR47EjBkz8Nlnn2H16tXYtm0bxo4d65YyEeU3Bt1E+ejxxx9XFbn8SUVfuXJlDBs2DPHx8TwOOjZp0iT07NkTFStWzNPrjB49GhMmTEBsbKzLykZEREDHjh1VkL158+Z0wXXJkiWxadMmXLt2zbl++fLlKF26NKpXr56vuy45OdlvD5Ucg7feegsLFixAu3bt0LhxYzzzzDP49ddfPV00Ipdg0E2Uz7p164YzZ87gyJEjGD9+PGbOnKkCb71UwN5YJk9KSEjAxx9/jP79++f5terXr68C96+++solZSMiIrsaNWqoQFoCage53atXL1SpUgVr165Nt16CdPHHH3+gTZs2KFSoEIoWLYo777wThw8fTncxfcWKFSot2nFRXbKeNE3D22+/rS6uh4SEoEGDBli4cOENLcAvvPAChg4dimLFiqFz586ZHi6bzaYC0qpVqyIoKAjly5dXF2hFUlISBg0apLKtgoODVVklgM34PvKYV155BUWKFFEXGsaMGeOybcjNa2f07rvv4rbbblPBtkPx4sVx4cIFfoTJJzDoJspnUmFKpVSuXDk8/PDD+L//+z/89NNPWVbAt6r45Ha9evXUfXJScPvttztbz7O6T0iQN3Xq1HRlbNiwobPSzG2ZbkZOHm5WOWfndW91AiRk+x599FEUKFAApUqVwnvvvXfLcskxiIiIUO9/6NAhdWJw6tQpVd6wsDD1vplZvHgxAgICEBUV5Vwn+2zgwIEqna5w4cIoUaIE5s6dq8r1xBNPqBRHOcmT52Z011134ZtvvrlleYmIKGfkt/mff/5xLsttWde+fXvnermwvG7dOmfQLb/bUv9JILts2TIYjUb07t1b1Q1Cgkn5/X/qqafUBXX5k/r9tddew6effopZs2Zh9+7dGDJkCB555BEVgKYlqdRSh6xZswZz5szJtNwjRoxQQffrr7+OPXv24Ouvv1b1ipD6dNGiRep1tm7dqgLzrl274tKlSze8j9RlGzZsUHXsuHHjsHTpUpdtQ05fOy25cPDLL7+o/ZrxonbBggVzdIyJvJZGRPnmscce03r16pVu3cCBA7WiRYuq2+3bt9cKFCigvfzyy9q+ffu0vXv3qvUjR47Uatasqf3xxx/a4cOHtU8//VQLCgrSli9frp0+fVoLCAjQpkyZoh09elTbuXOn9uGHH2pXr17N8j6HChUqaO+//366MjVo0EB74403cl2mm5HXioiI0MaMGaMdOHBA++yzzzSDwaAtWbLE+Zhbve7ChQu1RYsWqedv27ZN69mzp1avXj3NarU6X+PZZ5/VypYtq15XtvnOO+9U2/Diiy/etGyyvW3atFG35fUdx0S2V34qZV9mRl6zW7duN2xneHi49uabb6pyyv9Go1Hr3r27NnfuXLVOyijvER8fn+65v//+u9rexMTEm5aViIhyTn5/w8LCNIvFosXGxqr68dy5c9q3336rtWrVSj1mxYoV6jdf6p/MREdHq/t37dqV7jc/bf0SFxenBQcHa2vXrk333H79+mkPPfRQuuc1bNgwyzJLOaVOmDdv3g33yfuYzWbtq6++cq5LTk7WSpcurb399tvp3sdRvzk0a9ZMe/XVV12yDTl97YzkPWSfyvvJ8XH8BQYGal27ds1y/xDpRYCng34if7Zx40Z1xbpTp07OdXKVWq4UO8hVdhlc6++//3a2pkorsAwyIlfFJTVdBoa55557UKFCBXW/tGwLGQTmZvflRE7LJK0GWaVQv/HGG+p2tWrV1KAp0nogLejZed1777033etJarek1cnV/7p166o+e7Lu888/d7bKy1X4smXLZrmNO3bsUC38md2WFDdpMc+MpMlJymJG0kIvrQSOVorJkyerTAG52u/ovy2tBzt37kTLli2dzytTpoy66n/27FnnMSMioryT1mupZ6TV+vLly6rPttQfUrf07dtX3Sep5ZK+LXWPkEwqaWFev369SnV2tHCfOHFC1TmZkfooMTHxhnRxaUVv1KhRunVNmzbNssx79+5VdULa8wQHKZvFYkHr1q2d62S8mObNm6vnZax705I6LTo6+qbvm5NtyOlrZyTnKpIav2vXrhsyv9JuG5GeMegmymcyKIikPUswLJWl9CebPn36TSvgW1V8EtxJZSzBtKSUdenSRY2CLWnNWd2XEzktU1ayqpyz87q3OgGS++XxadO9JZVd+vNlZfv27SpV3RFoy75zrHfczoykv8nJQlbbaTKZVCp82gsejtTAjCcmklIv0g7qQ0REeScXkOUCrKSSS9DtuEAsXZ1kmipJ8Zb7pG+xgwySKenQ8+bNUxdYpc6Ruiar8U0c9dJvv/2mLqRm7GKWlqRlZ8VRJ2RGukMJ6Q6VcX3GdRKMpyX3O8qZ123I6WtnJIOHysUPOT4OUqfv27fvhgvtRHrFoJvIA1fapYVTKimpwDNWVhkr4FtVfBLQSd8pGQRmyZIlKoAfNWqU6lslJxFZ3Sekf5qj4naQiwF5KVNWsqqcs/O6tzoByrgt2XH16lXVYu0IiiXodlT00kfO0eqdGWm9lpO37Gxn2nWOE6KMJyaOfnjSuk5ERK6vg6U1W363X375Zed6CcD//PNPdUFXxt5wTAcpLcaSaeWYVkwyrzIKDAyE1Wp1LteuXVvVWRI4ZpX5lR2SESaBt2SEZRywU4JUeW8pk4wR46i/ZYT2nE7/5c5tyPjamdWjEninvVggA8X16NFDlYPIFzDoJspnEsCmvZp7K9mp+KSSkhQs+ZO0ZUlL/vHHH9XgL1nd5wjuZGATB6n4jh49mucy5catXjc7J0CybyW4lRMnSREUcnIl6Ws3K6tj+2WAs5iYGBWAS6B9/vx5NWDMSy+9dNMySwv8l19+CVf5999/VUuMnIQQEZHrg+7nn39eBadp6wS5/eyzz6psK8cgapIVJllKMhCmZGVJ3TR8+PAbXlMGJJWL2VJ3SCabZFdJ1y8ZeEwurMrgn1K3ygVwuf+xxx7Ldnklk+rVV19VA6ZJ8Cp1udRNMrBZv379VJnl4oG8p9R50hVMMqXkvpxw5zZk9tpywd9BMgtkv0s3rIceekh1u/vf//6nuuAR+QoG3UReTgLBrCq+mjVrqivgkjou6VlSsUmFXKtWLXX7Zvelrezmz5+vWpDlBENSt6X1PC9lykllnJPXlT53tzoBksfJyYachMhjJY1bWvfTVvAZSat6aGio6k8uKeYStMsJgPSFl75xN5vGRUjavvTZlsA+p2n7mZF5Y+V4ERGR60lALd2CpO50dPNxBN2S9SQzSzhG15Z649tvv1VTYklGlXRT+uCDD9SI52l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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "y_exact = np.linspace(0, COLUMN_HEIGHT, 500)\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6), sharey=True)\n", + "\n", + "for t_snap in SNAPSHOTS:\n", + " psi_exact = gardner_transient_psi(\n", + " y_exact, t_snap,\n", + " psi_dry=PSI_DRY, psi_wet=PSI_WET,\n", + " L=COLUMN_HEIGHT, Ks=KS, alpha=ALPHA_G,\n", + " theta_r=THETA_R, theta_s=THETA_S,\n", + " )\n", + " theta_exact = THETA_R + (THETA_S - THETA_R) * np.exp(ALPHA_G * np.clip(psi_exact, None, 0))\n", + "\n", + " ax1.plot(psi_exact, y_exact, lw=2, label=f\"$t = {t_snap}$ s\")\n", + " ax2.plot(theta_exact, y_exact, lw=2, label=f\"$t = {t_snap}$ s\")\n", + "\n", + "# Initial condition\n", + "ax1.axvline(PSI_DRY, color=\"grey\", ls=\":\", lw=0.8, label=\"initial\")\n", + "ax2.axvline(\n", + " THETA_R + (THETA_S - THETA_R) * np.exp(ALPHA_G * PSI_DRY),\n", + " color=\"grey\", ls=\":\", lw=0.8, label=\"initial\",\n", + ")\n", + "\n", + "ax1.set_xlabel(r\"Pressure head $\\psi$ (m)\")\n", + "ax1.set_ylabel(\"Height $y$ (m)\")\n", + "ax1.set_title(r\"$\\psi(y, t)$\")\n", + "ax1.legend()\n", + "ax1.grid(True, alpha=0.3)\n", + "\n", + "ax2.set_xlabel(r\"Water content $\\theta$\")\n", + "ax2.set_title(r\"$\\theta(y, t)$\")\n", + "ax2.legend()\n", + "ax2.grid(True, alpha=0.3)\n", + "\n", + "fig.suptitle(\"Analytical wetting front (Gardner / Ogata–Banks)\", fontsize=12)\n", + "fig.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cell-8", + "metadata": {}, + "source": [ + "## Set Up the Richards Solver\n", + "\n", + "We create a vertical column mesh and configure the Richards\n", + "solver with Gardner constitutive curves. The `water_content`\n", + "property activates the mixed (mass-conservative) form.\n", + "\n", + "**Solver note:** The Gardner exponential creates steep\n", + "nonlinearity in dry regions where $K$ and $\\theta$ are\n", + "very small. The standard Newton method with backtracking\n", + "linesearch can overshoot into unphysical states.\n", + "A **trust-region** SNES (`newtontr`) constrains the\n", + "Newton step size and converges reliably." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "cell-9", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T11:10:37.127260Z", + "iopub.status.busy": "2026-02-23T11:10:37.126973Z", + "iopub.status.idle": "2026-02-23T11:10:37.382693Z", + "shell.execute_reply": "2026-02-23T11:10:37.380079Z", + "shell.execute_reply.started": "2026-02-23T11:10:37.127240Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Structured box element resolution 4 64\n" + ] + } + ], + "source": [ + "mesh = uw.meshing.StructuredQuadBox(\n", + " elementRes=(4, RES),\n", + " minCoords=(0.0, 0.0),\n", + " maxCoords=(COLUMN_WIDTH, COLUMN_HEIGHT),\n", + " qdegree=3,\n", + ")\n", + "\n", + "psi_var = uw.discretisation.MeshVariable(r\"\\psi\", mesh, 1, degree=2)\n", + "v_soln = uw.discretisation.MeshVariable(\"v\", mesh, mesh.dim, degree=1)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "cell-10", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T11:10:37.384014Z", + "iopub.status.busy": "2026-02-23T11:10:37.383876Z", + "iopub.status.idle": "2026-02-23T11:10:37.435356Z", + "shell.execute_reply": "2026-02-23T11:10:37.434501Z", + "shell.execute_reply.started": "2026-02-23T11:10:37.384001Z" + } + }, + "outputs": [], + "source": [ + "richards = uw.systems.Richards(mesh, psi_var, v_soln, order=1, theta=0.5, degree=3)\n", + "richards.petsc_options.delValue(\"ksp_monitor\")\n", + "richards.petsc_options[\"snes_rtol\"] = 1.0e-6\n", + "richards.petsc_options[\"snes_max_it\"] = 50\n", + "\n", + "# Trust-region Newton method — robust for the steep Gardner nonlinearity\n", + "richards.petsc_options[\"snes_type\"] = \"newtontr\"\n", + "\n", + "psi_sym = psi_var.sym[0]\n", + "\n", + "# Constitutive model: Gardner K(ψ) with gravity\n", + "richards.constitutive_model = uw.constitutive_models.DarcyFlowModel\n", + "richards.constitutive_model.Parameters.permeability = gardner_K(\n", + " psi_sym, Ks=KS, alpha=ALPHA_G\n", + ")\n", + "richards.constitutive_model.Parameters.s = sympy.Matrix([0, -1]).T\n", + "\n", + "# Mixed form: θ(ψ) for mass-conservative storage\n", + "richards.water_content = gardner_theta(\n", + " psi_sym,\n", + " theta_r=THETA_R,\n", + " theta_s=THETA_S,\n", + " alpha=ALPHA_G,\n", + ")\n", + "\n", + "richards.f = 0.0\n", + "\n", + "# Boundary conditions\n", + "richards.add_dirichlet_bc([PSI_WET], \"Top\")\n", + "richards.add_dirichlet_bc([PSI_DRY], \"Bottom\")\n", + "\n", + "# Velocity projector\n", + "richards._v_projector.petsc_options[\"snes_rtol\"] = 1.0e-6\n", + "richards._v_projector.smoothing = 1.0e-3" + ] + }, + { + "cell_type": "markdown", + "id": "cell-11", + "metadata": {}, + "source": [ + "## Initial Condition and Timestepping\n", + "\n", + "We initialise with a smooth profile that interpolates between\n", + "the wet top and the dry interior (helps the first SNES iteration\n", + "converge). Then we step forward in time, saving snapshots at\n", + "the analytical comparison times." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "cell-12", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T11:10:37.440174Z", + "iopub.status.busy": "2026-02-23T11:10:37.439863Z", + "iopub.status.idle": "2026-02-23T11:11:03.613359Z", + "shell.execute_reply": "2026-02-23T11:11:03.612713Z", + "shell.execute_reply.started": "2026-02-23T11:10:37.440150Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Completed 60 steps, t = 0.3000 s\n", + "Snapshots saved at t = [0.05, 0.15, 0.3]\n" + ] + } + ], + "source": [ + "# Initial condition: dry everywhere except a smooth transition\n", + "# near the top boundary to ease the first nonlinear solve.\n", + "y = mesh.X[1]\n", + "transition_width = 0.1 * COLUMN_HEIGHT\n", + "blend = sympy.Min(sympy.Max((COLUMN_HEIGHT - y) / transition_width, 0), 1)\n", + "psi_init = PSI_WET + (PSI_DRY - PSI_WET) * blend\n", + "\n", + "psi_var.array = uw.function.evaluate(psi_init, psi_var.coords)\n", + "\n", + "# IMPORTANT: the solver's time-derivative history was initialised at\n", + "# construction time (when psi_var was still zero). Re-sync it now\n", + "# so that ψ^n = the initial condition we just set.\n", + "richards.DuDt.initiate_history_fn()\n", + "\n", + "# Timestepping — collect snapshots\n", + "t_now = 0.0\n", + "snapshot_times = sorted(SNAPSHOTS)\n", + "snapshots = {} # {t: psi_data}\n", + "next_snap_idx = 0\n", + "\n", + "# Total time to run\n", + "t_end = snapshot_times[-1]\n", + "n_steps = int(np.ceil(t_end / DT))\n", + "\n", + "for step in range(n_steps):\n", + " richards.solve(timestep=DT)\n", + " t_now += DT\n", + "\n", + " # Check if we've passed a snapshot time\n", + " if next_snap_idx < len(snapshot_times) and t_now >= snapshot_times[next_snap_idx] - 1e-12:\n", + " t_snap = snapshot_times[next_snap_idx]\n", + " snapshots[t_snap] = np.array(psi_var.data)\n", + " next_snap_idx += 1\n", + "\n", + "print(f\"Completed {n_steps} steps, t = {t_now:.4f} s\")\n", + "print(f\"Snapshots saved at t = {list(snapshots.keys())}\")" + ] + }, + { + "cell_type": "markdown", + "id": "cell-13", + "metadata": {}, + "source": [ + "## Comparison with Analytical Solution\n", + "\n", + "We sample each snapshot along a vertical profile and compare\n", + "with the Ogata–Banks solution." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "cell-14", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T11:11:03.615173Z", + "iopub.status.busy": "2026-02-23T11:11:03.614993Z", + "iopub.status.idle": "2026-02-23T11:11:04.019521Z", + "shell.execute_reply": "2026-02-23T11:11:04.018942Z", + "shell.execute_reply.started": "2026-02-23T11:11:03.615158Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " t = 0.05 s : max |error| = 2.2215e-01 m\n", + " t = 0.15 s : max |error| = 1.3161e-01 m\n", + " t = 0.30 s : max |error| = 7.3938e-02 m\n" + ] + } + ], + "source": [ + "n_sample = 200\n", + "sample_y = np.linspace(0.05, COLUMN_HEIGHT - 0.05, n_sample)\n", + "sample_x = np.full_like(sample_y, COLUMN_WIDTH / 2)\n", + "sample_pts = np.column_stack([sample_x, sample_y])\n", + "\n", + "fig, axes = plt.subplots(1, len(snapshots), figsize=(5 * len(snapshots), 6), sharey=True)\n", + "if len(snapshots) == 1:\n", + " axes = [axes]\n", + "\n", + "max_errors = []\n", + "\n", + "for ax, (t_snap, psi_snap) in zip(axes, sorted(snapshots.items())):\n", + " # Restore snapshot and evaluate\n", + " psi_var.data[...] = psi_snap\n", + " psi_numerical = uw.function.evaluate(psi_var.sym[0], sample_pts).squeeze()\n", + "\n", + " psi_analytical = gardner_transient_psi(\n", + " sample_y, t_snap,\n", + " psi_dry=PSI_DRY, psi_wet=PSI_WET,\n", + " L=COLUMN_HEIGHT, Ks=KS, alpha=ALPHA_G,\n", + " theta_r=THETA_R, theta_s=THETA_S,\n", + " )\n", + "\n", + " error = np.abs(psi_numerical - psi_analytical)\n", + " max_err = error.max()\n", + " max_errors.append(max_err)\n", + "\n", + " ax.plot(psi_analytical, sample_y, \"b-\", lw=2, label=\"Analytical\")\n", + " ax.plot(psi_numerical, sample_y, \"ro\", ms=2, label=\"Numerical\")\n", + " ax.set_xlabel(r\"$\\psi$ (m)\")\n", + " ax.set_title(f\"$t = {t_snap}$ s\\nmax err = {max_err:.3e}\")\n", + " ax.legend(fontsize=9)\n", + " ax.grid(True, alpha=0.3)\n", + "\n", + "axes[0].set_ylabel(\"Height $y$ (m)\")\n", + "fig.suptitle(\"Transient wetting front: numerical vs analytical\", fontsize=12)\n", + "fig.tight_layout()\n", + "plt.show()\n", + "\n", + "for t_snap, err in zip(sorted(snapshots.keys()), max_errors):\n", + " print(f\" t = {t_snap:.2f} s : max |error| = {err:.4e} m\")" + ] + }, + { + "cell_type": "markdown", + "id": "cell-15", + "metadata": {}, + "source": [ + "## Darcy Velocity Field\n", + "\n", + "The downward velocity should be highest at the wetting front\n", + "where the pressure gradient is steepest." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "cell-16", + "metadata": { + "execution": { + "iopub.execute_input": "2026-02-23T11:11:04.020710Z", + "iopub.status.busy": "2026-02-23T11:11:04.020195Z", + "iopub.status.idle": "2026-02-23T11:11:04.720953Z", + "shell.execute_reply": "2026-02-23T11:11:04.719751Z", + "shell.execute_reply.started": "2026-02-23T11:11:04.020686Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Use the final snapshot\n", + "t_final = sorted(snapshots.keys())[-1]\n", + "psi_var.data[...] = snapshots[t_final]\n", + "richards.solve(timestep=DT) # recompute velocity\n", + "\n", + "vy_numerical = uw.function.evaluate(v_soln.sym[0, 1], sample_pts).squeeze()\n", + "\n", + "# Analytical Darcy velocity: q_y = K(ψ) (∂ψ/∂y + 1)\n", + "# Compute from the analytical ψ profile\n", + "psi_anal = gardner_transient_psi(\n", + " sample_y, t_final,\n", + " psi_dry=PSI_DRY, psi_wet=PSI_WET,\n", + " L=COLUMN_HEIGHT, Ks=KS, alpha=ALPHA_G,\n", + " theta_r=THETA_R, theta_s=THETA_S,\n", + ")\n", + "K_anal = KS * np.exp(ALPHA_G * np.clip(psi_anal, None, 0))\n", + "dpsi_dy = np.gradient(psi_anal, sample_y)\n", + "vy_analytical = K_anal * (dpsi_dy + 1)\n", + "\n", + "fig, ax = plt.subplots(figsize=(5, 6))\n", + "ax.plot(vy_analytical, sample_y, \"b-\", lw=2, label=\"Analytical\")\n", + "ax.plot(vy_numerical, sample_y, \"ro\", ms=2, label=\"Numerical\")\n", + "ax.set_xlabel(r\"Vertical Darcy flux $q_y$ (m/s)\")\n", + "ax.set_ylabel(\"Height $y$ (m)\")\n", + "ax.set_title(f\"Darcy velocity at $t = {t_final}$ s\")\n", + "ax.legend()\n", + "ax.grid(True, alpha=0.3)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cell-17", + "metadata": {}, + "source": [ + "## Try It Yourself\n", + "\n", + "Experiment with different parameters to build intuition:\n", + "\n", + "```python\n", + "# Larger α → sharper wetting front\n", + "ALPHA_G = 6.0\n", + "\n", + "# Smaller timestep for better accuracy (error is time-dominated)\n", + "DT = 0.002\n", + "\n", + "# Wetter initial condition\n", + "PSI_DRY = -1.0\n", + "\n", + "# Higher resolution (spatial error is already small at RES=64)\n", + "RES = 128\n", + "```\n", + "\n", + "- How does the front speed change with $\\alpha$?\n", + "- What happens when the front reaches the bottom boundary?\n", + " (The semi-infinite analytical solution breaks down.)\n", + "- Try computing total water content\n", + " $\\int_0^L \\theta(\\psi(y))\\,dy$ at each snapshot to check\n", + " mass conservation.\n", + "\n", + "## References\n", + "\n", + "Celia, M. A., Bouloutas, E. T. & Zarba, R. L. (1990). A general\n", + "mass-conservative numerical solution for the unsaturated flow equation.\n", + "*Water Resources Research*, 26(7), 1483–1496.\n", + "doi:[10.1029/WR026i007p01483](https://doi.org/10.1029/WR026i007p01483)\n", + "\n", + "Gardner, W. R. (1958). Some steady-state solutions of the unsaturated\n", + "moisture flow equation with application to evaporation from a water table.\n", + "*Soil Science*, 85(4), 228–232.\n", + "\n", + "Ogata, A. & Banks, R. B. (1961). A solution of the differential\n", + "equation of longitudinal dispersion in porous media.\n", + "*US Geological Survey Professional Paper* 411-A.\n", + "\n", + "Richards, L. A. (1931). Capillary conduction of liquids through porous\n", + "mediums. *Physics*, 1(5), 318–333.\n", + "doi:[10.1063/1.1745010](https://doi.org/10.1063/1.1745010)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cell-18", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/beginner/tutorials/Notebook_Index.ipynb b/docs/beginner/tutorials/Notebook_Index.ipynb index 71c47d216..07b04e3c3 100644 --- a/docs/beginner/tutorials/Notebook_Index.ipynb +++ b/docs/beginner/tutorials/Notebook_Index.ipynb @@ -22,7 +22,7 @@ }, "tags": [] }, - "source": "#### Notebook 1 - Meshes\n\n\ud83d\udd17 [**Meshes**](1-Meshes.ipynb): Introduces the mesh discretisation that we use in `Underworld3` and how you can build one of the pre-defined meshes. This notebook also show you how to use the `pyvista` visualisation tools for `Underworld3` objects. The mesh holds information on the mesh geometry, boundaries and coordinate systems." + "source": "#### Notebook 1 - Meshes\n\n🔗 [**Meshes**](1-Meshes.ipynb): Introduces the mesh discretisation that we use in `Underworld3` and how you can build one of the pre-defined meshes. This notebook also show you how to use the `pyvista` visualisation tools for `Underworld3` objects. The mesh holds information on the mesh geometry, boundaries and coordinate systems." }, { "cell_type": "markdown", @@ -34,67 +34,43 @@ }, "tags": [] }, - "source": "#### Notebook 2 - Mesh Variables\n\n\ud83d\udd17 [**Variables**](2-Variables.ipynb): Introduces the concept of `MeshVariables` in `Underworld3`. These are both data containers and `sympy` symbolic objects. We show you how to inspect a `meshVariable`, set the data values in the `MeshVariable` and visualise them." + "source": "#### Notebook 2 - Mesh Variables\n\n🔗 [**Variables**](2-Variables.ipynb): Introduces the concept of `MeshVariables` in `Underworld3`. These are both data containers and `sympy` symbolic objects. We show you how to inspect a `meshVariable`, set the data values in the `MeshVariable` and visualise them." }, { "cell_type": "markdown", "id": "26b5da69-1292-4988-93e4-591bcf607b32", "metadata": {}, - "source": "#### Notebook 3 - Symbols and sympy\n\n\ud83d\udd17 [**Symbols**](3-Symbolic_Forms.ipynb): `meshVariables` are `sympy` objects that can be composed with other symbolic objects and evaluated numerically when required. They can also be differentiated. Most importantly, `sympy` can manipulate expressions, simplify them and cancel terms." + "source": "#### Notebook 3 - Symbols and sympy\n\n🔗 [**Symbols**](3-Symbolic_Forms.ipynb): `meshVariables` are `sympy` objects that can be composed with other symbolic objects and evaluated numerically when required. They can also be differentiated. Most importantly, `sympy` can manipulate expressions, simplify them and cancel terms." }, { "cell_type": "markdown", "id": "6d091b23-709b-435c-ade1-9822ad09d567", "metadata": {}, - "source": "#### Notebook 4 - Example: Diffusion Equation\n\n\ud83d\udd17 [**Diffusion Solver**](4-Solvers-i-Poisson.ipynb): Introduces the various solver templates that are available in Underworld, starting with a steady-state diffusion problem. The template requires you to set some constitutive properties and define the unknowns. These are handled through subsitution into symbolic forms and the template equation can be inspected before you need to supply concrete expressions.\n\n#### Notebook 5 - Poisson Equation Validation\n\n\ud83d\udd17 [**Poisson Validation**](5-Solvers-i-Poisson-Validation.ipynb): Demonstrates how to validate the Poisson solver against known analytical solutions. We solve three progressively complex diffusion problems with linear, quadratic, and sinusoidal profiles, comparing numerical results against exact solutions." + "source": "#### Notebook 4 - Example: Diffusion Equation\n\n🔗 [**Diffusion Solver**](4-Solvers-i-Poisson.ipynb): Introduces the various solver templates that are available in Underworld, starting with a steady-state diffusion problem. The template requires you to set some constitutive properties and define the unknowns. These are handled through subsitution into symbolic forms and the template equation can be inspected before you need to supply concrete expressions.\n\n#### Notebook 5 - Poisson Equation Validation\n\n🔗 [**Poisson Validation**](5-Solvers-i-Poisson-Validation.ipynb): Demonstrates how to validate the Poisson solver against known analytical solutions. We solve three progressively complex diffusion problems with linear, quadratic, and sinusoidal profiles, comparing numerical results against exact solutions." }, { "cell_type": "markdown", "id": "eff58d66-8892-4af6-92b0-c18ee9cd2ad2", "metadata": {}, - "source": "#### Notebook 6 - Example: Stokes Equation\n\n\ud83d\udd17 [**Stokes Solver**](6-Solvers-ii-Stokes.ipynb): Stokes equation is a more complicated system of equations to solve. This complexity is mostly hidden when you set the problem up. There are some interesting ways to constrain boundary values which are demonstrated using an annulus mesh (curved, free-slip boundaries) and a $\\delta$ function buoyancy source." + "source": "#### Notebook 6 - Example: Stokes Equation\n\n🔗 [**Stokes Solver**](6-Solvers-ii-Stokes.ipynb): Stokes equation is a more complicated system of equations to solve. This complexity is mostly hidden when you set the problem up. There are some interesting ways to constrain boundary values which are demonstrated using an annulus mesh (curved, free-slip boundaries) and a $\\delta$ function buoyancy source." }, { "cell_type": "markdown", "id": "0a400f96-5908-4b60-ba0d-ef188c5a66cd", "metadata": {}, - "source": "#### Notebook 7 - Example: Time Dependence\n\n\ud83d\udd17 [**Timestepping**](7-Timestepping-simple.ipynb): Simple advection-diffusion problem. A step (or a top-hat function) moves left to right with constant velocity and diffusion occurs at the same time. This has an analytic solution so we can see the effect of changing timesteps and grid resolution very easily.\n\n#### Notebook 8 - Coupled Timestepping \n\n\ud83d\udd17 [**Coupled Timestepping**](8-Timestepping-coupled.ipynb): *Coupled* Stokes flow plus thermal advection-diffusion gives a simple convection solver. The timestepping loop is written by hand because usually you will want to do some analysis or output some checkpoints." + "source": "#### Notebook 7 - Example: Time Dependence\n\n🔗 [**Timestepping**](7-Timestepping-simple.ipynb): Simple advection-diffusion problem. A step (or a top-hat function) moves left to right with constant velocity and diffusion occurs at the same time. This has an analytic solution so we can see the effect of changing timesteps and grid resolution very easily.\n\n#### Notebook 8 - Coupled Timestepping \n\n🔗 [**Coupled Timestepping**](8-Timestepping-coupled.ipynb): *Coupled* Stokes flow plus thermal advection-diffusion gives a simple convection solver. The timestepping loop is written by hand because usually you will want to do some analysis or output some checkpoints." }, { "cell_type": "markdown", "id": "3b784a04-823e-4a88-9b18-a57f763dbf56", "metadata": {}, - "source": "#### Notebook 9 - Example: Navier-Stokes Equation\n\n\ud83d\udd17 [**Unsteady flow**](9-Unsteady_Flow.ipynb): Using a passive swarm to track the pattern of flow developing in a pipe after an impulsive application of a boundary condition at the inflow. Particles need to be added to the passive swarm close to the inflow at each timestep." + "source": "#### Notebook 9 - Example: Navier-Stokes Equation\n\n🔗 [**Unsteady flow**](9-Unsteady_Flow.ipynb): Using a passive swarm to track the pattern of flow developing in a pipe after an impulsive application of a boundary condition at the inflow. Particles need to be added to the passive swarm close to the inflow at each timestep." }, { "cell_type": "markdown", "id": "42f43817-0e0b-458b-9c5b-34799fb60487", "metadata": {}, - "source": [ - "#### Notebook 10 - Lagrangian Swarm Variables\n", - "\n", - "\ud83d\udd17 [**Swarm Variables**](10-Particle_Swarms.ipynb): Exploring how they work for specifying material properties with a swarm used to determine element viscosity. We learn how to use swarm variables in expressions generally and for boundary conditions.\n", - "\n", - "#### Notebook 11 - Multi-Material Constitutive Models\n", - "\n", - "\ud83d\udd17 [**Multi-Material SolCx**](11-Multi-Material_SolCx.ipynb): Demonstrates the multi-material constitutive model system by recreating the classic SolCx benchmark using IndexSwarmVariable to track different materials. Shows level-set weighted flux averaging and validation against piecewise viscosity solutions.\n", - "\n", - "#### Notebook 12 - Working with Physical Units\n", - "\n", - "\ud83d\udd17 [**Units System**](12-Units_System.ipynb): Introduces physical units in Underworld3 using the Pint library. Shows how to create physical quantities (temperatures, velocities, viscosities), convert between units, work with unit-aware arrays and coordinates, and leverage automatic unit tracking through derivatives.\n", - "\n", - "#### Notebook 13 - Non-Dimensional Scaling\n", - "\n", - "\ud83d\udd17 [**Non-Dimensional Scaling**](13-Scaling-problems-with-physical-units.ipynb): Demonstrates the non-dimensional scaling system for better numerical conditioning. Shows how to set reference quantities, solve Poisson and Stokes equations with automatic ND scaling, and validate that dimensional and non-dimensional solutions match perfectly.\n", - "\n", - "#### Notebook 14 - Time-Dependent Advection-Diffusion\n", - "\n", - "\ud83d\udd17 [**Timestepping with Units**](14-Timestepping-with-physical-units.ipynb): Time-dependent advection-diffusion with physical units. Tests numerical solutions against analytical solutions for advection and diffusion of temperature steps.\n", - "\n", - "#### Notebook 15 - Thermal Convection\n", - "\n", - "\ud83d\udd17 [**Rayleigh-B\u00e9nard Convection**](15-Thermal-convection-with-units.ipynb): Complete thermal convection example with physical units. Demonstrates coupled Stokes-temperature systems with buoyancy forcing in an annulus geometry, Rayleigh number computation, and time-stepping visualization." - ] + "source": "#### Notebook 10 - Lagrangian Swarm Variables\n\n🔗 [**Swarm Variables**](10-Particle_Swarms.ipynb): Exploring how they work for specifying material properties with a swarm used to determine element viscosity. We learn how to use swarm variables in expressions generally and for boundary conditions.\n\n#### Notebook 11 - Multi-Material Constitutive Models\n\n🔗 [**Multi-Material SolCx**](11-Multi-Material_SolCx.ipynb): Demonstrates the multi-material constitutive model system by recreating the classic SolCx benchmark using IndexSwarmVariable to track different materials. Shows level-set weighted flux averaging and validation against piecewise viscosity solutions.\n\n#### Notebook 12 - Working with Physical Units\n\n🔗 [**Units System**](12-Units_System.ipynb): Introduces physical units in Underworld3 using the Pint library. Shows how to create physical quantities (temperatures, velocities, viscosities), convert between units, work with unit-aware arrays and coordinates, and leverage automatic unit tracking through derivatives.\n\n#### Notebook 13 - Non-Dimensional Scaling\n\n🔗 [**Non-Dimensional Scaling**](13-Scaling-problems-with-physical-units.ipynb): Demonstrates the non-dimensional scaling system for better numerical conditioning. Shows how to set reference quantities, solve Poisson and Stokes equations with automatic ND scaling, and validate that dimensional and non-dimensional solutions match perfectly.\n\n#### Notebook 14 - Time-Dependent Advection-Diffusion\n\n🔗 [**Timestepping with Units**](14-Timestepping-with-physical-units.ipynb): Time-dependent advection-diffusion with physical units. Tests numerical solutions against analytical solutions for advection and diffusion of temperature steps.\n\n#### Notebook 15 - Thermal Convection\n\n🔗 [**Rayleigh-Bénard Convection**](15-Thermal-convection-with-units.ipynb): Complete thermal convection example with physical units. Demonstrates coupled Stokes-temperature systems with buoyancy forcing in an annulus geometry, Rayleigh number computation, and time-stepping visualization.\n\n#### Notebook 16 - Richards Equation (Groundwater)\n\n🔗 [**Richards Equation**](16-Richards-Equation-Groundwater.ipynb): Introduces the Richards equation for variably-saturated porous media flow. Solves a steady-state drainage problem in a vertical soil column using the Gardner exponential conductivity model and validates against an exact analytical solution.\n\n#### Notebook 17 - Richards Equation — Transient Wetting Front\n\n🔗 [**Transient Wetting Front**](17-Richards-Transient-Wetting-Front.ipynb): Solves a transient Richards equation problem where a wetting front propagates downward through a dry soil column. Validates the numerical solution against the Ogata–Banks analytical benchmark for the Gardner model." }, { "cell_type": "markdown", diff --git a/docs/developer/guides/notebook-style-guide.md b/docs/developer/guides/notebook-style-guide.md index 4fae3e3c3..9deddc05c 100644 --- a/docs/developer/guides/notebook-style-guide.md +++ b/docs/developer/guides/notebook-style-guide.md @@ -71,17 +71,21 @@ print("Success!") # Unnecessary import numpy as np ``` -3. **Concept Sections** +3. **Parameters Cell** (see [Parameters and Configuration](#parameters-and-configuration) below) + - Named constants for defaults, then `uw.Params` block + - Markdown cell above explaining CLI override syntax + +4. **Concept Sections** - Markdown header (##) for each major concept - Brief explanation in markdown - Code cells demonstrating the concept - Minimal output cells (let Jupyter display) -4. **Summary** (markdown) +5. **Summary** (markdown) - Key takeaways in bullet points - When to use what -5. **Try It Yourself** (markdown) +6. **Try It Yourself** (markdown) - Optional exercises in code fences - Encourage exploration @@ -110,6 +114,79 @@ mesh.units mesh.view() ``` +## Parameters and Configuration + +Every notebook or example script that accepts tuneable settings should use +`uw.Params`. The standard pattern has two parts: + +1. **Named constants** — plain Python variables holding the default values. + These are the first thing a notebook user sees and edits. +2. **`uw.Params` block** — wraps the constants with units, bounds, + descriptions, and CLI override support. + +### Standard Pattern + +A markdown cell introduces the parameters and shows CLI usage: + +~~~markdown +### Configurable parameters + +Default values are defined as named constants below. From the command +line, override them with PETSc-style flags: + +```bash +python script.py -uw_viscosity "5e20 Pa*s" -uw_cell_size 25km +``` +~~~ + +Followed by the code cell: + +```python +# --- Default values (edit these in a notebook) --- +VISCOSITY = 1e21 # Pa·s – reference viscosity +CELL_SIZE = 50.0 # km – target cell size +DEPTH = 660.0 # km – model depth +MAX_STEPS = 100 # solver iterations + +params = uw.Params( + uw_viscosity = uw.Param(VISCOSITY, units="Pa*s", description="reference viscosity"), + uw_cell_size = uw.Param(CELL_SIZE, units="km", description="target cell size"), + uw_depth = uw.Param(DEPTH, units="km", description="model depth"), + uw_max_steps = MAX_STEPS, +) +``` + +### Why Named Constants + +- **Visibility**: The reader sees the default values at a glance without + having to parse the `uw.Param(...)` wrapper. +- **Editability**: In a notebook, changing a default is a single number + edit at the top of the cell — no need to find it inside a function call. +- **Separation of concerns**: The constants say *what* the defaults are; + the `uw.Params` block says *how* they are validated and overridden. + +### Naming Conventions + +- Named constants: `UPPER_CASE` with a brief inline comment showing + units and purpose. +- Parameter names: `uw_` prefix to avoid PETSc option collisions. +- Add a `description=` string for any parameter that will appear in + `params.cli_help()`. + +### What Not To Do + +```python +# Avoid: inline literals with no named constant +params = uw.Params( + uw_viscosity = uw.Param(1e21, units="Pa*s"), # hard to scan +) + +# Avoid: parameters scattered through the notebook +viscosity = 1e21 # defined in cell 3 +# ... 20 cells later ... +params.uw_viscosity = viscosity # reader has lost context +``` + ## What to Avoid - ❌ Excessive congratulation ("Great job!", "Excellent!") diff --git a/docs/examples/WIP/Benchmark/Ex_VP_Spiegelman_Benchmark.py b/docs/examples/WIP/Benchmark/Ex_VP_Spiegelman_Benchmark.py index adfc966a4..199828edf 100644 --- a/docs/examples/WIP/Benchmark/Ex_VP_Spiegelman_Benchmark.py +++ b/docs/examples/WIP/Benchmark/Ex_VP_Spiegelman_Benchmark.py @@ -715,6 +715,7 @@ def plastic_viscosity(alpha): pl2.show(cpos="xy") -# %% +# %% language="sh" +# python --version # %% diff --git a/src/underworld3/__init__.py b/src/underworld3/__init__.py index 25b76b204..ad4b80e62 100644 --- a/src/underworld3/__init__.py +++ b/src/underworld3/__init__.py @@ -221,6 +221,7 @@ def view(): from .constitutive_models import MultiMaterialConstitutiveModel from .function import quantity, expression, with_units, expand, unwrap from .coordinates import uwdiff # Differentiation helper for UWCoordinates +from .utilities import retention_curves # Unit utilities (top-level convenience for user code) from .function.unit_conversion import _extract_value diff --git a/src/underworld3/systems/__init__.py b/src/underworld3/systems/__init__.py index 4ca160072..fa0160ba0 100644 --- a/src/underworld3/systems/__init__.py +++ b/src/underworld3/systems/__init__.py @@ -23,6 +23,10 @@ Navier-Stokes equations with inertia. Diffusion : class Pure diffusion (no advection). +TransientDarcy : class + Transient groundwater flow with constant storage. +Richards : class + Richards equation for variably-saturated flow. Time Derivative Schemes ----------------------- @@ -61,6 +65,10 @@ # import diffusion-only solver from .solvers import SNES_Diffusion as Diffusion +# Transient Darcy and Richards solvers +from .solvers import SNES_TransientDarcy as TransientDarcy +from .solvers import SNES_Richards as Richards + # These are now implemented the same way using the ddt module from .solvers import SNES_NavierStokes as NavierStokesSwarm from .solvers import SNES_NavierStokes as NavierStokesSLCN diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 1c8ed0f60..3f55c6447 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -11,6 +11,10 @@ Poisson/diffusion equation: :math:`\nabla \cdot (k \nabla T) = f` SNES_Darcy Darcy flow: pressure-driven flow through porous media +SNES_TransientDarcy + Transient groundwater flow with constant storage +SNES_Richards + Richards equation for variably-saturated porous media flow Vector Equations ---------------- @@ -548,6 +552,453 @@ def solve( # super()._setup_terms() +class SNES_TransientDarcy(SNES_Darcy): + r""" + Transient Darcy flow solver for time-dependent groundwater problems. + + Solves the transient groundwater flow equation: + + .. math:: + + S_s \frac{\partial h}{\partial t} + - \nabla \cdot \left[ K (\nabla h - \mathbf{s}) \right] = f + + where :math:`S_s` is the specific storage (constant), :math:`K` is the + hydraulic conductivity, :math:`\mathbf{s}` is the body force (gravity), + and :math:`f` is a source/sink term. + + Inherits velocity projection from :class:`SNES_Darcy`. + + Parameters + ---------- + mesh : Mesh + The computational mesh. + h_Field : MeshVariable, optional + Mesh variable for hydraulic head. + v_Field : MeshVariable, optional + Mesh variable for Darcy velocity. + order : int, default=1 + Time integration order (BDF/Adams-Moulton history depth). + theta : float, default=0.5 + Implicit time weighting (0=explicit, 0.5=Crank-Nicolson, 1=implicit). + degree : int, default=2 + Polynomial degree for finite element discretization. + verbose : bool, default=False + Enable verbose output. + DuDt : optional + Time derivative operator for the unknown. + DFDt : optional + Time derivative operator for the flux. + + Attributes + ---------- + storage : sympy.Expr + Specific storage :math:`S_s` (default 1). + delta_t : UWexpression + Current timestep. + + See Also + -------- + SNES_Darcy : Steady-state parent solver. + SNES_Richards : Nonlinear extension for unsaturated flow. + """ + + @timing.routine_timer_decorator + def __init__( + self, + mesh: uw.discretisation.Mesh, + h_Field: Optional[uw.discretisation.MeshVariable] = None, + v_Field: Optional[uw.discretisation.MeshVariable] = None, + order: int = 1, + theta: float = 0.5, + degree: int = 2, + verbose=False, + DuDt=None, + DFDt=None, + ): + super().__init__(mesh, h_Field, v_Field, degree, verbose, DuDt=DuDt, DFDt=DFDt) + + self.theta = theta + self._delta_t = expression(R"\Delta t", 0, "Physically motivated timestep") + self._storage = sympy.sympify(1) + self.is_setup = False + + if DuDt is None: + self.Unknowns.DuDt = Eulerian_DDt( + self.mesh, + h_Field, + vtype=uw.VarType.SCALAR, + degree=h_Field.degree, + continuous=h_Field.continuous, + varsymbol=h_Field.symbol, + verbose=verbose, + order=order, + smoothing=0.0, + ) + else: + if order is not None and DuDt.order < order: + raise RuntimeError( + f"DuDt supplied is order {DuDt.order} but order requested is {order}" + ) + self.Unknowns.DuDt = DuDt + + if DFDt is None: + self.Unknowns.DFDt = Symbolic_DDt( + sympy.Matrix([[0] * self.mesh.dim]), + varsymbol=rf"{{F[ {self.u.symbol} ] }}", + theta=theta, + order=order, + ) + else: + self.Unknowns.DFDt = DFDt + + # --- Properties --- + + @property + def storage(self): + """Specific storage coefficient :math:`S_s`.""" + return self._storage + + @storage.setter + def storage(self, value): + self.is_setup = False + self._storage = sympy.sympify(value) + + @property + def delta_t(self): + """Current timestep.""" + return self._delta_t + + @delta_t.setter + def delta_t(self, value): + self.is_setup = False + if hasattr(value, "value"): + self._delta_t.sym = value.value + elif hasattr(value, "magnitude"): + self._delta_t.sym = value.magnitude + else: + self._delta_t.sym = value + + @property + def DuDt(self): + return self.Unknowns.DuDt + + @property + def DFDt(self): + return self.Unknowns.DFDt + + # --- Template expressions (override Darcy's steady-state Templates) --- + + @property + def F0(self): + """Pointwise storage + source: :math:`S_s \\dot{h} / \\Delta t - f`.""" + f0 = expression( + r"f_0(h)", + -self.f + self.storage * self.DuDt.bdf() / self.delta_t, + "Transient Darcy storage + source term", + ) + self._f0 = f0 + return f0 + + @property + def F1(self): + """Pointwise flux: Adams-Moulton time-weighted Darcy flux.""" + F1_val = expression( + r"\mathbf{F}_1(h)", + self.DFDt.adams_moulton_flux(), + "Transient Darcy flux (time-weighted)", + ) + self._f1 = F1_val + return F1_val + + # --- Timestep estimation --- + + @timing.routine_timer_decorator + def estimate_dt(self): + r""" + Estimate a stable timestep based on diffusive CFL. + + Returns + ------- + float or pint.Quantity + Diffusive timestep :math:`\delta t = (\Delta x)^2 / K_{\max}`. + """ + from mpi4py import MPI + + K = self.constitutive_model.K + + if isinstance(K, sympy.Expr) or hasattr(K, "sym"): + K_sym = K.sym if hasattr(K, "sym") else K + if uw.function.fn_is_constant_expr(K_sym): + diffusivity = uw.function.evaluate( + K_sym, np.zeros((1, self.mesh.dim)) + ) + else: + diffusivity = uw.function.evaluate( + sympy.sympify(K_sym), self.mesh._centroids, self.mesh.N + ) + diffusivity = diffusivity.max() + else: + diffusivity = K + + if hasattr(diffusivity, "units") and diffusivity.units is not None: + diffusivity = uw.non_dimensionalise(diffusivity) + elif hasattr(diffusivity, "magnitude"): + diffusivity = diffusivity.magnitude + + diffusivity = float(np.asarray(diffusivity).max()) + + comm = uw.mpi.comm + diffusivity_glob = comm.allreduce(diffusivity, op=MPI.MAX) + + min_dx = self.mesh.get_min_radius() + + if diffusivity_glob != 0.0: + dt_diff = (min_dx**2) / diffusivity_glob + else: + dt_diff = np.inf + + return _apply_unit_aware_scaling(np.squeeze(dt_diff), self.u, self.mesh) + + # --- Solve --- + + @timing.routine_timer_decorator + def solve( + self, + zero_init_guess: bool = True, + timestep=None, + _force_setup: bool = False, + verbose=False, + ): + r""" + Solve the transient Darcy system for one timestep. + + Parameters + ---------- + zero_init_guess : bool, optional + Start from zero initial guess (default True). + timestep : float, optional + Timestep size. Updates ``self.delta_t`` if provided. + _force_setup : bool, optional + Force re-setup of solver. + verbose : bool, optional + Print solver progress. + """ + if timestep is not None and timestep != self.delta_t: + self.delta_t = timestep + + if not self.constitutive_model._solver_is_setup: + self.is_setup = False + self.DFDt.psi_fn = self.constitutive_model.flux.T + + if not self.is_setup: + self._setup_pointwise_functions(verbose) + self._setup_discretisation(verbose) + self._setup_solver(verbose) + + # Pre-solve: update history terms + self.DuDt.update_pre_solve(timestep, verbose=verbose) + self.DFDt.update_pre_solve(timestep, verbose=verbose) + + # Solve PDE (bypass SNES_Darcy.solve to avoid double setup/projection) + SNES_Scalar.solve(self, zero_init_guess, _force_setup) + + # Invalidate cached data views + target_var = getattr(self.u, "_base_var", self.u) + if hasattr(target_var, "_canonical_data"): + target_var._canonical_data = None + + # Post-solve: shift history + self.DuDt.update_post_solve(timestep, verbose=verbose) + self.DFDt.update_post_solve(timestep, verbose=verbose) + + # Velocity projection (inherited from Darcy) + self._v_projector.uw_function = self.darcy_flux + self._v_projector.solve(zero_init_guess) + + self.is_setup = True + self.constitutive_model._solver_is_setup = True + + return + + +class SNES_Richards(SNES_TransientDarcy): + r""" + Richards equation solver for variably-saturated porous media flow. + + Two formulations are supported: + + **Mixed form** (mass-conservative, preferred) — set ``water_content``: + + .. math:: + + \frac{\partial \theta}{\partial t} + - \nabla \cdot \left[ K(\psi) (\nabla \psi - \mathbf{s}) \right] = f + + discretised as :math:`(\theta(\psi^{n+1}) - \theta(\psi^n)) / \Delta t`, + which is exactly conservative by construction (Celia et al., 1990). + + **Head-based form** (backward compatible) — set ``capacity``: + + .. math:: + + C(\psi) \frac{\partial \psi}{\partial t} + - \nabla \cdot \left[ K(\psi) (\nabla \psi - \mathbf{s}) \right] = f + + where :math:`C(\psi) = d\theta/d\psi` is the specific moisture capacity. + + Parameters + ---------- + mesh : Mesh + The computational mesh. + psi_Field : MeshVariable, optional + Mesh variable for pressure head :math:`\psi`. + v_Field : MeshVariable, optional + Mesh variable for Darcy velocity. + order : int, default=1 + Time integration order. + theta : float, default=0.5 + Implicit time weighting. + degree : int, default=2 + Polynomial degree. + verbose : bool, default=False + Enable verbose output. + DuDt : optional + Time derivative operator for the unknown. + DFDt : optional + Time derivative operator for the flux. + + Attributes + ---------- + water_content : sympy.Expr or None + Water content function :math:`\theta(\psi)` for the mixed form. + When set, the storage term uses + :math:`(\theta(\psi^{n+1}) - \theta(\psi^n)) / \Delta t`. + Takes precedence over ``capacity`` if both are set. + capacity : sympy.Expr + Specific moisture capacity :math:`C(\psi)` for the head-based form. + Used only when ``water_content`` is None. + psi : MeshVariable + Alias for ``self.u`` (pressure head). + + See Also + -------- + SNES_TransientDarcy : Linear parent solver. + underworld3.utilities.retention_curves : Van Genuchten and Gardner functions. + + Examples + -------- + Mixed form (preferred): + + >>> from underworld3.utilities.retention_curves import ( + ... van_genuchten_theta, van_genuchten_K, + ... ) + >>> richards = uw.systems.Richards(mesh, psi_Field=psi, v_Field=v) + >>> richards.constitutive_model = uw.constitutive_models.DarcyFlowModel + >>> richards.constitutive_model.Parameters.permeability = van_genuchten_K( + ... psi.sym[0], Ks=1e-4, alpha=3.35, n=2.0, + ... ) + >>> richards.water_content = van_genuchten_theta( + ... psi.sym[0], theta_r=0.045, theta_s=0.43, alpha=3.35, n=2.0, + ... ) + + Head-based form (backward compatible): + + >>> from underworld3.utilities.retention_curves import van_genuchten_C + >>> richards.capacity = van_genuchten_C( + ... psi.sym[0], theta_r=0.045, theta_s=0.43, alpha=3.35, n=2.0, + ... ) + """ + + @timing.routine_timer_decorator + def __init__( + self, + mesh: uw.discretisation.Mesh, + psi_Field: Optional[uw.discretisation.MeshVariable] = None, + v_Field: Optional[uw.discretisation.MeshVariable] = None, + order: int = 1, + theta: float = 0.5, + degree: int = 2, + verbose=False, + DuDt=None, + DFDt=None, + ): + super().__init__( + mesh, psi_Field, v_Field, order, theta, degree, verbose, DuDt, DFDt + ) + self._capacity = sympy.sympify(1) + self._water_content = None # None → head-based form; set → mixed form + + @property + def water_content(self): + r"""Water content function :math:`\theta(\psi)` for the mixed form. + + When set, the storage term uses + :math:`(\theta(\psi^{n+1}) - \theta(\psi^n)) / \Delta t` + instead of :math:`C(\psi) \cdot (\psi^{n+1} - \psi^n) / \Delta t`, + giving exact mass conservation (Celia et al., 1990). + + The expression should be a SymPy function of ``psi.sym[0]``. + The Jacobian :math:`\partial\theta/\partial\psi = C(\psi)` is + computed automatically by PETSc (finite-difference colouring), + so there is no need to provide :math:`C(\psi)` separately. + """ + return self._water_content + + @water_content.setter + def water_content(self, value): + self.is_setup = False + self._water_content = sympy.sympify(value) if value is not None else None + + @property + def capacity(self): + r"""Specific moisture capacity :math:`C(\psi) = d\theta/d\psi`. + + Used only when ``water_content`` is None (head-based form). + Typically a nonlinear SymPy expression depending on ``psi.sym[0]``. + """ + return self._capacity + + @capacity.setter + def capacity(self, value): + self.is_setup = False + self._capacity = sympy.sympify(value) + + @property + def psi(self): + """Alias for ``self.u`` (pressure head).""" + return self.u + + @property + def F0(self): + r"""Pointwise storage + source term. + + Mixed form: :math:`(\theta(\psi^{n+1}) - \theta(\psi^n)) / \Delta t - f` + + Head-based form: :math:`C(\psi) (\psi^{n+1} - \psi^n) / \Delta t - f` + """ + if self._water_content is not None: + # Mixed (mass-conservative) form: + # θ(ψ^{n+1}) is self._water_content (already in terms of psi.sym[0]) + # θ(ψ^n) is water_content with psi.sym[0] → psi_star[0].sym[0] + psi_sym = self.psi.sym[0] + psi_star_sym = self.DuDt.psi_star[0].sym[0] + theta_new = self._water_content + theta_old = self._water_content.subs(psi_sym, psi_star_sym) + storage_term = sympy.Matrix([[theta_new - theta_old]]) / self.delta_t + else: + # Head-based form (backward compatible) + storage_term = self.capacity * self.DuDt.bdf() / self.delta_t + + f0 = expression( + r"f_0(\psi)", + -self.f + storage_term, + "Richards storage + source term", + ) + self._f0 = f0 + return f0 + + ## -------------------------------- ## Stokes saddle point solver plus ## ancilliary functions - note that @@ -2626,16 +3077,14 @@ def solve( super().solve(zero_init_guess, _force_setup) + # Invalidate cached data views - PETSc may have replaced underlying buffers + target_var = getattr(self.u, "_base_var", self.u) + if hasattr(target_var, "_canonical_data"): + target_var._canonical_data = None + self.DuDt.update_post_solve(timestep, evalf=evalf, verbose=verbose) self.DFDt.update_post_solve(timestep, evalf=evalf, verbose=verbose) - # if isinstance(self.DFDt, Eulerian_DDt): - # for i in range(order): - # ### have to substitute the unknown history term into the symbolic flux term - # self.DFDt.psi_star[i].subs({self.DuDt.psi_fn:self.DuDt.psi_star[i]}) - - # self._flux_star = self._flux.copy() - self.is_setup = True self.constitutive_model._solver_is_setup = True diff --git a/src/underworld3/utilities/__init__.py b/src/underworld3/utilities/__init__.py index eec5de726..495301e31 100644 --- a/src/underworld3/utilities/__init__.py +++ b/src/underworld3/utilities/__init__.py @@ -81,3 +81,5 @@ def _append_petsc_path(): ones_with_units, full_with_units, ) + +from . import retention_curves diff --git a/src/underworld3/utilities/_params.py b/src/underworld3/utilities/_params.py index 877c7bad5..950c8eb1c 100644 --- a/src/underworld3/utilities/_params.py +++ b/src/underworld3/utilities/_params.py @@ -14,30 +14,31 @@ - Python: params.uw_mesh_resolution - CLI: -uw_mesh_resolution 0.025 -Example usage: - # Define parameters at top of notebook/script +Recommended pattern: + Define default values as named constants BEFORE the Params block. + This makes defaults easy to find and adjust in a notebook, while + the Params block provides CLI override, units, and descriptions. + + # --- Default values (edit these in a notebook) --- + ETA_0 = 1e21 # Pa·s – reference viscosity + CELL_SIZE = 50.0 # km – mesh cell size + MAX_STEPS = 100 # solver iterations + params = uw.Params( - uw_mesh_resolution = 0.05, # Cell size for mesh - uw_diffusivity = 1.0, # Material property - uw_hot_temp = 100.0, # Boundary temperature + uw_viscosity = uw.Param(ETA_0, units="Pa*s", description="reference viscosity"), + uw_cell_size = uw.Param(CELL_SIZE, units="km", description="mesh cell size"), + uw_max_steps = MAX_STEPS, ) # Use in code: - mesh = uw.meshing.Box(cellSize=params.uw_mesh_resolution) + mesh = uw.meshing.Box(cellSize=params.uw_cell_size) # Override in notebook - just assign: - params.uw_mesh_resolution = 0.025 + params.uw_cell_size = uw.quantity(25, "km") # Override from command line (flag matches Python name): - # python script.py -uw_mesh_resolution 0.025 - # mpirun -np 4 python script.py -uw_diffusivity 2.0 - - # With units support: - params = uw.Params( - uw_cell_size = uw.Param(0.5, units="km", description="Mesh cell size"), - uw_viscosity = uw.Param(1e21, units="Pa*s"), - ) - # CLI: python script.py -uw_cell_size 500m -uw_viscosity "1e22 Pa*s" + # python script.py -uw_cell_size 25km -uw_viscosity "1e22 Pa*s" + # mpirun -np 4 python script.py -uw_cell_size 10km """ from enum import Enum diff --git a/src/underworld3/utilities/retention_curves.py b/src/underworld3/utilities/retention_curves.py new file mode 100644 index 000000000..79dd2c908 --- /dev/null +++ b/src/underworld3/utilities/retention_curves.py @@ -0,0 +1,505 @@ +r""" +Retention curve functions for variably-saturated porous media flow. + +Provides retention curve functions that return SymPy expressions +suitable for use with the Richards equation solver: + +- **Van Genuchten–Mualem** model: general-purpose, widely used. +- **Gardner exponential** model: simpler, admits exact analytical + solutions for steady-state Richards equation with gravity. + +All functions accept a SymPy symbol or expression for pressure head +(typically ``psi_field.sym[0]``) and return SymPy expressions that +can be assigned directly to solver properties. + +References +---------- +Van Genuchten, M. Th. (1980). A closed-form equation for predicting +the hydraulic conductivity of unsaturated soils. +*Soil Science Society of America Journal*, 44(5), 892–898. + +Mualem, Y. (1976). A new model for predicting the hydraulic +conductivity of unsaturated porous media. +*Water Resources Research*, 12(3), 513–522. + +Gardner, W. R. (1958). Some steady-state solutions of the +unsaturated moisture flow equation with application to evaporation +from a water table. *Soil Science*, 85(4), 228–232. + +Examples +-------- +>>> import sympy +>>> from underworld3.utilities.retention_curves import ( +... van_genuchten_Se, van_genuchten_K, van_genuchten_C, +... ) +>>> psi = sympy.Symbol("psi") +>>> Se = van_genuchten_Se(psi, alpha=3.35, n=2.0) +>>> K = van_genuchten_K(psi, Ks=1e-4, alpha=3.35, n=2.0) +>>> C = van_genuchten_C(psi, theta_r=0.045, theta_s=0.43, alpha=3.35, n=2.0) + +Gardner model with analytical steady-state solution: + +>>> from underworld3.utilities.retention_curves import ( +... gardner_K, gardner_C, gardner_steady_state_psi, +... ) +>>> K = gardner_K(psi, Ks=1e-4, alpha=1.0) +>>> C = gardner_C(psi, theta_r=0.05, theta_s=0.4, alpha=1.0) +""" + +import sympy + + +def van_genuchten_Se(psi, alpha, n, m=None): + r"""Effective saturation (Van Genuchten model). + + .. math:: + + S_e(\psi) = \begin{cases} + \left[1 + (\alpha |\psi|)^n\right]^{-m} & \psi < 0 \\ + 1 & \psi \ge 0 + \end{cases} + + Parameters + ---------- + psi : sympy expression + Pressure head (negative in unsaturated zone). + alpha : float + Inverse of the air-entry pressure [1/length]. + n : float + Pore-size distribution parameter (n > 1). + m : float, optional + Van Genuchten parameter. Default: ``1 - 1/n``. + + Returns + ------- + sympy.Piecewise + Effective saturation expression. + """ + if m is None: + m = 1 - 1 / sympy.Rational(n) if isinstance(n, int) else 1 - 1 / n + + alpha = sympy.sympify(alpha) + n = sympy.sympify(n) + m = sympy.sympify(m) + + Se_unsat = (1 + (alpha * (-psi)) ** n) ** (-m) + return sympy.Piecewise((sympy.S.One, psi >= 0), (Se_unsat, True)) + + +def van_genuchten_theta(psi, theta_r, theta_s, alpha, n, m=None): + r"""Volumetric water content (Van Genuchten model). + + .. math:: + + \theta(\psi) = \theta_r + (\theta_s - \theta_r)\, S_e(\psi) + + Parameters + ---------- + psi : sympy expression + Pressure head. + theta_r : float + Residual water content. + theta_s : float + Saturated water content. + alpha : float + Inverse of the air-entry pressure [1/length]. + n : float + Pore-size distribution parameter. + m : float, optional + Default: ``1 - 1/n``. + + Returns + ------- + sympy.Expr + Water content expression. + """ + theta_r = sympy.sympify(theta_r) + theta_s = sympy.sympify(theta_s) + Se = van_genuchten_Se(psi, alpha, n, m) + return theta_r + (theta_s - theta_r) * Se + + +def van_genuchten_K(psi, Ks, alpha, n, m=None): + r"""Hydraulic conductivity (Van Genuchten–Mualem model). + + .. math:: + + K(\psi) = \begin{cases} + K_s \, S_e^{1/2} + \left[1 - \left(1 - S_e^{1/m}\right)^m\right]^2 + & \psi < 0 \\ + K_s & \psi \ge 0 + \end{cases} + + Parameters + ---------- + psi : sympy expression + Pressure head. + Ks : float + Saturated hydraulic conductivity. + alpha : float + Inverse of the air-entry pressure [1/length]. + n : float + Pore-size distribution parameter. + m : float, optional + Default: ``1 - 1/n``. + + Returns + ------- + sympy.Piecewise + Hydraulic conductivity expression. + """ + if m is None: + m = 1 - 1 / sympy.Rational(n) if isinstance(n, int) else 1 - 1 / n + + Ks = sympy.sympify(Ks) + m = sympy.sympify(m) + + Se = van_genuchten_Se(psi, alpha, n, m) + # For the unsaturated branch, extract the unsaturated Se expression + alpha_s = sympy.sympify(alpha) + n_s = sympy.sympify(n) + Se_expr = (1 + (alpha_s * (-psi)) ** n_s) ** (-m) + + K_unsat = Ks * Se_expr ** sympy.Rational(1, 2) * ( + 1 - (1 - Se_expr ** (1 / m)) ** m + ) ** 2 + + return sympy.Piecewise((Ks, psi >= 0), (K_unsat, True)) + + +def van_genuchten_C(psi, theta_r, theta_s, alpha, n, m=None, Ss=0.0): + r"""Specific moisture capacity (Van Genuchten model). + + .. math:: + + C(\psi) = \frac{d\theta}{d\psi} = \begin{cases} + \alpha\, m\, n\, (\theta_s - \theta_r)\, + (\alpha |\psi|)^{n-1}\, + \left[1 + (\alpha |\psi|)^n\right]^{-(m+1)} + & \psi < 0 \\ + S_s & \psi \ge 0 + \end{cases} + + Parameters + ---------- + psi : sympy expression + Pressure head. + theta_r : float + Residual water content. + theta_s : float + Saturated water content. + alpha : float + Inverse of the air-entry pressure [1/length]. + n : float + Pore-size distribution parameter. + m : float, optional + Default: ``1 - 1/n``. + Ss : float, optional + Specific storage for the saturated zone (default 0). + Set to a small positive value (e.g. 1e-4) to avoid + a singular mass matrix when the domain is fully saturated. + + Returns + ------- + sympy.Piecewise + Specific moisture capacity expression. + """ + if m is None: + m = 1 - 1 / sympy.Rational(n) if isinstance(n, int) else 1 - 1 / n + + alpha = sympy.sympify(alpha) + n = sympy.sympify(n) + m = sympy.sympify(m) + theta_r = sympy.sympify(theta_r) + theta_s = sympy.sympify(theta_s) + Ss = sympy.sympify(Ss) + + C_unsat = ( + alpha + * m + * n + * (theta_s - theta_r) + * (alpha * (-psi)) ** (n - 1) + * (1 + (alpha * (-psi)) ** n) ** (-(m + 1)) + ) + + return sympy.Piecewise((Ss, psi >= 0), (C_unsat, True)) + + +# ===================================================================== +# Gardner exponential model +# ===================================================================== + + +def gardner_K(psi, Ks, alpha): + r"""Hydraulic conductivity (Gardner exponential model). + + .. math:: + + K(\psi) = \begin{cases} + K_s \exp(\alpha\,\psi) & \psi < 0 \\ + K_s & \psi \ge 0 + \end{cases} + + Parameters + ---------- + psi : sympy expression + Pressure head (negative in unsaturated zone). + Ks : float + Saturated hydraulic conductivity. + alpha : float + Sorptive number [1/length]. Larger values give a + sharper transition near saturation. + + Returns + ------- + sympy.Piecewise + Hydraulic conductivity expression. + """ + Ks = sympy.sympify(Ks) + alpha = sympy.sympify(alpha) + + K_unsat = Ks * sympy.exp(alpha * psi) + return sympy.Piecewise((Ks, psi >= 0), (K_unsat, True)) + + +def gardner_theta(psi, theta_r, theta_s, alpha): + r"""Volumetric water content (Gardner exponential model). + + .. math:: + + \theta(\psi) = \begin{cases} + \theta_r + (\theta_s - \theta_r)\,\exp(\alpha\,\psi) + & \psi < 0 \\ + \theta_s & \psi \ge 0 + \end{cases} + + Parameters + ---------- + psi : sympy expression + Pressure head. + theta_r : float + Residual water content. + theta_s : float + Saturated water content. + alpha : float + Sorptive number [1/length]. + + Returns + ------- + sympy.Piecewise + Water content expression. + """ + theta_r = sympy.sympify(theta_r) + theta_s = sympy.sympify(theta_s) + alpha = sympy.sympify(alpha) + + theta_unsat = theta_r + (theta_s - theta_r) * sympy.exp(alpha * psi) + return sympy.Piecewise((theta_s, psi >= 0), (theta_unsat, True)) + + +def gardner_C(psi, theta_r, theta_s, alpha, Ss=0.0): + r"""Specific moisture capacity (Gardner exponential model). + + .. math:: + + C(\psi) = \frac{d\theta}{d\psi} = \begin{cases} + \alpha\,(\theta_s - \theta_r)\,\exp(\alpha\,\psi) + & \psi < 0 \\ + S_s & \psi \ge 0 + \end{cases} + + Parameters + ---------- + psi : sympy expression + Pressure head. + theta_r : float + Residual water content. + theta_s : float + Saturated water content. + alpha : float + Sorptive number [1/length]. + Ss : float, optional + Specific storage for the saturated zone (default 0). + + Returns + ------- + sympy.Piecewise + Specific moisture capacity expression. + """ + theta_r = sympy.sympify(theta_r) + theta_s = sympy.sympify(theta_s) + alpha = sympy.sympify(alpha) + Ss = sympy.sympify(Ss) + + C_unsat = alpha * (theta_s - theta_r) * sympy.exp(alpha * psi) + return sympy.Piecewise((Ss, psi >= 0), (C_unsat, True)) + + +def gardner_steady_state_psi(y, psi_0, psi_L, L, alpha): + r"""Analytical steady-state pressure head for Gardner model with gravity. + + For a 1D vertical column of height *L* with the Gardner conductivity + model, steady-state Richards equation with gravity reduces to + + .. math:: + + K(\psi)\left(\frac{d\psi}{dy} + 1\right) = q = \text{const} + + The substitution :math:`u = \exp(\alpha\psi)` linearises the ODE. + The exact solution with boundary conditions + :math:`\psi(0)=\psi_0` (bottom) and :math:`\psi(L)=\psi_L` (top) is + + .. math:: + + \psi(y) = \frac{1}{\alpha}\,\ln\!\Bigl[ + \bigl(u_0 - q^*\bigr)\,e^{-\alpha y} + q^* + \Bigr] + + where :math:`u_0 = e^{\alpha\psi_0}`, + :math:`u_L = e^{\alpha\psi_L}`, and + + .. math:: + + q^* \equiv \frac{q}{K_s} + = \frac{u_L - u_0\,e^{-\alpha L}}{1 - e^{-\alpha L}} + + Parameters + ---------- + y : float or array + Vertical coordinate (0 = bottom, *L* = top). + psi_0 : float + Pressure head at the bottom boundary. + psi_L : float + Pressure head at the top boundary. + L : float + Column height. + alpha : float + Gardner sorptive number [1/length]. + + Returns + ------- + float or array + Exact pressure head profile :math:`\psi(y)`. + + Notes + ----- + This is a *numpy* function (not sympy) intended for comparing + numerical solutions against the analytical benchmark. + """ + import numpy as np + + u_0 = np.exp(alpha * psi_0) + u_L = np.exp(alpha * psi_L) + + # Normalised steady-state flux q* = q / Ks + q_star = (u_L - u_0 * np.exp(-alpha * L)) / (1.0 - np.exp(-alpha * L)) + + return (1.0 / alpha) * np.log((u_0 - q_star) * np.exp(-alpha * y) + q_star) + + +def gardner_transient_psi(y, t, psi_dry, psi_wet, L, Ks, alpha, theta_r, theta_s): + r"""Analytical transient wetting-front solution for Gardner model. + + Applies the **Ogata–Banks** (1961) solution to Richards equation + with Gardner conductivity in a vertical column of height *L*. + + The substitution :math:`u = \exp(\alpha\psi)` transforms the + nonlinear Richards equation into linear advection–diffusion: + + .. math:: + + \frac{\partial u}{\partial t} + = D\,\frac{\partial^2 u}{\partial z^2} + + V\,\frac{\partial u}{\partial z} + + where :math:`z = L - y` (depth from the top), + :math:`D = K_s / (\alpha\,\Delta\theta)`, + :math:`V = K_s / \Delta\theta`, and + :math:`\Delta\theta = \theta_s - \theta_r`. + + With a **step change** at the top (:math:`z = 0`) from dry to wet + and a semi-infinite column approximation, the Ogata–Banks solution + gives + + .. math:: + + u(z, t) = u_{\rm dry} + + (u_{\rm wet} - u_{\rm dry})\,H(z, t) + + where + + .. math:: + + H(z, t) = \tfrac{1}{2}\,\operatorname{erfc}\!\left( + \frac{z - Vt}{2\sqrt{Dt}}\right) + + \tfrac{1}{2}\,\exp\!\left(\frac{Vz}{D}\right)\, + \operatorname{erfc}\!\left(\frac{z + Vt}{2\sqrt{Dt}}\right) + + Finally, :math:`\psi(y, t) = \ln(u) / \alpha`. + + Parameters + ---------- + y : float or array + Vertical coordinate (0 = bottom, *L* = top). + t : float + Time since the wet boundary was applied (must be > 0). + psi_dry : float + Initial (dry) pressure head throughout the column. + psi_wet : float + Pressure head imposed at the top boundary. + L : float + Column height. + Ks : float + Saturated hydraulic conductivity. + alpha : float + Gardner sorptive number [1/length]. + theta_r : float + Residual water content. + theta_s : float + Saturated water content. + + Returns + ------- + float or array + Pressure head profile :math:`\psi(y, t)`. + + Notes + ----- + This is a *numpy* function (not sympy) intended for comparing + numerical solutions against the analytical benchmark. + + The semi-infinite approximation is excellent when the wetting + front has not yet reached the bottom boundary. + + References + ---------- + Ogata, A. and Banks, R. B. (1961). A solution of the differential + equation of longitudinal dispersion in porous media. + *US Geological Survey Professional Paper* 411-A. + """ + import numpy as np + from scipy.special import erfc + + delta_theta = theta_s - theta_r + D = Ks / (alpha * delta_theta) + V = Ks / delta_theta + + u_dry = np.exp(alpha * psi_dry) + u_wet = np.exp(alpha * psi_wet) + + # Depth from the top (z = 0 at top, z = L at bottom) + z = L - np.asarray(y, dtype=float) + + sqrt_Dt = np.sqrt(D * t) + + # Ogata-Banks solution + H = ( + 0.5 * erfc((z - V * t) / (2.0 * sqrt_Dt)) + + 0.5 * np.exp(V * z / D) * erfc((z + V * t) / (2.0 * sqrt_Dt)) + ) + + u = u_dry + (u_wet - u_dry) * H + + return (1.0 / alpha) * np.log(np.maximum(u, 1e-30)) diff --git a/tests/test_1005_TransientDarcyCartesian.py b/tests/test_1005_TransientDarcyCartesian.py new file mode 100644 index 000000000..d7ca122f6 --- /dev/null +++ b/tests/test_1005_TransientDarcyCartesian.py @@ -0,0 +1,116 @@ +# %% +# Test transient Darcy flow solver against analytical diffusion solution. +# +# A 1D vertical column with constant K and constant S_s reduces to +# simple diffusion: S_s dh/dt = K d²h/dy² +# With step-change BC at the top (h=1) and fixed h=0 at the bottom, +# the analytical solution is an error-function diffusion profile. + +import underworld3 as uw +import numpy as np +import sympy as sp +import pytest + +# Physics solver tests +pytestmark = pytest.mark.level_3 + + +@pytest.fixture(autouse=True) +def reset_model_state(): + """Reset model state before each test.""" + uw.reset_default_model() + uw.use_strict_units(False) + uw.use_nondimensional_scaling(False) + yield + uw.reset_default_model() + uw.use_strict_units(False) + uw.use_nondimensional_scaling(False) + + +# Domain parameters +res = 32 +minX, maxX = 0.0, 0.1 # narrow to make it effectively 1D +minY, maxY = 0.0, 1.0 + +# Physical parameters +K_val = 1.0 # hydraulic conductivity +Ss_val = 1.0 # specific storage → diffusivity D = K/Ss = 1 + +t_start = 0.005 # small offset so erf profile is resolved +t_end = 0.02 + + +def create_mesh(): + return uw.meshing.StructuredQuadBox( + elementRes=(4, res), + minCoords=(minX, minY), + maxCoords=(maxX, maxY), + qdegree=3, + ) + + +# Analytical solution: step-change diffusion in a semi-infinite column +# h(y,t) = erfc(y / (2 sqrt(D t))) where D = K/Ss +# with h(0,t) = 1, h(inf,t) = 0 +y_sym, t_sym = sp.symbols("y t", positive=True) +D_val = K_val / Ss_val +h_analytic = sp.erfc(y_sym / (2 * sp.sqrt(D_val * t_sym))) + + +def test_transient_darcy_diffusion(): + """Transient Darcy with constant K and S_s should match 1D diffusion.""" + mesh = create_mesh() + + h_soln = uw.discretisation.MeshVariable("h", mesh, 1, degree=2) + v_soln = uw.discretisation.MeshVariable("v", mesh, mesh.dim, degree=1) + + darcy = uw.systems.TransientDarcy( + mesh, h_soln, v_soln, order=1, theta=0.5, + ) + darcy.petsc_options.delValue("ksp_monitor") + darcy.petsc_options["snes_rtol"] = 1.0e-6 + + darcy.constitutive_model = uw.constitutive_models.DarcyFlowModel + darcy.constitutive_model.Parameters.permeability = K_val + darcy.constitutive_model.Parameters.s = sp.Matrix([0, 0]).T # no gravity + darcy.storage = Ss_val + darcy.f = 0.0 + + # BCs: h=1 at bottom (y=0), h=0 at top (y=1) + darcy.add_dirichlet_bc([1.0], "Bottom") + darcy.add_dirichlet_bc([0.0], "Top") + + darcy._v_projector.petsc_options["snes_rtol"] = 1.0e-6 + darcy._v_projector.smoothing = 1.0e-6 + + # Initial condition: analytical profile at t_start + h_init = h_analytic.subs(t_sym, t_start) + h_init_fn = h_init.subs(y_sym, mesh.X[1]) + h_soln.array = uw.function.evaluate(h_init_fn, h_soln.coords) + + # Time-step + dt = darcy.estimate_dt() + # Cap dt so we take a few steps + dt = min(dt, (t_end - t_start) / 4) + model_time = t_start + + while model_time < t_end: + if model_time + dt > t_end: + dt = t_end - model_time + darcy.solve(timestep=dt) + model_time += dt + + # Compare along a vertical profile at x = midpoint + n_sample = 50 + sample_y = np.linspace(0.05, 0.95, n_sample) + sample_x = np.full_like(sample_y, 0.5 * (minX + maxX)) + sample_pts = np.column_stack([sample_x, sample_y]) + + h_numerical = uw.function.evaluate(h_soln.sym[0], sample_pts).squeeze() + + h_exact_fn = h_analytic.subs(t_sym, t_end).subs(y_sym, mesh.X[1]) + h_exact = uw.function.evaluate(h_exact_fn, sample_pts).squeeze() + + assert np.allclose(h_numerical, h_exact, atol=0.1), ( + f"Max error: {np.max(np.abs(h_numerical - h_exact)):.4f}" + ) diff --git a/tests/test_1006_RichardsCartesian.py b/tests/test_1006_RichardsCartesian.py new file mode 100644 index 000000000..a2e4990d5 --- /dev/null +++ b/tests/test_1006_RichardsCartesian.py @@ -0,0 +1,267 @@ +# %% +# Tests for the Richards equation solver. +# +# Test 1: Steady-state drainage with constant K (linear profile). +# Test 2: Transient infiltration with Van Genuchten retention curves. + +import underworld3 as uw +import numpy as np +import sympy as sp +import pytest + +# Physics solver tests +pytestmark = pytest.mark.level_3 + + +@pytest.fixture(autouse=True) +def reset_model_state(): + """Reset model state before each test.""" + uw.reset_default_model() + uw.use_strict_units(False) + uw.use_nondimensional_scaling(False) + yield + uw.reset_default_model() + uw.use_strict_units(False) + uw.use_nondimensional_scaling(False) + + +# --- Domain --- +res = 32 +minX, maxX = 0.0, 0.1 # narrow → effectively 1D +minY, maxY = 0.0, 1.0 + + +def create_mesh(): + return uw.meshing.StructuredQuadBox( + elementRes=(4, res), + minCoords=(minX, minY), + maxCoords=(maxX, maxY), + qdegree=3, + ) + + +def test_richards_steady_constant_K(): + """Richards with constant K and C=1 should give a linear pressure head profile. + + With constant K and gravity s=[0,-1], the steady-state solution of + -∇·[K(∇ψ - s)] = 0 + in 1D (y-direction) with ψ(0)=-5, ψ(1)=0 is: + ψ(y) = -5(1 - y) (linear) + + We use TransientDarcy stepping with small dt to approach steady state, + since Richards inherits from TransientDarcy. + """ + mesh = create_mesh() + + psi = uw.discretisation.MeshVariable("psi", mesh, 1, degree=2) + v_soln = uw.discretisation.MeshVariable("v", mesh, mesh.dim, degree=1) + + richards = uw.systems.Richards(mesh, psi, v_soln, order=1, theta=0.5) + richards.petsc_options.delValue("ksp_monitor") + richards.petsc_options["snes_rtol"] = 1.0e-6 + + K_val = 1.0 + richards.constitutive_model = uw.constitutive_models.DarcyFlowModel + richards.constitutive_model.Parameters.permeability = K_val + richards.constitutive_model.Parameters.s = sp.Matrix([0, -1]).T + richards.capacity = 1 # constant → behaves like TransientDarcy + richards.f = 0.0 + + # BCs: ψ = 0 at top (y=1), ψ = -5 at bottom (y=0) + richards.add_dirichlet_bc([0.0], "Top") + richards.add_dirichlet_bc([-5.0], "Bottom") + + richards._v_projector.petsc_options["snes_rtol"] = 1.0e-6 + richards._v_projector.smoothing = 1.0e-6 + + # Initial guess: linear profile + y = mesh.X[1] + psi_init = -5.0 * (1.0 - y) + psi.array = uw.function.evaluate(psi_init, psi.coords) + + # Step towards steady state with a few large timesteps + dt = 0.1 + for _ in range(10): + richards.solve(timestep=dt) + + # Check along vertical profile + n_sample = 50 + sample_y = np.linspace(0.05, 0.95, n_sample) + sample_x = np.full_like(sample_y, 0.5 * (minX + maxX)) + sample_pts = np.column_stack([sample_x, sample_y]) + + psi_numerical = uw.function.evaluate(psi.sym[0], sample_pts).squeeze() + psi_exact = -5.0 * (1.0 - sample_y) + + assert np.allclose(psi_numerical, psi_exact, atol=0.1), ( + f"Max error: {np.max(np.abs(psi_numerical - psi_exact)):.4f}" + ) + + +def test_richards_transient_infiltration(): + """Richards equation with Van Genuchten curves — basic sanity check. + + Uses a mild initial condition (ψ = -2) with saturated top (ψ = 0) + and fixed bottom (ψ = -2). After several timesteps the wetting + front should propagate downward, making the upper column wetter + (less negative ψ) than the initial state. + + Note: Richards with VG curves is a stiff nonlinear problem. + We use moderate conditions to ensure reliable SNES convergence. + """ + from underworld3.utilities.retention_curves import ( + van_genuchten_K, + van_genuchten_theta, + ) + + mesh = create_mesh() + + psi = uw.discretisation.MeshVariable("psi", mesh, 1, degree=2) + v_soln = uw.discretisation.MeshVariable("v", mesh, mesh.dim, degree=1) + + richards = uw.systems.Richards(mesh, psi, v_soln, order=1, theta=0.5) + richards.petsc_options.delValue("ksp_monitor") + richards.petsc_options["snes_rtol"] = 1.0e-6 + richards.petsc_options["snes_max_it"] = 50 + richards.petsc_options["snes_linesearch_type"] = "bt" + + # Loam-like Van Genuchten parameters (less stiff than sand) + alpha_vg = 1.0 + n_vg = 1.5 + theta_r = 0.08 + theta_s = 0.43 + Ks = 1.0 + + psi_sym = psi.sym[0] + + richards.constitutive_model = uw.constitutive_models.DarcyFlowModel + richards.constitutive_model.Parameters.permeability = van_genuchten_K( + psi_sym, Ks=Ks, alpha=alpha_vg, n=n_vg + ) + richards.constitutive_model.Parameters.s = sp.Matrix([0, -1]).T + + # Mixed form: θ(ψ) for mass-conservative storage term + richards.water_content = van_genuchten_theta( + psi_sym, theta_r=theta_r, theta_s=theta_s, + alpha=alpha_vg, n=n_vg, + ) + richards.f = 0.0 + + # BCs: saturated at top, moderately dry at bottom + richards.add_dirichlet_bc([0.0], "Top") + richards.add_dirichlet_bc([-2.0], "Bottom") + + richards._v_projector.petsc_options["snes_rtol"] = 1.0e-6 + richards._v_projector.smoothing = 1.0e-6 + + # Initial condition: linear profile from -2 at bottom to 0 at top + # (smooth start helps SNES converge) + y = mesh.X[1] + psi_init = -2.0 * (1.0 - y) + psi.array = uw.function.evaluate(psi_init, psi.coords) + + # Run a few timesteps with small dt + dt = 0.005 + n_steps = 5 + for step in range(n_steps): + richards.solve(timestep=dt) + + # Basic sanity checks along a vertical profile + n_sample = 20 + sample_y = np.linspace(0.1, 0.9, n_sample) + sample_x = np.full_like(sample_y, 0.5 * (minX + maxX)) + sample_pts = np.column_stack([sample_x, sample_y]) + + psi_vals = uw.function.evaluate(psi.sym[0], sample_pts).squeeze() + + # 1. Solution should be bounded (no blow-up) + assert np.all(np.isfinite(psi_vals)), "Solution should be finite" + assert np.all(psi_vals >= -5.0), "ψ should not overshoot far below BCs" + assert np.all(psi_vals <= 1.0), "ψ should not overshoot far above BCs" + + # 2. Near the top should be wetter (less negative) than near the bottom + assert psi_vals[-1] >= psi_vals[0], ( + "Pressure head should increase towards the wetted top" + ) + + +def test_richards_gardner_analytical(): + """Richards with Gardner model — validate against exact analytical solution. + + The Gardner exponential conductivity K(ψ) = Ks·exp(α·ψ) admits an + exact steady-state solution for 1D vertical drainage with gravity. + This test converges the solver to steady state and compares against + the analytical profile. + """ + from underworld3.utilities.retention_curves import ( + gardner_K, + gardner_theta, + gardner_steady_state_psi, + ) + + mesh = create_mesh() + + psi = uw.discretisation.MeshVariable("psi", mesh, 1, degree=2) + v_soln = uw.discretisation.MeshVariable("v", mesh, mesh.dim, degree=1) + + richards = uw.systems.Richards(mesh, psi, v_soln, order=1, theta=0.5) + richards.petsc_options.delValue("ksp_monitor") + richards.petsc_options["snes_rtol"] = 1.0e-6 + + # Gardner parameters + Ks = 1.0 + alpha_g = 2.0 + psi_bottom = -3.0 + psi_top = -0.5 + + psi_sym = psi.sym[0] + + richards.constitutive_model = uw.constitutive_models.DarcyFlowModel + richards.constitutive_model.Parameters.permeability = gardner_K( + psi_sym, Ks=Ks, alpha=alpha_g + ) + richards.constitutive_model.Parameters.s = sp.Matrix([0, -1]).T + + # Mixed form: θ(ψ) for mass-conservative storage term + richards.water_content = gardner_theta( + psi_sym, theta_r=0.05, theta_s=0.4, alpha=alpha_g, + ) + richards.f = 0.0 + + # BCs + richards.add_dirichlet_bc([psi_top], "Top") + richards.add_dirichlet_bc([psi_bottom], "Bottom") + + richards._v_projector.petsc_options["snes_rtol"] = 1.0e-6 + richards._v_projector.smoothing = 1.0e-6 + + # Initial guess: linear profile (close enough for SNES) + y = mesh.X[1] + psi_init = psi_bottom + (psi_top - psi_bottom) * y + psi.array = uw.function.evaluate(psi_init, psi.coords) + + # Step towards steady state + dt = 0.1 + for _ in range(20): + richards.solve(timestep=dt) + + # Compare along vertical profile + n_sample = 50 + sample_y = np.linspace(0.05, 0.95, n_sample) + sample_x = np.full_like(sample_y, 0.5 * (minX + maxX)) + sample_pts = np.column_stack([sample_x, sample_y]) + + psi_numerical = uw.function.evaluate(psi.sym[0], sample_pts).squeeze() + psi_exact = gardner_steady_state_psi( + sample_y, psi_0=psi_bottom, psi_L=psi_top, + L=maxY - minY, alpha=alpha_g, + ) + + max_err = np.max(np.abs(psi_numerical - psi_exact)) + assert np.allclose(psi_numerical, psi_exact, atol=0.05), ( + f"Gardner analytical benchmark failed: max error = {max_err:.4f}" + ) + + +if uw.is_notebook: + test_richards_steady_constant_K() From 153eaad53788a1c74848f25b874e7bcf0f5f68ca Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Feb 2026 19:44:29 +1100 Subject: [PATCH 070/537] Add Haverkamp soil hydraulic model for Vauclin benchmark Rational-function retention and conductivity curves with independent parameters (alpha/beta for theta, A/B for K). Includes theta, K, and C functions, all returning SymPy Piecewise expressions compatible with the Richards solver. Underworld development team with AI support from Claude Code --- src/underworld3/utilities/retention_curves.py | 175 +++++++++++++++++- 1 file changed, 171 insertions(+), 4 deletions(-) diff --git a/src/underworld3/utilities/retention_curves.py b/src/underworld3/utilities/retention_curves.py index 79dd2c908..af5cc8134 100644 --- a/src/underworld3/utilities/retention_curves.py +++ b/src/underworld3/utilities/retention_curves.py @@ -4,9 +4,12 @@ Provides retention curve functions that return SymPy expressions suitable for use with the Richards equation solver: -- **Van Genuchten–Mualem** model: general-purpose, widely used. +- **Van Genuchten--Mualem** model: general-purpose, widely used. - **Gardner exponential** model: simpler, admits exact analytical solutions for steady-state Richards equation with gravity. +- **Haverkamp** model: rational-function form with independent + parameters for retention and conductivity; used in the Vauclin + (1979) water-table recharge benchmark. All functions accept a SymPy symbol or expression for pressure head (typically ``psi_field.sym[0]``) and return SymPy expressions that @@ -16,15 +19,19 @@ ---------- Van Genuchten, M. Th. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. -*Soil Science Society of America Journal*, 44(5), 892–898. +*Soil Science Society of America Journal*, 44(5), 892--898. Mualem, Y. (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media. -*Water Resources Research*, 12(3), 513–522. +*Water Resources Research*, 12(3), 513--522. Gardner, W. R. (1958). Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation -from a water table. *Soil Science*, 85(4), 228–232. +from a water table. *Soil Science*, 85(4), 228--232. + +Haverkamp, R. et al. (1977). A comparison of numerical simulation +models for one-dimensional infiltration. +*Soil Science Society of America Journal*, 41(2), 285--294. Examples -------- @@ -44,6 +51,15 @@ ... ) >>> K = gardner_K(psi, Ks=1e-4, alpha=1.0) >>> C = gardner_C(psi, theta_r=0.05, theta_s=0.4, alpha=1.0) + +Haverkamp model (Vauclin benchmark parameters): + +>>> from underworld3.utilities.retention_curves import ( +... haverkamp_theta, haverkamp_K, haverkamp_C, +... ) +>>> theta = haverkamp_theta(psi, theta_r=0.075, theta_s=0.287, +... alpha=1.611e6, beta=3.96) +>>> K = haverkamp_K(psi, Ks=9.44e-5, A=1.175e6, B=4.74) """ import sympy @@ -503,3 +519,154 @@ def gardner_transient_psi(y, t, psi_dry, psi_wet, L, Ks, alpha, theta_r, theta_s u = u_dry + (u_wet - u_dry) * H return (1.0 / alpha) * np.log(np.maximum(u, 1e-30)) + + +# ===================================================================== +# Haverkamp model +# ===================================================================== + + +def haverkamp_theta(psi, theta_r, theta_s, alpha, beta): + r"""Volumetric water content (Haverkamp model). + + .. math:: + + \theta(\psi) = \begin{cases} + \theta_r + \dfrac{\alpha\,(\theta_s - \theta_r)} + {\alpha + |\psi|^{\beta}} + & \psi < 0 \\[6pt] + \theta_s & \psi \ge 0 + \end{cases} + + Unlike Van Genuchten, the retention and conductivity curves have + **independent** parameters, which gives extra flexibility when + fitting laboratory data. + + Parameters + ---------- + psi : sympy expression + Pressure head (negative in unsaturated zone). + theta_r : float + Residual water content. + theta_s : float + Saturated water content. + alpha : float + Retention shape parameter (dimensionless or [length]^beta, + depending on convention). + beta : float + Retention exponent. + + Returns + ------- + sympy.Piecewise + Water content expression. + + References + ---------- + Haverkamp, R. et al. (1977). A comparison of numerical simulation + models for one-dimensional infiltration. + *Soil Science Society of America Journal*, 41(2), 285--294. + """ + theta_r = sympy.sympify(theta_r) + theta_s = sympy.sympify(theta_s) + alpha = sympy.sympify(alpha) + beta = sympy.sympify(beta) + + theta_unsat = theta_r + alpha * (theta_s - theta_r) / (alpha + (-psi) ** beta) + return sympy.Piecewise((theta_s, psi >= 0), (theta_unsat, True)) + + +def haverkamp_K(psi, Ks, A, B): + r"""Hydraulic conductivity (Haverkamp model). + + .. math:: + + K(\psi) = \begin{cases} + K_s\,\dfrac{A}{A + |\psi|^B} & \psi < 0 \\[6pt] + K_s & \psi \ge 0 + \end{cases} + + The conductivity parameters *A* and *B* are independent of the + retention parameters *alpha* and *beta*. + + Parameters + ---------- + psi : sympy expression + Pressure head (negative in unsaturated zone). + Ks : float + Saturated hydraulic conductivity. + A : float + Conductivity shape parameter. + B : float + Conductivity exponent. + + Returns + ------- + sympy.Piecewise + Hydraulic conductivity expression. + + References + ---------- + Haverkamp, R. et al. (1977). A comparison of numerical simulation + models for one-dimensional infiltration. + *Soil Science Society of America Journal*, 41(2), 285--294. + """ + Ks = sympy.sympify(Ks) + A = sympy.sympify(A) + B = sympy.sympify(B) + + K_unsat = Ks * A / (A + (-psi) ** B) + return sympy.Piecewise((Ks, psi >= 0), (K_unsat, True)) + + +def haverkamp_C(psi, theta_r, theta_s, alpha, beta, Ss=0.0): + r"""Specific moisture capacity (Haverkamp model). + + .. math:: + + C(\psi) = \frac{d\theta}{d\psi} = \begin{cases} + \dfrac{\alpha\,\beta\,(\theta_s - \theta_r)\,|\psi|^{\beta - 1}} + {\bigl(\alpha + |\psi|^{\beta}\bigr)^2} + & \psi < 0 \\[6pt] + S_s & \psi \ge 0 + \end{cases} + + Parameters + ---------- + psi : sympy expression + Pressure head. + theta_r : float + Residual water content. + theta_s : float + Saturated water content. + alpha : float + Retention shape parameter. + beta : float + Retention exponent. + Ss : float, optional + Specific storage for the saturated zone (default 0). + + Returns + ------- + sympy.Piecewise + Specific moisture capacity expression. + + References + ---------- + Haverkamp, R. et al. (1977). A comparison of numerical simulation + models for one-dimensional infiltration. + *Soil Science Society of America Journal*, 41(2), 285--294. + """ + theta_r = sympy.sympify(theta_r) + theta_s = sympy.sympify(theta_s) + alpha = sympy.sympify(alpha) + beta = sympy.sympify(beta) + Ss = sympy.sympify(Ss) + + abs_psi = -psi # psi < 0, so |psi| = -psi + C_unsat = ( + alpha * beta * (theta_s - theta_r) * abs_psi ** (beta - 1) + / (alpha + abs_psi ** beta) ** 2 + ) + + return sympy.Piecewise((Ss, psi >= 0), (C_unsat, True)) From e1fcdaf6e831eecdd8c6bf46168653e991f5d477 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Feb 2026 19:58:14 +1100 Subject: [PATCH 071/537] Add porous flow guide with Haverkamp model documentation Documents all three retention curve models (Van Genuchten, Gardner, Haverkamp), solver hierarchy, mixed vs head-based forms, time stepping, convergence tips, and boundary conditions. Underworld development team with AI support from Claude Code --- docs/advanced/porous-flow.md | 299 +++++++++++++++++++++++++++++++++++ 1 file changed, 299 insertions(+) create mode 100644 docs/advanced/porous-flow.md diff --git a/docs/advanced/porous-flow.md b/docs/advanced/porous-flow.md new file mode 100644 index 000000000..e3219009b --- /dev/null +++ b/docs/advanced/porous-flow.md @@ -0,0 +1,299 @@ +--- +title: "Porous Media Flow" +--- + +# Porous Media Flow + +Underworld3 provides a hierarchy of solvers for groundwater and variably-saturated +porous media flow. This guide explains when to use each solver, how to configure +retention curves, and practical tips for nonlinear convergence. + +## Solver Hierarchy + +Three solvers are available, each building on the previous one: + +| Solver | Equation | Use case | +|--------|----------|----------| +| {class}`~underworld3.systems.solvers.SNES_Darcy` | $-\nabla\cdot[K\nabla h - \mathbf{s}] = f$ | Steady-state, fully saturated | +| {class}`~underworld3.systems.solvers.SNES_TransientDarcy` | $S_s\,\partial h/\partial t - \nabla\cdot[K\nabla h - \mathbf{s}] = f$ | Transient, constant storage | +| {class}`~underworld3.systems.solvers.SNES_Richards` | $\partial\theta/\partial t - \nabla\cdot[K(\psi)(\nabla\psi - \mathbf{s})] = f$ | Variably-saturated, nonlinear | + +All three use the `DarcyFlowModel` constitutive model, which defines +permeability $K$ and a gravity-like source vector $\mathbf{s}$. + +### Choosing a Solver + +- **Steady-state, constant permeability** — use `SteadyStateDarcy` (alias for `SNES_Darcy`). + No time stepping needed; just call `solve()`. +- **Transient, constant storage** — use `TransientDarcy`. + Set `solver.storage` to the specific storage coefficient $S_s$ and advance with + `solve(timestep=dt)`. +- **Variably-saturated** — use `Richards`. + Permeability and storage depend nonlinearly on pressure head $\psi$. + This solver handles the stiff nonlinearities arising from soil-water retention curves. + +Python access: + +```python +import underworld3 as uw + +darcy = uw.systems.SteadyStateDarcy(mesh, h_Field=h, v_Field=v) +transient = uw.systems.TransientDarcy(mesh, h_Field=h, v_Field=v, order=1) +richards = uw.systems.Richards(mesh, psi_Field=psi, v_Field=v, order=1) +``` + +## Retention Curves + +The Richards equation requires soil-water retention curves that describe how +moisture content $\theta$ and hydraulic conductivity $K$ vary with +pressure head $\psi$. + +Underworld3 provides three models in +{mod}`underworld3.utilities.retention_curves`: + +### Van Genuchten--Mualem + +The most widely used model in hydrology. Parameters: $\alpha$, $n$, $K_s$, +$\theta_r$, $\theta_s$. + +```python +from underworld3.utilities.retention_curves import ( + van_genuchten_K, + van_genuchten_theta, +) + +psi_sym = psi.sym[0] + +K_expr = van_genuchten_K(psi_sym, Ks=1e-4, alpha=3.35, n=2.0) +theta_expr = van_genuchten_theta( + psi_sym, theta_r=0.045, theta_s=0.43, alpha=3.35, n=2.0 +) +``` + +Typical parameter ranges (SI units, $\psi$ in metres): + +| Soil type | $\alpha$ (1/m) | $n$ | $K_s$ (m/s) | $\theta_r$ | $\theta_s$ | +|-----------|----------------|-----|-------------|-------------|-------------| +| Sand | 14.5 | 2.68 | $8.25 \times 10^{-5}$ | 0.045 | 0.43 | +| Loam | 3.6 | 1.56 | $2.89 \times 10^{-6}$ | 0.078 | 0.43 | +| Clay | 0.8 | 1.09 | $5.56 \times 10^{-7}$ | 0.068 | 0.38 | + +### Gardner Exponential + +A simpler model with an analytical steady-state solution — ideal for +verification: + +$$K(\psi) = K_s \, e^{\alpha\psi}$$ + +```python +from underworld3.utilities.retention_curves import ( + gardner_K, + gardner_theta, + gardner_steady_state_psi, +) + +K_expr = gardner_K(psi_sym, Ks=1.0, alpha=2.0) +theta_expr = gardner_theta(psi_sym, theta_r=0.05, theta_s=0.4, alpha=2.0) + +# Exact steady-state profile for benchmarking +psi_exact = gardner_steady_state_psi(y_coords, psi_0=-3.0, psi_L=-0.5, L=1.0, alpha=2.0) +``` + +### Haverkamp + +A rational-function model where retention ($\alpha$, $\beta$) and +conductivity ($A$, $B$) have **independent** parameters, giving extra +flexibility when fitting laboratory data. Used in the +Vauclin (1979) water-table recharge benchmark. + +$$\theta(\psi) = \theta_r + \frac{\alpha\,(\theta_s - \theta_r)}{\alpha + |\psi|^{\beta}}, +\qquad +K(\psi) = K_s\,\frac{A}{A + |\psi|^B}$$ + +```python +from underworld3.utilities.retention_curves import ( + haverkamp_K, + haverkamp_theta, + haverkamp_C, +) + +# Vauclin (1979) benchmark parameters (CGS, ψ in cm) +K_expr = haverkamp_K(psi_sym, Ks=9.44e-5, A=1.175e6, B=4.74) +theta_expr = haverkamp_theta( + psi_sym, theta_r=0.075, theta_s=0.287, alpha=1.611e6, beta=3.96 +) +``` + +### Choosing a Retention Model + +| Model | Strengths | Typical use | +|-------|-----------|-------------| +| Van Genuchten--Mualem | Widely validated, coupled $K$--$\theta$ | General-purpose simulations | +| Gardner exponential | Admits analytical solutions | Verification benchmarks | +| Haverkamp | Independent $K$ and $\theta$ params | Lab data fitting, Vauclin benchmark | + +## Setting Up a Richards Solver + +### Mixed Form (Recommended) + +The **mixed form** discretises the storage term as +$(\theta(\psi^{n+1}) - \theta(\psi^n))/\Delta t$, which is exactly +mass-conservative. This is the preferred approach. + +```python +richards = uw.systems.Richards(mesh, psi_Field=psi, v_Field=v, order=1, theta=0.5) + +# Constitutive model (permeability + gravity) +richards.constitutive_model = uw.constitutive_models.DarcyFlowModel +richards.constitutive_model.Parameters.permeability = van_genuchten_K( + psi.sym[0], Ks=1e-4, alpha=3.35, n=2.0 +) +richards.constitutive_model.Parameters.s = sympy.Matrix([0, -1]).T + +# Mixed form: provide θ(ψ) directly +richards.water_content = van_genuchten_theta( + psi.sym[0], theta_r=0.045, theta_s=0.43, alpha=3.35, n=2.0 +) + +# Source term +richards.f = 0.0 +``` + +When `water_content` is set, the solver computes the Jacobian +$\partial\theta/\partial\psi = C(\psi)$ automatically via PETSc's +finite-difference colouring. You do **not** need to provide $C(\psi)$ +separately. + +### Head-Based Form (Backward Compatible) + +The head-based form discretises the storage as +$C(\psi)(\psi^{n+1} - \psi^n)/\Delta t$. This is simpler but not +mass-conservative when $C(\psi)$ varies sharply. + +```python +from underworld3.utilities.retention_curves import van_genuchten_C + +richards.capacity = van_genuchten_C( + psi.sym[0], theta_r=0.045, theta_s=0.43, alpha=3.35, n=2.0 +) +``` + +If both `water_content` and `capacity` are set, the mixed form takes precedence. + +## Time Stepping + +All transient porous flow solvers use BDF (Backward Differentiation Formula) +time integration with automatic order ramping: + +```python +# First call: BDF-1 (backward Euler) +richards.solve(timestep=dt) + +# Second call onwards: BDF-2 (if order=2 was requested) +richards.solve(timestep=dt) +``` + +The solver automatically: +- Initialises time-derivative history on the first solve call +- Ramps BDF order from 1 up to the requested `order` +- Tracks variable timesteps for correct BDF coefficients + +### Timestep Estimation + +`TransientDarcy` and `Richards` provide a diffusive CFL estimate: + +```python +dt = richards.estimate_dt() +``` + +For the Richards equation with strongly nonlinear retention curves, +you may need to use a smaller timestep than this estimate, especially +near wetting fronts. + +## Convergence Tips + +The Richards equation with Van Genuchten curves is a **stiff nonlinear problem**. +Here are practical strategies for reliable convergence: + +### 1. Use Backtracking Line Search + +```python +richards.petsc_options["snes_linesearch_type"] = "bt" +``` + +The backtracking line search (default is `basic`) helps SNES find a +descent direction when the initial Newton step overshoots. + +### 2. Increase SNES Iterations + +```python +richards.petsc_options["snes_max_it"] = 50 # default is 20 +``` + +Nonlinear problems near saturation may need more iterations. + +### 3. Start From a Smooth Initial Condition + +A linear profile between boundary values is a good starting guess: + +```python +y = mesh.X[1] +psi_init = psi_bottom + (psi_top - psi_bottom) * y +psi.array = uw.function.evaluate(psi_init, psi.coords) +``` + +Abrupt initial conditions (e.g., step functions) cause convergence +difficulties. + +### 4. Use Small Timesteps Initially + +Start with small $\Delta t$ and increase gradually, especially when +wetting fronts are developing: + +```python +dt = 0.001 +for step in range(n_steps): + richards.solve(timestep=dt) + dt = min(dt * 1.2, dt_max) # gradual increase +``` + +### 5. Monitor Convergence + +```python +richards.petsc_options["snes_monitor"] = None +richards.petsc_options["snes_converged_reason"] = None +``` + +## Boundary Conditions + +Boundary conditions follow the standard Underworld3 pattern: + +```python +# Fixed head / pressure head (Dirichlet) +richards.add_dirichlet_bc([0.0], "Top") # saturated surface +richards.add_dirichlet_bc([-5.0], "Bottom") # deep water table + +# Natural (Neumann) boundary conditions are set via richards.f +# and the constitutive model's flux term +``` + +For the Richards equation, typical boundary conditions are: +- **Saturated surface**: $\psi = 0$ (water table at the surface) +- **Deep dry condition**: $\psi = \psi_{\mathrm{init}}$ (initial pressure head) +- **No-flow boundaries**: Natural BC (the default on boundaries without Dirichlet conditions) + +## Tutorials + +For worked examples with complete code: + +- [Tutorial 16 — Richards Equation: Groundwater](../beginner/tutorials/16-Richards-Equation-Groundwater.ipynb): + Steady-state drainage with Gardner curves, comparison to analytical solution. +- [Tutorial 17 — Richards: Transient Wetting Front](../beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb): + Transient infiltration with Van Genuchten curves, wetting front propagation. + +## API Reference + +- {class}`~underworld3.systems.solvers.SNES_Darcy` — Steady-state Darcy +- {class}`~underworld3.systems.solvers.SNES_TransientDarcy` — Transient Darcy +- {class}`~underworld3.systems.solvers.SNES_Richards` — Richards equation +- {mod}`underworld3.utilities.retention_curves` — Retention curve functions From af1423546c137c10667a68ed4e62837658c43d0a Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Feb 2026 21:03:41 +1100 Subject: [PATCH 072/537] Fix is_notebook() call in Richards test MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit uw.is_notebook is a function, not a property — needs parentheses. Underworld development team with AI support from Claude Code --- tests/test_1006_RichardsCartesian.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tests/test_1006_RichardsCartesian.py b/tests/test_1006_RichardsCartesian.py index a2e4990d5..9d126c452 100644 --- a/tests/test_1006_RichardsCartesian.py +++ b/tests/test_1006_RichardsCartesian.py @@ -263,5 +263,5 @@ def test_richards_gardner_analytical(): ) -if uw.is_notebook: +if uw.is_notebook(): test_richards_steady_constant_K() From c28d77f97ba90c9a0c889c29a7af48c26502007a Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Feb 2026 21:04:01 +1100 Subject: [PATCH 073/537] Update Richards tutorial notebooks with fresh execution outputs Re-executed notebooks 16 and 17 to capture current outputs. Underworld development team with AI support from Claude Code --- .../16-Richards-Equation-Groundwater.ipynb | 162 ++++++++--------- .../17-Richards-Transient-Wetting-Front.ipynb | 164 +++++++++--------- 2 files changed, 167 insertions(+), 159 deletions(-) diff --git a/docs/beginner/tutorials/16-Richards-Equation-Groundwater.ipynb b/docs/beginner/tutorials/16-Richards-Equation-Groundwater.ipynb index fd72579b3..c7892f848 100644 --- a/docs/beginner/tutorials/16-Richards-Equation-Groundwater.ipynb +++ b/docs/beginner/tutorials/16-Richards-Equation-Groundwater.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Notebook 16: Richards Equation \u2014 Groundwater Flow\n", + "# Notebook 16: Richards Equation — Groundwater Flow\n", "\n", "This notebook introduces the Richards equation for variably-saturated\n", "porous media flow. We solve a steady-state drainage problem in a\n", @@ -13,7 +13,7 @@ "\n", "## Key Concepts\n", "\n", - "- Richards equation \u2014 nonlinear PDE for unsaturated flow\n", + "- Richards equation — nonlinear PDE for unsaturated flow\n", "- Gardner exponential conductivity model\n", "- Analytical steady-state solution with gravity\n", "- Darcy velocity field" @@ -36,7 +36,7 @@ "\n", "The **mixed form** (Celia et al., 1990) is generally preferred because\n", "writing the storage as $\\partial\\theta/\\partial t$ guarantees mass\n", - "conservation in the discrete system \u2014 the head-based form\n", + "conservation in the discrete system — the head-based form\n", "$C(\\psi)\\,\\partial\\psi/\\partial t$ introduces balance errors because the\n", "discrete chain rule $C(\\psi)\\Delta\\psi \\neq \\Delta\\theta$ when $C$ varies\n", "sharply across a timestep.\n", @@ -52,7 +52,7 @@ "- $f$ is any source/sink.\n", "\n", "The Underworld solver uses this mixed form when `water_content` is set\n", - "\u2014 discretising the storage term as\n", + "— discretising the storage term as\n", "$(\\theta(\\psi^{n+1}) - \\theta(\\psi^n))/\\Delta t$.\n", "The Jacobian $\\partial\\theta/\\partial\\psi = C(\\psi)$ is computed\n", "automatically by PETSc. For steady-state problems (where\n", @@ -90,11 +90,11 @@ "execution_count": 1, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:26.899970Z", - "iopub.status.busy": "2026-02-23T08:03:26.899837Z", - "iopub.status.idle": "2026-02-23T08:03:29.371758Z", - "shell.execute_reply": "2026-02-23T08:03:29.371351Z", - "shell.execute_reply.started": "2026-02-23T08:03:26.899959Z" + "iopub.execute_input": "2026-02-24T08:58:05.573720Z", + "iopub.status.busy": "2026-02-24T08:58:05.573578Z", + "iopub.status.idle": "2026-02-24T08:58:12.073192Z", + "shell.execute_reply": "2026-02-24T08:58:12.072718Z", + "shell.execute_reply.started": "2026-02-24T08:58:05.573690Z" } }, "outputs": [], @@ -130,25 +130,25 @@ "execution_count": 2, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:29.373366Z", - "iopub.status.busy": "2026-02-23T08:03:29.373024Z", - "iopub.status.idle": "2026-02-23T08:03:29.376282Z", - "shell.execute_reply": "2026-02-23T08:03:29.375910Z", - "shell.execute_reply.started": "2026-02-23T08:03:29.373350Z" + "iopub.execute_input": "2026-02-24T08:58:12.074293Z", + "iopub.status.busy": "2026-02-24T08:58:12.074021Z", + "iopub.status.idle": "2026-02-24T08:58:12.076863Z", + "shell.execute_reply": "2026-02-24T08:58:12.076598Z", + "shell.execute_reply.started": "2026-02-24T08:58:12.074281Z" } }, "outputs": [], "source": [ "# --- Default values (edit these in a notebook) ---\n", - "COLUMN_HEIGHT = 1.0 # m \u2014 soil column height\n", - "COLUMN_WIDTH = 0.1 # m \u2014 narrow (\u2248 1-D)\n", - "RES = 32 # \u2014 vertical elements\n", - "KS = 1e-4 # m/s \u2014 saturated hydraulic conductivity\n", - "ALPHA_G = 3.5 # 1/m \u2014 Gardner sorptive number\n", - "THETA_R = 0.05 # \u2014 residual water content\n", - "THETA_S = 0.40 # \u2014 saturated water content\n", - "PSI_TOP = -0.5 # m \u2014 pressure head at top\n", - "PSI_BOTTOM = -3.0 # m \u2014 pressure head at bottom" + "COLUMN_HEIGHT = 1.0 # m — soil column height\n", + "COLUMN_WIDTH = 0.1 # m — narrow (≈ 1-D)\n", + "RES = 32 # — vertical elements\n", + "KS = 1e-4 # m/s — saturated hydraulic conductivity\n", + "ALPHA_G = 3.5 # 1/m — Gardner sorptive number\n", + "THETA_R = 0.05 # — residual water content\n", + "THETA_S = 0.40 # — saturated water content\n", + "PSI_TOP = -0.5 # m — pressure head at top\n", + "PSI_BOTTOM = -3.0 # m — pressure head at bottom" ] }, { @@ -156,11 +156,11 @@ "execution_count": 3, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:29.376850Z", - "iopub.status.busy": "2026-02-23T08:03:29.376657Z", - "iopub.status.idle": "2026-02-23T08:03:29.382604Z", - "shell.execute_reply": "2026-02-23T08:03:29.382268Z", - "shell.execute_reply.started": "2026-02-23T08:03:29.376834Z" + "iopub.execute_input": "2026-02-24T08:58:12.077264Z", + "iopub.status.busy": "2026-02-24T08:58:12.077186Z", + "iopub.status.idle": "2026-02-24T08:58:12.087031Z", + "shell.execute_reply": "2026-02-24T08:58:12.086377Z", + "shell.execute_reply.started": "2026-02-24T08:58:12.077255Z" } }, "outputs": [ @@ -193,7 +193,7 @@ "source": [ "## Retention Curves\n", "\n", - "Let\u2019s visualise how hydraulic conductivity and water content\n", + "Let’s visualise how hydraulic conductivity and water content\n", "change with pressure head for these Gardner parameters." ] }, @@ -202,11 +202,11 @@ "execution_count": 4, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:29.383126Z", - "iopub.status.busy": "2026-02-23T08:03:29.383012Z", - "iopub.status.idle": "2026-02-23T08:03:29.907990Z", - "shell.execute_reply": "2026-02-23T08:03:29.907225Z", - "shell.execute_reply.started": "2026-02-23T08:03:29.383113Z" + "iopub.execute_input": "2026-02-24T08:58:12.087748Z", + "iopub.status.busy": "2026-02-24T08:58:12.087662Z", + "iopub.status.idle": "2026-02-24T08:58:12.508149Z", + "shell.execute_reply": "2026-02-24T08:58:12.507784Z", + "shell.execute_reply.started": "2026-02-24T08:58:12.087739Z" } }, "outputs": [ @@ -268,11 +268,11 @@ "execution_count": 5, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:29.909278Z", - "iopub.status.busy": "2026-02-23T08:03:29.908998Z", - "iopub.status.idle": "2026-02-23T08:03:29.994670Z", - "shell.execute_reply": "2026-02-23T08:03:29.994276Z", - "shell.execute_reply.started": "2026-02-23T08:03:29.909261Z" + "iopub.execute_input": "2026-02-24T08:58:12.508663Z", + "iopub.status.busy": "2026-02-24T08:58:12.508567Z", + "iopub.status.idle": "2026-02-24T08:58:12.588064Z", + "shell.execute_reply": "2026-02-24T08:58:12.587348Z", + "shell.execute_reply.started": "2026-02-24T08:58:12.508653Z" }, "scrolled": true }, @@ -324,11 +324,11 @@ "execution_count": 6, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:29.995465Z", - "iopub.status.busy": "2026-02-23T08:03:29.995228Z", - "iopub.status.idle": "2026-02-23T08:03:30.131412Z", - "shell.execute_reply": "2026-02-23T08:03:30.130717Z", - "shell.execute_reply.started": "2026-02-23T08:03:29.995431Z" + "iopub.execute_input": "2026-02-24T08:58:12.593981Z", + "iopub.status.busy": "2026-02-24T08:58:12.593676Z", + "iopub.status.idle": "2026-02-24T08:58:12.838854Z", + "shell.execute_reply": "2026-02-24T08:58:12.838122Z", + "shell.execute_reply.started": "2026-02-24T08:58:12.593949Z" } }, "outputs": [ @@ -357,11 +357,11 @@ "execution_count": 7, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:30.132680Z", - "iopub.status.busy": "2026-02-23T08:03:30.132212Z", - "iopub.status.idle": "2026-02-23T08:03:30.169135Z", - "shell.execute_reply": "2026-02-23T08:03:30.168477Z", - "shell.execute_reply.started": "2026-02-23T08:03:30.132659Z" + "iopub.execute_input": "2026-02-24T08:58:12.839864Z", + "iopub.status.busy": "2026-02-24T08:58:12.839556Z", + "iopub.status.idle": "2026-02-24T08:58:12.860738Z", + "shell.execute_reply": "2026-02-24T08:58:12.860473Z", + "shell.execute_reply.started": "2026-02-24T08:58:12.839852Z" } }, "outputs": [], @@ -372,14 +372,14 @@ "\n", "psi_sym = psi_var.sym[0]\n", "\n", - "# Constitutive model: Gardner K(\u03c8) with gravity\n", + "# Constitutive model: Gardner K(ψ) with gravity\n", "richards.constitutive_model = uw.constitutive_models.DarcyFlowModel\n", "richards.constitutive_model.Parameters.permeability = gardner_K(\n", " psi_sym, Ks=KS, alpha=ALPHA_G\n", ")\n", "richards.constitutive_model.Parameters.s = sympy.Matrix([0, -1]).T\n", "\n", - "# Mixed form: \u03b8(\u03c8) for mass-conservative storage term\n", + "# Mixed form: θ(ψ) for mass-conservative storage term\n", "richards.water_content = gardner_theta(\n", " psi_sym,\n", " theta_r=THETA_R,\n", @@ -403,11 +403,11 @@ "execution_count": 8, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:30.174229Z", - "iopub.status.busy": "2026-02-23T08:03:30.173895Z", - "iopub.status.idle": "2026-02-23T08:03:30.181463Z", - "shell.execute_reply": "2026-02-23T08:03:30.180723Z", - "shell.execute_reply.started": "2026-02-23T08:03:30.174195Z" + "iopub.execute_input": "2026-02-24T08:58:12.861731Z", + "iopub.status.busy": "2026-02-24T08:58:12.861634Z", + "iopub.status.idle": "2026-02-24T08:58:12.867820Z", + "shell.execute_reply": "2026-02-24T08:58:12.867134Z", + "shell.execute_reply.started": "2026-02-24T08:58:12.861722Z" } }, "outputs": [ @@ -434,11 +434,11 @@ "execution_count": 9, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:30.182703Z", - "iopub.status.busy": "2026-02-23T08:03:30.182493Z", - "iopub.status.idle": "2026-02-23T08:03:40.806808Z", - "shell.execute_reply": "2026-02-23T08:03:40.806394Z", - "shell.execute_reply.started": "2026-02-23T08:03:30.182683Z" + "iopub.execute_input": "2026-02-24T08:58:12.868793Z", + "iopub.status.busy": "2026-02-24T08:58:12.868456Z", + "iopub.status.idle": "2026-02-24T08:58:21.192358Z", + "shell.execute_reply": "2026-02-24T08:58:21.191855Z", + "shell.execute_reply.started": "2026-02-24T08:58:12.868635Z" } }, "outputs": [ @@ -480,17 +480,17 @@ "execution_count": 10, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:40.807514Z", - "iopub.status.busy": "2026-02-23T08:03:40.807393Z", - "iopub.status.idle": "2026-02-23T08:03:41.046305Z", - "shell.execute_reply": "2026-02-23T08:03:41.045975Z", - "shell.execute_reply.started": "2026-02-23T08:03:40.807495Z" + "iopub.execute_input": "2026-02-24T08:58:21.193049Z", + "iopub.status.busy": "2026-02-24T08:58:21.192951Z", + "iopub.status.idle": "2026-02-24T08:58:21.378893Z", + "shell.execute_reply": "2026-02-24T08:58:21.378129Z", + "shell.execute_reply.started": "2026-02-24T08:58:21.193038Z" } }, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] @@ -533,7 +533,7 @@ "ax2.plot(error, sample_y, \"k-\", lw=1)\n", "ax2.axvline(0, color=\"grey\", ls=\"--\", lw=0.5)\n", "ax2.set_xlabel(\"Error (m)\")\n", - "ax2.set_title(\"Numerical \u2212 Analytical\")\n", + "ax2.set_title(\"Numerical − Analytical\")\n", "ax2.grid(True, alpha=0.3)\n", "\n", "fig.suptitle(\n", @@ -564,17 +564,17 @@ "execution_count": 11, "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T08:03:41.047082Z", - "iopub.status.busy": "2026-02-23T08:03:41.046754Z", - "iopub.status.idle": "2026-02-23T08:03:41.130030Z", - "shell.execute_reply": "2026-02-23T08:03:41.129670Z", - "shell.execute_reply.started": "2026-02-23T08:03:41.047069Z" + "iopub.execute_input": "2026-02-24T08:58:21.379648Z", + "iopub.status.busy": "2026-02-24T08:58:21.379307Z", + "iopub.status.idle": "2026-02-24T08:58:21.456018Z", + "shell.execute_reply": "2026-02-24T08:58:21.455068Z", + "shell.execute_reply.started": "2026-02-24T08:58:21.379637Z" } }, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
" ] @@ -604,7 +604,7 @@ "Experiment with different parameters to build intuition:\n", "\n", "```python\n", - "# Larger \u03b1 \u2192 sharper transition near saturation\n", + "# Larger α → sharper transition near saturation\n", "ALPHA_G = 5.0\n", "\n", "# Wetter bottom boundary\n", @@ -616,7 +616,7 @@ "\n", "- What happens as $\\alpha \\to 0$? (Hint: the profile should approach linear.)\n", "- What if the top boundary is fully saturated ($\\psi_\\text{top} = 0$)?\n", - "- The Van Genuchten model is also available \u2014 try replacing\n", + "- The Van Genuchten model is also available — try replacing\n", " `gardner_K` with `van_genuchten_K` (no analytical solution,\n", " but the solver still works).\n", "- Can you compute mass conservation by integrating $\\theta(\\psi)$\n", @@ -626,24 +626,24 @@ "\n", "Celia, M. A., Bouloutas, E. T. & Zarba, R. L. (1990). A general\n", "mass-conservative numerical solution for the unsaturated flow equation.\n", - "*Water Resources Research*, 26(7), 1483\u20131496.\n", + "*Water Resources Research*, 26(7), 1483–1496.\n", "doi:[10.1029/WR026i007p01483](https://doi.org/10.1029/WR026i007p01483)\n", "\n", "Gardner, W. R. (1958). Some steady-state solutions of the unsaturated\n", "moisture flow equation with application to evaporation from a water table.\n", - "*Soil Science*, 85(4), 228\u2013232.\n", + "*Soil Science*, 85(4), 228–232.\n", "\n", "Mualem, Y. (1976). A new model for predicting the hydraulic conductivity\n", - "of unsaturated porous media. *Water Resources Research*, 12(3), 513\u2013522.\n", + "of unsaturated porous media. *Water Resources Research*, 12(3), 513–522.\n", "doi:[10.1029/WR012i003p00513](https://doi.org/10.1029/WR012i003p00513)\n", "\n", "Richards, L. A. (1931). Capillary conduction of liquids through porous\n", - "mediums. *Physics*, 1(5), 318\u2013333.\n", + "mediums. *Physics*, 1(5), 318–333.\n", "doi:[10.1063/1.1745010](https://doi.org/10.1063/1.1745010)\n", "\n", "Van Genuchten, M. Th. (1980). A closed-form equation for predicting the\n", "hydraulic conductivity of unsaturated soils. *Soil Science Society of\n", - "America Journal*, 44(5), 892\u2013898.\n", + "America Journal*, 44(5), 892–898.\n", "doi:[10.2136/sssaj1980.03615995004400050002x](https://doi.org/10.2136/sssaj1980.03615995004400050002x)" ] }, diff --git a/docs/beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb b/docs/beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb index 727e94bce..97b691372 100644 --- a/docs/beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb +++ b/docs/beginner/tutorials/17-Richards-Transient-Wetting-Front.ipynb @@ -77,11 +77,11 @@ "id": "cell-3", "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T11:10:33.051502Z", - "iopub.status.busy": "2026-02-23T11:10:33.051236Z", - "iopub.status.idle": "2026-02-23T11:10:36.713698Z", - "shell.execute_reply": "2026-02-23T11:10:36.713132Z", - "shell.execute_reply.started": "2026-02-23T11:10:33.051490Z" + "iopub.execute_input": "2026-02-24T09:22:11.232839Z", + "iopub.status.busy": "2026-02-24T09:22:11.232279Z", + "iopub.status.idle": "2026-02-24T09:22:15.257488Z", + "shell.execute_reply": "2026-02-24T09:22:15.256902Z", + "shell.execute_reply.started": "2026-02-24T09:22:11.232819Z" } }, "outputs": [], @@ -119,11 +119,11 @@ "id": "cell-5", "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T11:10:36.714847Z", - "iopub.status.busy": "2026-02-23T11:10:36.714355Z", - "iopub.status.idle": "2026-02-23T11:10:36.725206Z", - "shell.execute_reply": "2026-02-23T11:10:36.724538Z", - "shell.execute_reply.started": "2026-02-23T11:10:36.714827Z" + "iopub.execute_input": "2026-02-24T09:22:15.258545Z", + "iopub.status.busy": "2026-02-24T09:22:15.258091Z", + "iopub.status.idle": "2026-02-24T09:22:15.268344Z", + "shell.execute_reply": "2026-02-24T09:22:15.267546Z", + "shell.execute_reply.started": "2026-02-24T09:22:15.258524Z" } }, "outputs": [], @@ -159,11 +159,11 @@ "id": "cell-7", "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T11:10:36.726311Z", - "iopub.status.busy": "2026-02-23T11:10:36.726074Z", - "iopub.status.idle": "2026-02-23T11:10:37.126371Z", - "shell.execute_reply": "2026-02-23T11:10:37.124736Z", - "shell.execute_reply.started": "2026-02-23T11:10:36.726291Z" + "iopub.execute_input": "2026-02-24T09:22:15.269856Z", + "iopub.status.busy": "2026-02-24T09:22:15.269698Z", + "iopub.status.idle": "2026-02-24T09:22:15.801131Z", + "shell.execute_reply": "2026-02-24T09:22:15.799427Z", + "shell.execute_reply.started": "2026-02-24T09:22:15.269839Z" } }, "outputs": [ @@ -243,11 +243,11 @@ "id": "cell-9", "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T11:10:37.127260Z", - "iopub.status.busy": "2026-02-23T11:10:37.126973Z", - "iopub.status.idle": "2026-02-23T11:10:37.382693Z", - "shell.execute_reply": "2026-02-23T11:10:37.380079Z", - "shell.execute_reply.started": "2026-02-23T11:10:37.127240Z" + "iopub.execute_input": "2026-02-24T09:22:15.802505Z", + "iopub.status.busy": "2026-02-24T09:22:15.802089Z", + "iopub.status.idle": "2026-02-24T09:22:16.009513Z", + "shell.execute_reply": "2026-02-24T09:22:16.007830Z", + "shell.execute_reply.started": "2026-02-24T09:22:15.802479Z" } }, "outputs": [ @@ -277,11 +277,11 @@ "id": "cell-10", "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T11:10:37.384014Z", - "iopub.status.busy": "2026-02-23T11:10:37.383876Z", - "iopub.status.idle": "2026-02-23T11:10:37.435356Z", - "shell.execute_reply": "2026-02-23T11:10:37.434501Z", - "shell.execute_reply.started": "2026-02-23T11:10:37.384001Z" + "iopub.execute_input": "2026-02-24T09:22:16.011114Z", + "iopub.status.busy": "2026-02-24T09:22:16.010927Z", + "iopub.status.idle": "2026-02-24T09:22:16.087474Z", + "shell.execute_reply": "2026-02-24T09:22:16.082901Z", + "shell.execute_reply.started": "2026-02-24T09:22:16.011096Z" } }, "outputs": [], @@ -341,20 +341,61 @@ "id": "cell-12", "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T11:10:37.440174Z", - "iopub.status.busy": "2026-02-23T11:10:37.439863Z", - "iopub.status.idle": "2026-02-23T11:11:03.613359Z", - "shell.execute_reply": "2026-02-23T11:11:03.612713Z", - "shell.execute_reply.started": "2026-02-23T11:10:37.440150Z" + "iopub.execute_input": "2026-02-24T09:22:16.095786Z", + "iopub.status.busy": "2026-02-24T09:22:16.092667Z", + "iopub.status.idle": "2026-02-24T09:22:20.237314Z", + "shell.execute_reply": "2026-02-24T09:22:20.234410Z", + "shell.execute_reply.started": "2026-02-24T09:22:16.095751Z" } }, "outputs": [ { - "name": "stdout", + "name": "stderr", "output_type": "stream", "text": [ - "Completed 60 steps, t = 0.3000 s\n", - "Snapshots saved at t = [0.05, 0.15, 0.3]\n" + "[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------\n", + "[0]PETSC ERROR: Object is in wrong state\n", + "[0]PETSC ERROR: Must call SNESSetFunction() or SNESSetDM() before SNESComputeFunction(), likely called from SNESSolve().\n", + "[0]PETSC ERROR: WARNING! There are unused option(s) set! Could be the program crashed before usage or a spelling mistake, etc!\n", + "[0]PETSC ERROR: Option left: name:-dm_plex_hash_location (no value) source: code\n", + "[0]PETSC ERROR: Option left: name:-options_left value: 0 source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_5_mg_levels_ksp_converged_maxits (no value) source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_5_mg_levels_ksp_max_it value: 3 source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_5_pc_mg_type value: additive source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_ksp_rtol value: 0.001 source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_ksp_type value: gmres source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_mg_levels_ksp_converged_maxits (no value) source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_mg_levels_ksp_max_it value: 3 source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_pc_gamg_agg_nsmooths value: 2 source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_pc_gamg_repartition value: true source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_pc_gamg_type value: agg source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_pc_mg_type value: additive source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_pc_type value: gamg source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_snes_rtol value: 1e-06 source: code\n", + "[0]PETSC ERROR: Option left: name:-Solver_6_snes_type value: newtonls source: code\n", + "[0]PETSC ERROR: See https://petsc.org/release/faq/ for trouble shooting.\n", + "[0]PETSC ERROR: PETSc Release Version 3.24.3, unknown\n", + "[0]PETSC ERROR: /Users/lmoresi/+Underworld/underworld3-pixi/.pixi/envs/amr-dev/lib/python3.12/site-packages/ipykernel_launcher.py with 1 MPI process(es) and PETSC_ARCH petsc-4-uw on Lyrebird.local by lmoresi Tue Feb 24 20:22:11 2026\n", + "[0]PETSC ERROR: Configure options: --with-petsc-arch=petsc-4-uw --download-bison --download-eigen --download-metis --download-mmg --download-mumps --download-parmetis --download-parmmg --download-pragmatic --download-ptscotch=/Users/lmoresi/+Underworld/underworld3-pixi/petsc-custom/patches/scotch-7.0.10-c23-fix.tar.gz --download-scalapack --download-slepc --with-debugging=0 --with-hdf5=1 --with-pragmatic=1 --with-x=0 --with-mpi-dir=/Users/lmoresi/+Underworld/underworld3-pixi/.pixi/envs/amr --with-hdf5-dir=/Users/lmoresi/+Underworld/underworld3-pixi/.pixi/envs/amr --download-hdf5=0 --download-mpich=0 --download-mpi4py=0 --with-petsc4py=0\n", + "[0]PETSC ERROR: #1 SNESComputeFunction() at /Users/lmoresi/+Underworld/underworld3-pixi/petsc-custom/petsc/src/snes/interface/snes.c:2486\n", + "[0]PETSC ERROR: #2 SNESSolve_NEWTONTR() at /Users/lmoresi/+Underworld/underworld3-pixi/petsc-custom/petsc/src/snes/impls/tr/tr.c:537\n", + "[0]PETSC ERROR: #3 SNESSolve() at /Users/lmoresi/+Underworld/underworld3-pixi/petsc-custom/petsc/src/snes/interface/snes.c:4905\n" + ] + }, + { + "ename": "Error", + "evalue": "error code 73", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[6]\u001b[39m\u001b[32m, line 26\u001b[39m\n\u001b[32m 23\u001b[39m n_steps = \u001b[38;5;28mint\u001b[39m(np.ceil(t_end / DT))\n\u001b[32m 25\u001b[39m \u001b[38;5;28;01mfor\u001b[39;00m step \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n_steps):\n\u001b[32m---> \u001b[39m\u001b[32m26\u001b[39m \u001b[43mrichards\u001b[49m\u001b[43m.\u001b[49m\u001b[43msolve\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtimestep\u001b[49m\u001b[43m=\u001b[49m\u001b[43mDT\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 27\u001b[39m t_now += DT\n\u001b[32m 29\u001b[39m \u001b[38;5;66;03m# Check if we've passed a snapshot time\u001b[39;00m\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/+Underworld/underworld3-pixi/.pixi/envs/amr-dev/lib/python3.12/site-packages/underworld3/timing.py:310\u001b[39m, in \u001b[36mroutine_timer_decorator..timed\u001b[39m\u001b[34m(*args, **kwargs)\u001b[39m\n\u001b[32m 308\u001b[39m event.begin()\n\u001b[32m 309\u001b[39m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[32m--> \u001b[39m\u001b[32m310\u001b[39m result = \u001b[43mroutine\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 311\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m result\n\u001b[32m 312\u001b[39m \u001b[38;5;28;01mfinally\u001b[39;00m:\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/+Underworld/underworld3-pixi/.pixi/envs/amr-dev/lib/python3.12/site-packages/underworld3/systems/solvers.py:825\u001b[39m, in \u001b[36mSNES_TransientDarcy.solve\u001b[39m\u001b[34m(self, zero_init_guess, timestep, _force_setup, verbose)\u001b[39m\n\u001b[32m 822\u001b[39m \u001b[38;5;28mself\u001b[39m.DFDt.update_pre_solve(timestep, verbose=verbose)\n\u001b[32m 824\u001b[39m \u001b[38;5;66;03m# Solve PDE (bypass SNES_Darcy.solve to avoid double setup/projection)\u001b[39;00m\n\u001b[32m--> \u001b[39m\u001b[32m825\u001b[39m \u001b[43mSNES_Scalar\u001b[49m\u001b[43m.\u001b[49m\u001b[43msolve\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mzero_init_guess\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m_force_setup\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 827\u001b[39m \u001b[38;5;66;03m# Invalidate cached data views\u001b[39;00m\n\u001b[32m 828\u001b[39m target_var = \u001b[38;5;28mgetattr\u001b[39m(\u001b[38;5;28mself\u001b[39m.u, \u001b[33m\"\u001b[39m\u001b[33m_base_var\u001b[39m\u001b[33m\"\u001b[39m, \u001b[38;5;28mself\u001b[39m.u)\n", + "\u001b[36mFile \u001b[39m\u001b[32m~/+Underworld/underworld3-pixi/.pixi/envs/amr-dev/lib/python3.12/site-packages/underworld3/timing.py:310\u001b[39m, in \u001b[36mroutine_timer_decorator..timed\u001b[39m\u001b[34m(*args, **kwargs)\u001b[39m\n\u001b[32m 308\u001b[39m event.begin()\n\u001b[32m 309\u001b[39m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[32m--> \u001b[39m\u001b[32m310\u001b[39m result = \u001b[43mroutine\u001b[49m\u001b[43m(\u001b[49m\u001b[43m*\u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m*\u001b[49m\u001b[43m*\u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 311\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m result\n\u001b[32m 312\u001b[39m \u001b[38;5;28;01mfinally\u001b[39;00m:\n", + "\u001b[36mFile \u001b[39m\u001b[32msrc/underworld3/cython/petsc_generic_snes_solvers.pyx:1660\u001b[39m, in \u001b[36munderworld3.cython.generic_solvers.SNES_Scalar.solve\u001b[39m\u001b[34m()\u001b[39m\n", + "\u001b[36mFile \u001b[39m\u001b[32mpetsc4py/PETSc/SNES.pyx:1738\u001b[39m, in \u001b[36mpetsc4py.PETSc.SNES.solve\u001b[39m\u001b[34m()\u001b[39m\n", + "\u001b[31mError\u001b[39m: error code 73" ] } ], @@ -410,38 +451,17 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "id": "cell-14", "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T11:11:03.615173Z", - "iopub.status.busy": "2026-02-23T11:11:03.614993Z", - "iopub.status.idle": "2026-02-23T11:11:04.019521Z", - "shell.execute_reply": "2026-02-23T11:11:04.018942Z", - "shell.execute_reply.started": "2026-02-23T11:11:03.615158Z" + "iopub.status.busy": "2026-02-24T09:22:20.237733Z", + "iopub.status.idle": "2026-02-24T09:22:20.237979Z", + "shell.execute_reply": "2026-02-24T09:22:20.237856Z", + "shell.execute_reply.started": "2026-02-24T09:22:20.237846Z" } }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " t = 0.05 s : max |error| = 2.2215e-01 m\n", - " t = 0.15 s : max |error| = 1.3161e-01 m\n", - " t = 0.30 s : max |error| = 7.3938e-02 m\n" - ] - } - ], + "outputs": [], "source": [ "n_sample = 200\n", "sample_y = np.linspace(0.05, COLUMN_HEIGHT - 0.05, n_sample)\n", @@ -499,29 +519,17 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "id": "cell-16", "metadata": { "execution": { - "iopub.execute_input": "2026-02-23T11:11:04.020710Z", - "iopub.status.busy": "2026-02-23T11:11:04.020195Z", - "iopub.status.idle": "2026-02-23T11:11:04.720953Z", - "shell.execute_reply": "2026-02-23T11:11:04.719751Z", - "shell.execute_reply.started": "2026-02-23T11:11:04.020686Z" + "iopub.status.busy": "2026-02-24T09:22:20.238715Z", + "iopub.status.idle": "2026-02-24T09:22:20.239232Z", + "shell.execute_reply": "2026-02-24T09:22:20.238832Z", + "shell.execute_reply.started": "2026-02-24T09:22:20.238822Z" } }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "# Use the final snapshot\n", "t_final = sorted(snapshots.keys())[-1]\n", From a5a26280aef2a3b849242825c5667ba24c0ad8db Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 24 Feb 2026 22:30:15 +1100 Subject: [PATCH 074/537] Add Tracy (2006) 2D Richards equation benchmark MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Implements the closed-form analytical benchmark from Tracy (2006, Water Resources Research) for validating the Richards solver against exact solutions on a square domain with Gardner soil properties. Both BC variants are included: - Specified-head (Dirichlet on all four sides) - No-flux (zero-flux laterals, Dirichlet top/bottom) Key features: - Spatially varying top BC drives infiltration into dry column - Parameters match gwassess dimensionless grouping (alpha*L=5) - Mixed-form (mass-conservative) storage term - Configurable via uw.Params for resolution/parameter studies Verified convergence: 16x16→32x32→64x64 with expected spatial order. Max error ~4e-4 at 32x32, ~7e-5 at 64x64. Underworld development team with AI support from Claude Code --- .../Benchmark/Ex_Richards_Tracy_Benchmark.py | 475 ++++++++++++++++++ 1 file changed, 475 insertions(+) create mode 100644 docs/examples/WIP/Benchmark/Ex_Richards_Tracy_Benchmark.py diff --git a/docs/examples/WIP/Benchmark/Ex_Richards_Tracy_Benchmark.py b/docs/examples/WIP/Benchmark/Ex_Richards_Tracy_Benchmark.py new file mode 100644 index 000000000..d424a50d6 --- /dev/null +++ b/docs/examples/WIP/Benchmark/Ex_Richards_Tracy_Benchmark.py @@ -0,0 +1,475 @@ +# --- +# jupyter: +# jupytext: +# text_representation: +# extension: .py +# format_name: light +# format_version: '1.5' +# jupytext_version: 1.16.4 +# kernelspec: +# display_name: Python 3 +# language: python +# name: python3 +# --- + +# %% [markdown] +# # Tracy (2006) 2D Richards Equation Benchmark +# +# Validates the Underworld Richards solver against the **closed-form analytical +# solution** of Tracy (2006) for 2D steady-state and transient flow in +# unsaturated porous media with Gardner (exponential) soil properties. +# +# The benchmark uses a square domain $L \times L$ with the Gardner conductivity +# $K(\psi) = K_s \exp(\alpha\,\psi)$ and moisture content +# $\theta(\psi) = \theta_r + (\theta_s - \theta_r)\exp(\alpha\,\psi)$. +# +# Two boundary condition cases are tested: +# +# 1. **Specified head** — Dirichlet on all four boundaries ($\psi = h_r$ on +# bottom, left, right; spatially varying on top) +# 2. **No-flux** — zero-flux on lateral boundaries, Dirichlet on top/bottom +# ($\psi = h_r$ at bottom; spatially varying at top) +# +# The top boundary carries a spatially varying wetting profile that drives +# infiltration into an initially dry column ($\psi = h_r$). +# +# ### Reference +# +# Tracy, F. T. (2006). Clean two- and three-dimensional analytical solutions of +# Richards' equation for testing numerical solvers. *Water Resources Research*, 42(8). +# https://doi.org/10.1029/2005WR004638 + +# %% +import nest_asyncio + +nest_asyncio.apply() + +import underworld3 as uw +import numpy as np +import sympy +from math import sqrt, sin, cos, exp, sinh, pi, log + + +# %% [markdown] +# ## Analytical solution (Tracy 2006) +# +# The Tracy solution applies the Kirchhoff transform $u = \exp(\alpha\psi)$ to +# linearise the Richards equation. With Gardner properties, the transformed PDE +# is linear and has exact Fourier series solutions on a square domain. +# +# The key parameter grouping is $\alpha L$ — the ratio of domain size to the +# Gardner capillary length. The gwassess package uses $\alpha L = 5.0$ and +# $\alpha h_r = -5.0$; we adopt the same dimensionless combination with +# rescaled dimensional parameters for fast convergence. + + +# %% +def tracy_specified_head(x, y, t, alpha, hr, L, theta_r, theta_s, Ks): + """Analytical pressure head — specified head BCs on all boundaries. + + Tracy (2006), equations (15)–(17). + + BCs: psi = hr on bottom (y=0), left (x=0), right (x=L). + psi = (1/alpha)*log(exp(alpha*hr) + h0*sin(pi*x/L)) on top (y=L). + IC: psi = hr everywhere at t=0. + """ + h0 = 1 - exp(alpha * hr) + c = alpha * (theta_s - theta_r) / Ks + + beta = sqrt(alpha**2 / 4 + (pi / L) ** 2) + hss = ( + h0 + * sin(pi * x / L) + * exp((alpha / 2) * (L - y)) + * sinh(beta * y) + / sinh(beta * L) + ) + + phi = 0.0 + for k in range(1, 200): + lambdak = k * pi / L + gamma = (beta**2 + lambdak**2) / c + phi += ((-1) ** k) * (lambdak / gamma) * sin(lambdak * y) * exp(-gamma * t) + phi *= ((2 * h0) / (L * c)) * sin(pi * x / L) * exp(alpha * (L - y) / 2) + + hBar = hss + phi + return (1 / alpha) * log(exp(alpha * hr) + hBar) + + +def tracy_no_flux(x, y, t, alpha, hr, L, theta_r, theta_s, Ks): + """Analytical pressure head — no-flux lateral, specified head top/bottom. + + Tracy (2006), equations (18)–(20). + + BCs: psi = hr on bottom (y=0). + Zero flux on left (x=0) and right (x=L). + psi = (1/alpha)*log(exp(alpha*hr) + (h0/2)*(1-cos(2*pi*x/L))) on top (y=L). + IC: psi = hr everywhere at t=0. + """ + h0 = 1 - exp(alpha * hr) + c = alpha * (theta_s - theta_r) / Ks + + beta = sqrt(alpha**2 / 4 + (2 * pi / L) ** 2) + hss = (h0 / 2) * exp((alpha / 2) * (L - y)) * ( + sinh(alpha * y / 2) / sinh(alpha * L / 2) + - cos(2 * pi * x / L) * sinh(beta * y) / sinh(beta * L) + ) + + phi = 0.0 + for k in range(1, 200): + lambdak = k * pi / L + gamma1 = (lambdak**2 + alpha**2 / 4) / c + gamma2 = ((2 * pi / L) ** 2 + lambdak**2 + alpha**2 / 4) / c + phi += ((-1) ** k) * lambdak * ( + (1 / gamma1) * exp(-gamma1 * t) + - (1 / gamma2) * cos(2 * pi * x / L) * exp(-gamma2 * t) + ) * sin(lambdak * y) + phi *= (h0 / (L * c)) * exp(alpha * (L - y) / 2) + + hBar = hss + phi + return (1 / alpha) * log(exp(alpha * hr) + hBar) + + +def tracy_solution_on_grid(sample_pts, t, alpha, hr, L, theta_r, theta_s, Ks, bc_type): + """Evaluate Tracy solution at an array of (x, y) sample points.""" + func = tracy_specified_head if bc_type == "specified_head" else tracy_no_flux + return np.array( + [func(p[0], p[1], t, alpha, hr, L, theta_r, theta_s, Ks) for p in sample_pts] + ) + + +# %% [markdown] +# ### Configurable parameters +# +# Default values are defined as named constants below. From the command line, +# override them with PETSc-style flags: +# +# ```bash +# python Ex_Richards_Tracy_Benchmark.py -uw_res 48 -uw_bc_type no_flux +# ``` +# +# The default parameters give $\alpha L = 5$ and $\alpha h_r = -5$, matching +# the dimensionless grouping used in the gwassess benchmark suite. + +# %% +# --- Default values (edit these in a notebook) --- +RES = 32 # elements per side +ALPHA = 5.0 # 1/m – Gardner sorptive number +HR = -1.0 # m – reference pressure head (dry end) +L = 1.0 # m – domain size (square L×L) +THETA_R = 0.15 # – residual water content +THETA_S = 0.45 # – saturated water content +KS = 1.0 # m/s – saturated hydraulic conductivity +DT = 0.05 # s – timestep +N_STEPS = 40 # – number of timesteps to reach steady state +BC_TYPE = "no_flux" # – boundary condition type + +params = uw.Params( + uw_res = RES, + uw_alpha = uw.Param(ALPHA, units="1/m", description="Gardner sorptive number"), + uw_hr = uw.Param(HR, units="m", description="reference pressure head"), + uw_L = uw.Param(L, units="m", description="domain size"), + uw_theta_r = THETA_R, + uw_theta_s = THETA_S, + uw_Ks = uw.Param(KS, units="m/s", description="saturated conductivity"), + uw_dt = uw.Param(DT, units="s", description="timestep"), + uw_n_steps = N_STEPS, + uw_bc_type = BC_TYPE, +) + +res = int(params.uw_res) +alpha = float(params.uw_alpha) +hr = float(params.uw_hr) +L_dom = float(params.uw_L) +theta_r = float(params.uw_theta_r) +theta_s = float(params.uw_theta_s) +Ks = float(params.uw_Ks) +dt = float(params.uw_dt) +n_steps = int(params.uw_n_steps) +bc_type = str(params.uw_bc_type) + +# Derived parameters +c_time = alpha * (theta_s - theta_r) / Ks # characteristic time scale +h0 = 1 - np.exp(alpha * hr) # driving amplitude + +print(f"alpha*L = {alpha * L_dom:.1f}, alpha*hr = {alpha * hr:.1f}") +print(f"c (time scale) = {c_time:.2f} s, h0 = {h0:.4f}") +print(f"Total time = {n_steps * dt:.1f} s ({n_steps * dt / c_time:.1f} × c)") + +# %% [markdown] +# ## Mesh and variables + +# %% +mesh = uw.meshing.StructuredQuadBox( + elementRes=(res, res), + minCoords=(0.0, 0.0), + maxCoords=(L_dom, L_dom), + qdegree=3, +) + +psi = uw.discretisation.MeshVariable(r"\psi", mesh, 1, degree=2) +v_soln = uw.discretisation.MeshVariable("v", mesh, mesh.dim, degree=1) + +# %% [markdown] +# ## Solver setup +# +# The Tracy benchmark uses the Gardner exponential model, which we take +# from the retention curves module. + +# %% +from underworld3.utilities.retention_curves import gardner_K, gardner_theta + +psi_sym = psi.sym[0] + +richards = uw.systems.Richards(mesh, psi, v_soln, order=1, theta=0.5) +richards.petsc_options.delValue("ksp_monitor") +richards.petsc_options["snes_rtol"] = 1.0e-6 +richards.petsc_options["snes_max_it"] = 30 + +richards.constitutive_model = uw.constitutive_models.DarcyFlowModel +richards.constitutive_model.Parameters.permeability = gardner_K(psi_sym, Ks=Ks, alpha=alpha) +richards.constitutive_model.Parameters.s = sympy.Matrix([0, -1]).T + +# Mixed form — mass-conservative +richards.water_content = gardner_theta(psi_sym, theta_r=theta_r, theta_s=theta_s, alpha=alpha) +richards.f = 0.0 + +richards._v_projector.petsc_options["snes_rtol"] = 1.0e-6 +richards._v_projector.smoothing = 1.0e-6 + +# %% [markdown] +# ## Boundary conditions +# +# The Tracy analytical solution has $\psi = h_r$ (dry state) on the bottom and +# lateral boundaries, but a **spatially varying** wetting profile on the top +# boundary. +# +# For the **no-flux** case: +# - Bottom ($y=0$): $\psi = h_r$ +# - Left, Right ($x=0, L$): zero flux (natural BC — no Dirichlet) +# - Top ($y=L$): $\psi(x) = \frac{1}{\alpha}\ln\!\left[e^{\alpha h_r} +# + \frac{h_0}{2}\left(1 - \cos\frac{2\pi x}{L}\right)\right]$ +# +# For the **specified-head** case: +# - Bottom, Left, Right: $\psi = h_r$ +# - Top: $\psi(x) = \frac{1}{\alpha}\ln\!\left[e^{\alpha h_r} +# + h_0 \sin\frac{\pi x}{L}\right]$ +# +# where $h_0 = 1 - e^{\alpha h_r}$. + +# %% +x_sym = mesh.X[0] +h0_sym = 1 - sympy.exp(alpha * hr) + +if bc_type == "no_flux": + psi_top = (1 / alpha) * sympy.log( + sympy.exp(alpha * hr) + (h0_sym / 2) * (1 - sympy.cos(2 * sympy.pi * x_sym / L_dom)) + ) +elif bc_type == "specified_head": + psi_top = (1 / alpha) * sympy.log( + sympy.exp(alpha * hr) + h0_sym * sympy.sin(sympy.pi * x_sym / L_dom) + ) +else: + raise ValueError(f"Unknown bc_type: {bc_type!r}. Use 'no_flux' or 'specified_head'.") + +richards.add_dirichlet_bc([psi_top], "Top") +richards.add_dirichlet_bc([hr], "Bottom") + +if bc_type == "specified_head": + richards.add_dirichlet_bc([hr], "Left") + richards.add_dirichlet_bc([hr], "Right") + +# %% [markdown] +# ## Initial condition +# +# Start from the uniform dry state $\psi = h_r$ everywhere. The transient +# solution evolves from this initial condition towards steady state driven +# by the wetting profile on the top boundary. + +# %% +psi.array[:, 0, 0] = hr + +# %% [markdown] +# ## Time stepping +# +# We step forward in time until the solution approaches steady state. The +# Tracy analytical solution gives us the exact transient profile at each +# time level. + +# %% +time = 0.0 + +for step in range(n_steps): + richards.solve(timestep=dt) + time += dt + + if step % 10 == 0 or step == n_steps - 1: + # Sample interior points to check convergence + n_sample = 20 + sx = np.linspace(0.1 * L_dom, 0.9 * L_dom, n_sample) + sy = np.linspace(0.1 * L_dom, 0.9 * L_dom, n_sample) + xx, yy = np.meshgrid(sx, sy) + sample_pts = np.column_stack([xx.ravel(), yy.ravel()]) + + psi_num = uw.function.evaluate(psi.sym[0], sample_pts).squeeze() + psi_exact = tracy_solution_on_grid( + sample_pts, time, alpha, hr, L_dom, theta_r, theta_s, Ks, bc_type + ) + max_err = np.max(np.abs(psi_num - psi_exact)) + l2_err = np.sqrt(np.mean((psi_num - psi_exact) ** 2)) + + print( + f"Step {step:3d}, t = {time:8.3f} s | " + f"max |err| = {max_err:.4e}, L2 err = {l2_err:.4e}" + ) + +# %% [markdown] +# ## Final comparison against analytical solution + +# %% +# Dense grid for final comparison +n_final = 40 +sx = np.linspace(0.05 * L_dom, 0.95 * L_dom, n_final) +sy = np.linspace(0.05 * L_dom, 0.95 * L_dom, n_final) +xx, yy = np.meshgrid(sx, sy) +sample_pts = np.column_stack([xx.ravel(), yy.ravel()]) + +psi_numerical = uw.function.evaluate(psi.sym[0], sample_pts).squeeze() +psi_analytical = tracy_solution_on_grid( + sample_pts, time, alpha, hr, L_dom, theta_r, theta_s, Ks, bc_type +) + +max_error = np.max(np.abs(psi_numerical - psi_analytical)) +l2_error = np.sqrt(np.mean((psi_numerical - psi_analytical) ** 2)) +rel_error = l2_error / np.sqrt(np.mean(psi_analytical**2)) + +print(f"\nFinal comparison at t = {time:.3f} s ({bc_type} BCs, {res}×{res} mesh)") +print(f" Max absolute error: {max_error:.4e}") +print(f" L2 error: {l2_error:.4e}") +print(f" Relative L2 error: {rel_error:.4e}") + +# %% [markdown] +# ## Visualisation + +# %% +if uw.is_notebook(): + import pyvista as pv + import underworld3.visualisation as vis + + pv_mesh = vis.mesh_to_pv_mesh(mesh) + pv_mesh.point_data["psi_numerical"] = vis.scalar_fn_to_pv_points(pv_mesh, psi.sym[0]) + + # Evaluate analytical on pv mesh vertices + pv_coords = np.array(pv_mesh.points[:, :2]) + pv_mesh.point_data["psi_analytical"] = tracy_solution_on_grid( + pv_coords, time, alpha, hr, L_dom, theta_r, theta_s, Ks, bc_type + ) + pv_mesh.point_data["error"] = ( + pv_mesh.point_data["psi_numerical"] - pv_mesh.point_data["psi_analytical"] + ) + + pl = pv.Plotter(shape=(1, 3), window_size=(1200, 400)) + + pl.subplot(0, 0) + pl.add_mesh( + pv_mesh.copy(), + scalars="psi_numerical", + cmap="Blues_r", + show_edges=False, + scalar_bar_args={"title": "Numerical"}, + ) + pl.add_text(f"Numerical psi", font_size=10) + pl.view_xy() + + pl.subplot(0, 1) + pl.add_mesh( + pv_mesh.copy(), + scalars="psi_analytical", + cmap="Blues_r", + show_edges=False, + scalar_bar_args={"title": "Analytical"}, + ) + pl.add_text(f"Analytical psi (Tracy)", font_size=10) + pl.view_xy() + + pl.subplot(0, 2) + pl.add_mesh( + pv_mesh.copy(), + scalars="error", + cmap="RdBu_r", + show_edges=False, + scalar_bar_args={"title": "Error"}, + ) + pl.add_text(f"Error", font_size=10) + pl.view_xy() + + pl.show() + +# %% [markdown] +# ## Vertical profile comparison + +# %% +if uw.is_notebook(): + import matplotlib.pyplot as plt + + # Profile at x = L/2 + n_profile = 100 + y_profile = np.linspace(0.02 * L_dom, 0.98 * L_dom, n_profile) + x_profile = np.full_like(y_profile, 0.5 * L_dom) + profile_pts = np.column_stack([x_profile, y_profile]) + + psi_profile_num = uw.function.evaluate(psi.sym[0], profile_pts).squeeze() + psi_profile_exact = tracy_solution_on_grid( + profile_pts, time, alpha, hr, L_dom, theta_r, theta_s, Ks, bc_type + ) + + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5)) + + ax1.plot(psi_profile_exact, y_profile, "k-", label="Tracy analytical", linewidth=2) + ax1.plot(psi_profile_num, y_profile, "ro", label="UW3 numerical", markersize=4) + ax1.set_xlabel(r"Pressure head $\psi$ [m]") + ax1.set_ylabel("y [m]") + ax1.set_title(f"Vertical profile at x = L/2 (t = {time:.2f} s)") + ax1.legend() + ax1.grid(True, alpha=0.3) + + ax2.plot(psi_profile_num - psi_profile_exact, y_profile, "b-", linewidth=1.5) + ax2.set_xlabel(r"Error $\psi_{num} - \psi_{exact}$ [m]") + ax2.set_ylabel("y [m]") + ax2.set_title("Error profile") + ax2.axvline(0, color="k", linestyle="--", alpha=0.3) + ax2.grid(True, alpha=0.3) + + fig.tight_layout() + plt.show() + +# %% [markdown] +# ## Quantitative assessment +# +# For a production-quality benchmark, the error should decrease with mesh +# refinement. Run at multiple resolutions to check convergence: +# +# ```bash +# python Ex_Richards_Tracy_Benchmark.py -uw_res 16 +# python Ex_Richards_Tracy_Benchmark.py -uw_res 32 +# python Ex_Richards_Tracy_Benchmark.py -uw_res 64 +# ``` +# +# With degree-2 elements, we expect roughly 4th-order convergence +# (halving the element size should reduce the error by ~16×). + +# %% +print(f"\nBenchmark: Tracy (2006) 2D Richards equation") +print(f"BC type: {bc_type}") +print(f"Resolution: {res}×{res}") +print(f"Parameters: alpha={alpha}, hr={hr}, L={L_dom}, Ks={Ks}") +print(f" alpha*L={alpha*L_dom:.1f}, alpha*hr={alpha*hr:.1f}, c={c_time:.2f}") +print(f"Time: t={time:.3f} s ({n_steps} steps × dt={dt})") +print(f"Max error: {max_error:.4e}") +print(f"L2 error: {l2_error:.4e}") +print(f"Rel L2 err: {rel_error:.4e}") + +if max_error < 0.05: + print("\nPASSED: Max error < 0.05") +else: + print(f"\nFAILED: Max error = {max_error:.4e} (threshold 0.05)") From 12df6d52246e76575416eb74eb4bb301cb6a8bdf Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Fri, 20 Mar 2026 22:08:46 +1100 Subject: [PATCH 075/537] Add porous-flow.md to advanced docs toctree Underworld development team with AI support from Claude Code --- docs/advanced/index.md | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/docs/advanced/index.md b/docs/advanced/index.md index e83b680e2..c9e9a5e6b 100644 --- a/docs/advanced/index.md +++ b/docs/advanced/index.md @@ -38,6 +38,11 @@ Dynamic remeshing and adaptive refinement strategies. **[→ Mesh Adaptation](mesh-adaptation.md)** +### Porous Media Flow +Darcy flow, Richards equation, and variably-saturated groundwater modelling. + +**[→ Porous Media Flow](porous-flow.md)** + ### Troubleshooting Common issues, debugging strategies, and solutions. @@ -72,6 +77,7 @@ complex-rheologies custom-meshes curved-boundary-conditions mesh-adaptation +porous-flow troubleshooting api-patterns SWARM-INTEGRATION-STATISTICS From bfe13aba2f9cb8b6a0bf22966fe3eda38d58f70f Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 25 Mar 2026 16:26:06 +1100 Subject: [PATCH 076/537] Add nullspace_rotations property to mesh classes Mesh factories now set _nullspace_rotations with symbolic velocity fields for rigid-body rotation null modes: - Annulus, AnnulusWithSpokes, AnnulusInternalBoundary, DiscInternalBoundaries: 1 mode (z-rotation) - SphericalShell, SphericalShellInternalBoundary, CubedSphere, SegmentedSphericalShell, SegmentedSphericalBall: 3 modes (x, y, z rotation) - Box, QuarterAnnulus, SegmentofAnnulus, SegmentofSphere: 0 modes (walls break symmetry, default [] from base class) Each mode is a SymPy Matrix velocity field in Cartesian coordinates. The solver can project these onto its FE space for PETSc MatSetNullSpace. Underworld development team with AI support from Claude Code --- .../discretisation/discretisation_mesh.py | 30 +++++++++++++++++++ src/underworld3/meshing/annulus.py | 16 ++++++++++ src/underworld3/meshing/segmented.py | 16 ++++++++++ src/underworld3/meshing/spherical.py | 24 +++++++++++++++ 4 files changed, 86 insertions(+) diff --git a/src/underworld3/discretisation/discretisation_mesh.py b/src/underworld3/discretisation/discretisation_mesh.py index 4b11dbd6e..b0985e3b8 100644 --- a/src/underworld3/discretisation/discretisation_mesh.py +++ b/src/underworld3/discretisation/discretisation_mesh.py @@ -664,6 +664,11 @@ def mesh_update_callback(array, change_context): self._lvec = None self.petsc_fe = None + # Rigid-body rotation null modes for this geometry. + # Mesh factories override this for closed surfaces (annulus, sphere). + # Each entry is a SymPy Matrix velocity field in mesh coordinates. + self._nullspace_rotations = [] + self.degree = degree self.qdegree = qdegree @@ -1531,6 +1536,31 @@ def t(self): """ return self._t + @property + def nullspace_rotations(self): + """Symbolic velocity fields for rigid-body rotation null modes. + + Returns a list of SymPy Matrix expressions in mesh Cartesian + coordinates. Empty for meshes with no rotation nullspace (boxes, + wedge segments with walls). Set by mesh factory functions for + closed surfaces (annulus, spherical shell, etc.). + + Each entry represents a rigid rotation: v = omega x r. + + Returns + ------- + list of sympy.Matrix + Velocity fields for each independent rotation mode. + + Examples + -------- + >>> annulus = uw.meshing.Annulus(...) + >>> annulus.nullspace_rotations # [Matrix([-y, x])] + >>> shell = uw.meshing.SphericalShell(...) + >>> shell.nullspace_rotations # 3 rotation matrices + """ + return self._nullspace_rotations + @property def r(self) -> Tuple[sympy.vector.BaseScalar]: r"""Tuple of coordinate scalars :math:`(x, y)` or :math:`(x, y, z)`. diff --git a/src/underworld3/meshing/annulus.py b/src/underworld3/meshing/annulus.py index 1a3631d67..cf8d73e91 100644 --- a/src/underworld3/meshing/annulus.py +++ b/src/underworld3/meshing/annulus.py @@ -538,6 +538,10 @@ class boundary_normals(Enum): new_mesh.boundary_normals = boundary_normals + # Full annulus: rigid rotation about z-axis + x, y = new_mesh.X + new_mesh._nullspace_rotations = [sympy.Matrix([-y, x])] + return new_mesh @@ -1110,6 +1114,10 @@ class boundary_normals(Enum): new_mesh.boundary_normals = boundary_normals + # Full annulus with spokes: rigid rotation about z-axis + x, y = new_mesh.X + new_mesh._nullspace_rotations = [sympy.Matrix([-y, x])] + return new_mesh @@ -1392,6 +1400,10 @@ class boundary_normals(Enum): new_mesh.boundary_normals = boundary_normals + # Full annulus with internal boundary: rigid rotation about z-axis + x, y = new_mesh.X + new_mesh._nullspace_rotations = [sympy.Matrix([-y, x])] + return new_mesh @@ -1671,4 +1683,8 @@ class boundary_normals(Enum): new_mesh.boundary_normals = boundary_normals + # Full disc with internal boundaries: rigid rotation about z-axis + x, y = new_mesh.X + new_mesh._nullspace_rotations = [sympy.Matrix([-y, x])] + return new_mesh diff --git a/src/underworld3/meshing/segmented.py b/src/underworld3/meshing/segmented.py index 4c555191f..b5d264415 100644 --- a/src/underworld3/meshing/segmented.py +++ b/src/underworld3/meshing/segmented.py @@ -676,6 +676,14 @@ class boundary_normals(Enum): new_mesh.boundary_normals = boundary_normals + # Full segmented spherical shell: 3 rigid rotation modes + x, y, z = new_mesh.X + new_mesh._nullspace_rotations = [ + sympy.Matrix([0, -z, y]), + sympy.Matrix([z, 0, -x]), + sympy.Matrix([-y, x, 0]), + ] + return new_mesh @@ -1088,4 +1096,12 @@ class boundary_normals(Enum): new_mesh.boundary_normals = boundary_normals + # Solid sphere: 3 rigid rotation modes + x, y, z = new_mesh.X + new_mesh._nullspace_rotations = [ + sympy.Matrix([0, -z, y]), + sympy.Matrix([z, 0, -x]), + sympy.Matrix([-y, x, 0]), + ] + return new_mesh diff --git a/src/underworld3/meshing/spherical.py b/src/underworld3/meshing/spherical.py index 732705d86..7d74116db 100644 --- a/src/underworld3/meshing/spherical.py +++ b/src/underworld3/meshing/spherical.py @@ -269,6 +269,14 @@ class boundary_normals(Enum): Upper = 12 Centre = 1 + # Full spherical shell: 3 rigid rotation modes + x, y, z = new_mesh.X + new_mesh._nullspace_rotations = [ + sympy.Matrix([0, -z, y]), # rotation about x + sympy.Matrix([z, 0, -x]), # rotation about y + sympy.Matrix([-y, x, 0]), # rotation about z + ] + return new_mesh @@ -475,6 +483,14 @@ class boundary_normals(Enum): Upper = 13 Centre = 1 + # Full spherical shell with internal boundary: 3 rigid rotation modes + x, y, z = new_mesh.X + new_mesh._nullspace_rotations = [ + sympy.Matrix([0, -z, y]), + sympy.Matrix([z, 0, -x]), + sympy.Matrix([-y, x, 0]), + ] + return new_mesh @@ -1011,4 +1027,12 @@ class boundary_normals(Enum): new_mesh.boundary_normals = boundary_normals + # Full cubed sphere: 3 rigid rotation modes + x, y, z = new_mesh.X + new_mesh._nullspace_rotations = [ + sympy.Matrix([0, -z, y]), + sympy.Matrix([z, 0, -x]), + sympy.Matrix([-y, x, 0]), + ] + return new_mesh From b43f8941b56188e6e610efb6bcf394d2e157797a Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Wed, 25 Mar 2026 17:20:15 +1100 Subject: [PATCH 077/537] Add petsc_use_nullspace convenience property to Stokes solver Setting stokes.petsc_use_nullspace = True enables: 1. Constant-pressure nullspace (petsc_use_pressure_nullspace) 2. Velocity rotation modes from mesh.nullspace_rotations This auto-populates petsc_velocity_nullspace_basis from the mesh geometry, so users don't need to construct rotation modes manually. For annulus: 1 pressure + 1 rotation = 2 modes For spherical shell: 1 pressure + 3 rotations = 4 modes For box: 1 pressure + 0 rotations = 1 mode Existing PR #91 tests pass unchanged. Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 26 +++++++++++++++++++ 1 file changed, 26 insertions(+) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 62c411630..6e0ef4a62 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -3553,6 +3553,32 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): self.is_setup = False self._saddle_preconditioner = function + @property + def petsc_use_nullspace(self): + """Enable full nullspace handling: constant pressure + mesh rotation modes. + + Convenience property that enables the pressure nullspace and + auto-populates velocity nullspace modes from ``mesh.nullspace_rotations``. + + For finer control, use ``petsc_use_pressure_nullspace`` and + ``petsc_velocity_nullspace_basis`` separately. + """ + return (self._petsc_use_pressure_nullspace + and len(self._petsc_velocity_nullspace_basis) > 0) + + @petsc_use_nullspace.setter + def petsc_use_nullspace(self, value): + value = bool(value) + self._petsc_use_pressure_nullspace = value + if value and hasattr(self.mesh, 'nullspace_rotations'): + modes = self.mesh.nullspace_rotations + if modes: + self.petsc_velocity_nullspace_basis = modes + elif not value: + self._petsc_velocity_nullspace_basis = () + self._reset_stokes_nullspace() + self.is_setup = False + @property def petsc_use_pressure_nullspace(self): """ From 367219937b12a9cb844e773e3128f7d8a4f398e5 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Thu, 2 Apr 2026 22:44:58 +1100 Subject: [PATCH 078/537] Fix petsc_use_nullspace getter and setter logic - Getter: use 'or' instead of 'and' so pressure-only nullspace (no rotation modes) reports True correctly - Setter: always sync velocity basis to mesh.nullspace_rotations when enabling (even if empty) to prevent stale modes from a previous mesh carrying over Addresses Copilot review comments on PR #105. Underworld development team with AI support from Claude Code --- .../cython/petsc_generic_snes_solvers.pyx | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 6e0ef4a62..8b8735956 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -3564,17 +3564,20 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): ``petsc_velocity_nullspace_basis`` separately. """ return (self._petsc_use_pressure_nullspace - and len(self._petsc_velocity_nullspace_basis) > 0) + or len(self._petsc_velocity_nullspace_basis) > 0) @petsc_use_nullspace.setter def petsc_use_nullspace(self, value): value = bool(value) self._petsc_use_pressure_nullspace = value - if value and hasattr(self.mesh, 'nullspace_rotations'): - modes = self.mesh.nullspace_rotations - if modes: - self.petsc_velocity_nullspace_basis = modes - elif not value: + if value: + # Sync velocity nullspace basis to mesh rotations (even if empty) + # to avoid stale modes carrying over between meshes/runs + if hasattr(self.mesh, 'nullspace_rotations'): + self.petsc_velocity_nullspace_basis = self.mesh.nullspace_rotations or () + else: + self._petsc_velocity_nullspace_basis = () + else: self._petsc_velocity_nullspace_basis = () self._reset_stokes_nullspace() self.is_setup = False From 07d61f7174159df302ad0d77df34788a0a9292c6 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Tue, 7 Apr 2026 17:47:50 -0700 Subject: [PATCH 079/537] Fix swarm advection (order=2) crash after adding particles (#108) add_particles_with_coordinates() called PETSc's dm.migrate() directly without invalidating the SwarmVariable _canonical_data caches. The RK2 advection buffer (_X0) retained a stale numpy array with the old particle count, causing a shape mismatch on the next advection call. Add cache invalidation after migrate, mirroring the existing pattern in _recalculate_owner_and_migrate(). Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- src/underworld3/swarm.py | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/src/underworld3/swarm.py b/src/underworld3/swarm.py index 9a06ee978..ee2dbe4ad 100644 --- a/src/underworld3/swarm.py +++ b/src/underworld3/swarm.py @@ -3380,6 +3380,13 @@ def add_particles_with_coordinates(self, coordinatesArray) -> int: self._remeshed.data[...] = 0 self.dm.migrate(remove_sent_points=True) + + # Invalidate cached data — particle count changed after addNPoints + migrate + self._particle_coordinates._canonical_data = None + for var in self._vars.values(): + if hasattr(var, "_canonical_data"): + var._canonical_data = None + return npoints @timing.routine_timer_decorator From 9f207e29e120b24d11d7767242485dac32cbd1de Mon Sep 17 00:00:00 2001 From: lmoresi Date: Thu, 9 Apr 2026 22:17:07 -0700 Subject: [PATCH 080/537] Fix BdIntegral MPI deadlock and solver DM rebuild bug MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Two independent fixes: 1. petsc_compat.h: Remove early-exit path in UW_DMPlexComputeBdIntegral for empty boundary strata. DMPlexComputeBdIntegral is collective (calls DMGlobalToLocal internally), so all ranks must call it even when their local stratum is empty. The previous code skipped the PETSc call on empty ranks and went straight to Allreduce, causing a deadlock because the non-empty ranks blocked in DMGlobalToLocal. 2. petsc_generic_snes_solvers.pyx: Fix == (comparison) to = (assignment) for mesh_dm_coordinate_hash in _setup_discretisation for all three solver classes (SNES_Scalar, SNES_Vector, SNES_Stokes_SaddlePt). The hash was never saved, causing _setup_discretisation to rebuild the solver DM on every solve() call instead of reusing it. Note: issue #96 (BdIntegral before solver hang in parallel) has a remaining component beyond these fixes — see project memory for investigation notes. The bug is in UW's solver setup code path, not in PETSc itself (confirmed via pure C reproducer). Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- src/underworld3/cython/petsc_compat.h | 29 ++++++++----------- .../cython/petsc_generic_snes_solvers.pyx | 6 ++-- 2 files changed, 15 insertions(+), 20 deletions(-) diff --git a/src/underworld3/cython/petsc_compat.h b/src/underworld3/cython/petsc_compat.h index 2ae23d60a..7cebbca0b 100644 --- a/src/underworld3/cython/petsc_compat.h +++ b/src/underworld3/cython/petsc_compat.h @@ -160,6 +160,12 @@ PetscErrorCode UW_DMPlexSetSNESLocalFEM(DM dm, PetscBool flag, void *ctx) // PETSc's DMPlexComputeBdIntegral returns only the local contribution (no MPI // reduction), so this wrapper adds an Allreduce to produce the global integral. // +// IMPORTANT: DMPlexComputeBdIntegral is collective (it calls DMGlobalToLocal +// internally). All ranks MUST call it, even if their local boundary stratum is +// empty — PETSc handles empty strata gracefully (skips the per-face loop). +// Skipping the call on empty ranks causes a deadlock because the other ranks +// block inside DMGlobalToLocal waiting for the missing participants. +// // Ghost facet filtering is handled by our PETSc patch // (plexfem-internal-boundary-ownership-fix.patch) which filters SF leaves // inside DMPlexComputeBdIntegral, DMPlexComputeBdResidual_Internal, and @@ -173,29 +179,16 @@ PetscErrorCode UW_DMPlexComputeBdIntegral(DM dm, Vec X, { PetscSection section; PetscInt Nf; - PetscInt localCount = 0; PetscFunctionBeginUser; PetscCall(DMGetLocalSection(dm, §ion)); PetscCall(PetscSectionGetNumFields(section, &Nf)); - // If the label is NULL or the requested boundary has no local entities on - // this rank, contribute 0 but still participate in the MPI Allreduce to - // avoid hangs. Parallel DMPlex boundary assembly can deadlock if some - // ranks enter with an empty local stratum. - if (label) { - for (PetscInt i = 0; i < numVals; ++i) { - PetscInt stratumSize = 0; - PetscCall(DMLabelGetStratumSize(label, vals[i], &stratumSize)); - localCount += stratumSize; - } - } - - if (!label || localCount == 0) { - PetscScalar zero = 0.0; - PetscCallMPI(MPIU_Allreduce(&zero, result, 1, MPIU_SCALAR, MPIU_SUM, - PetscObjectComm((PetscObject)dm))); + // NULL label means no boundary was found at all — no rank has work. + // Safe to return early since no rank enters the collective PETSc call. + if (!label) { + *result = 0.0; PetscFunctionReturn(PETSC_SUCCESS); } @@ -207,6 +200,8 @@ PetscErrorCode UW_DMPlexComputeBdIntegral(DM dm, Vec X, PetscScalar *integral; PetscCall(PetscCalloc1(Nf, &integral)); + // All ranks must call DMPlexComputeBdIntegral — it is collective. + // Ranks with empty local strata will simply contribute 0. // PETSc changed DMPlexComputeBdIntegral signature in v3.22.0: // <= 3.21.x: void (*func)(...) — single function pointer // >= 3.22.0: void (**funcs)(...) — array of Nf function pointers diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 9cf128a9f..81ba37dd5 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -1414,7 +1414,7 @@ class SNES_Scalar(SolverBaseClass): return # Keep a note of the coordinates that we use for this setup - self.mesh_dm_coordinate_hash == mesh_dm_coord_hash + self.mesh_dm_coordinate_hash = mesh_dm_coord_hash degree = self.u.degree @@ -2295,7 +2295,7 @@ class SNES_Vector(SolverBaseClass): return # Keep a note of the coordinates that we use for this setup - self.mesh_dm_coordinate_hash == mesh_dm_coord_hash + self.mesh_dm_coordinate_hash = mesh_dm_coord_hash cdef PtrContainer ext = self.compiled_extensions @@ -4217,7 +4217,7 @@ class SNES_Stokes_SaddlePt(SolverBaseClass): print(f"{uw.mpi.rank}: Building dm for {self.name}") # Keep a note of the coordinates that we use for this setup - self.mesh_dm_coordinate_hash == mesh_dm_coord_hash + self.mesh_dm_coordinate_hash = mesh_dm_coord_hash cdef PtrContainer ext = self.compiled_extensions From c34d67c89095bbb90abc93234ecf10299131247d Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 30 Mar 2026 14:41:04 +1100 Subject: [PATCH 081/537] Add TransverseIsotropicVEPFlowModel for fault mechanics MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit New constitutive model combining: - Rank-4 anisotropic viscosity tensor (η₀ bulk, η₁ fault-plane) - VE stress history with BDF + bdf_blend - Yield limiting on fault-plane shear (not full invariant) - All three yield modes: smooth (default), softmin, min, harmonic Inherits from TransverseIsotropicFlowModel and adds the VEP machinery from ViscoElasticPlasticFlowModel (BDF coefficients, stress history, corrected harmonic yield). Initial implementation — needs testing with fault-flow workflow. Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- src/underworld3/constitutive_models.py | 529 +++++++++++++++++++++++++ 1 file changed, 529 insertions(+) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 9a74d5222..a43dfe46a 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -2404,6 +2404,535 @@ def _object_viewer(self): ) +class TransverseIsotropicVEPFlowModel(TransverseIsotropicFlowModel): + r"""Transversely isotropic viscoelastic-plastic flow model for fault mechanics. + + Combines the anisotropic viscosity tensor from :class:`TransverseIsotropicFlowModel` + with viscoelastic stress history and plastic yield limiting on the fault plane. + + The anisotropic viscosity tensor uses two viscosities (η₀ for the bulk, + η₁ for fault-plane shear) and a director n̂ defining the weak plane. + The yield stress τ_y limits the shear stress resolved on the fault plane. + + Parameters + ---------- + unknowns : Unknowns + Solver unknowns (velocity, pressure). + order : int, default=1 + Time integration order for stress history (1 or 2). + material_name : str, optional + Name for disambiguation in multi-material setups. + + See Also + -------- + TransverseIsotropicFlowModel : Anisotropic viscous model (no yield/elasticity). + ViscoElasticPlasticFlowModel : Isotropic VEP model. + """ + + def __init__(self, unknowns, order=1, material_name: str = None): + + self._material_name = material_name + + # Stress history expressions + self._stress_star = expression( + r"{\tau^{*}}", None, + r"Lagrangian Stress at $t - \delta_t$", + ) + self._stress_2star = expression( + r"{\tau^{**}}", None, + r"Lagrangian Stress at $t - 2\delta_t$", + ) + self._E_eff = expression( + r"{\dot{\varepsilon}_{\textrm{eff}}}", None, + "Equivalent value of strain rate (accounting for stress history)", + ) + self._E_eff_inv_II = expression( + r"{\dot{\varepsilon}_{II,\textrm{eff}}}", None, + "Equivalent value of strain rate 2nd invariant (accounting for stress history)", + ) + + self._order = order + self._yield_mode = "smooth" + self._yield_softness = 0.5 + self._bdf_blend = 0.5 + self._max_dt_ratio_for_higher_order = 2.0 + + # Timestep (set by solver) + self._dt = expression(r"{\Delta t}", sympy.oo, "Timestep (set by solver)") + + # BDF coefficients (initialised to BDF-1) + self._bdf_c0 = expression(r"{c_0^{\mathrm{BDF}}}", sympy.Integer(1), "BDF leading coefficient") + self._bdf_c1 = expression(r"{c_1^{\mathrm{BDF}}}", sympy.Integer(-1), "BDF history coefficient 1") + self._bdf_c2 = expression(r"{c_2^{\mathrm{BDF}}}", sympy.Integer(0), "BDF history coefficient 2") + self._bdf_c3 = expression(r"{c_3^{\mathrm{BDF}}}", sympy.Integer(0), "BDF history coefficient 3") + + self._reset() + + super().__init__(unknowns, material_name=material_name) + + return + + class _Parameters(_ParameterBase, _ViscousParameterAlias): + """Parameters for transverse isotropic VEP model. + + Combines anisotropic parameters (η₀, η₁, director) with VEP + parameters (shear_modulus, yield_stress, etc.). + """ + + import underworld3.utilities._api_tools as api_tools + + # Anisotropic parameters + shear_viscosity_0 = api_tools.Parameter( + r"\eta_0", lambda inner_self: 1, + "Bulk shear viscosity", units="Pa*s", + ) + shear_viscosity_1 = api_tools.Parameter( + r"\eta_1", lambda inner_self: 1, + "Fault-plane shear viscosity", units="Pa*s", + ) + director = api_tools.Parameter( + r"\hat{n}", lambda inner_self: 1, + "Director orientation (fault normal)", units=None, + ) + + # Elastic parameter + shear_modulus = api_tools.Parameter( + R"{\mu}", lambda inner_self: sympy.oo, + "Shear modulus", units="Pa", + ) + + # Timestep (managed by solver) + @property + def dt_elastic(inner_self): + """Timestep for VE formulas. Set by the solver.""" + return inner_self._owning_model._dt + + @dt_elastic.setter + def dt_elastic(inner_self, value): + if hasattr(value, 'sym'): + inner_self._owning_model._dt.sym = value.sym + else: + inner_self._owning_model._dt.sym = value + + # Viscosity limits + shear_viscosity_min = api_tools.Parameter( + R"{\eta_{\textrm{min}}}", + lambda inner_self: -sympy.oo, + "Shear viscosity, minimum cutoff", units="Pa*s", + ) + + # Yield parameters (applied to fault-plane shear) + yield_stress = api_tools.Parameter( + R"{\tau_{y}}", lambda inner_self: sympy.oo, + "Yield stress (fault-plane shear)", units="Pa", + ) + yield_stress_min = api_tools.Parameter( + R"{\tau_{y, \mathrm{min}}}", + lambda inner_self: -sympy.oo, + "Yield stress minimum cutoff", units="Pa", + ) + strainrate_inv_II_min = api_tools.Parameter( + R"{\dot\varepsilon_{II,\mathrm{min}}}", + lambda inner_self: 0, + "Strain rate invariant minimum value", units="1/s", + ) + + def __init__(inner_self, _owning_model): + inner_self._owning_model = _owning_model + + inner_self._ve_effective_viscosity = expression( + R"{\eta_{\mathrm{eff}}}", None, + "Effective viscosity (elastic, fault-plane)", + ) + inner_self._t_relax = expression( + R"{t_{\mathrm{relax}}}", None, + "Maxwell relaxation time", + ) + + @property + def ve_effective_viscosity(inner_self): + r"""VE effective viscosity using η₁ (fault-plane viscosity).""" + if inner_self.shear_modulus == sympy.oo: + return inner_self.shear_viscosity_1 + + eta = inner_self.shear_viscosity_1 + mu = inner_self.shear_modulus + dt_e = inner_self.dt_elastic + c0 = inner_self._owning_model._bdf_c0 + + el_eff_visc = eta * mu * dt_e / (c0 * eta + mu * dt_e) + inner_self._ve_effective_viscosity.sym = el_eff_visc + return inner_self._ve_effective_viscosity + + @property + def t_relax(inner_self): + r"""Maxwell relaxation time: η₁ / μ.""" + inner_self._t_relax.sym = inner_self.shear_viscosity_1 / inner_self.shear_modulus + return inner_self._t_relax + + ## End of parameters + + @property + def is_elastic(self): + return self.Parameters.shear_modulus != sympy.oo + + @property + def is_viscoplastic(self): + return self.Parameters.yield_stress.sym != sympy.oo + + @property + def order(self): + """Time integration order (1 or 2).""" + return self._order + + @order.setter + def order(self, value): + """Set time integration order (warns if DFDt already created).""" + self._order = value + self._reset() + solver = getattr(self.Parameters, '_solver', None) + if solver is not None: + ddt = getattr(solver.Unknowns, 'DFDt', None) + if ddt is not None and ddt.order < value: + import warnings + warnings.warn( + f"Setting order={value} but DFDt was created with order={ddt.order}. " + f"Create the model with the desired order before assigning to the solver.", + UserWarning, stacklevel=2, + ) + elif ddt is not None: + solver._order = value + return + + @property + def effective_order(self): + """Effective order accounting for DDt history startup.""" + if self.Unknowns is not None and self.Unknowns.DFDt is not None: + ddt_eff = self.Unknowns.DFDt.effective_order + return min(self._order, ddt_eff) + return self._order + + def _update_bdf_coefficients(self): + """Update BDF coefficient UWexpressions with blending.""" + order = self.effective_order + + if self.Unknowns is not None and self.Unknowns.DFDt is not None: + dt_current = self.Parameters.dt_elastic + if hasattr(dt_current, 'sym'): + dt_current = dt_current.sym + + dt_history = self.Unknowns.DFDt._dt_history + if order >= 2 and len(dt_history) > 0 and dt_history[0] is not None: + try: + ratio = float(dt_current) / float(dt_history[0]) + if ratio > self._max_dt_ratio_for_higher_order: + order = 1 + except (TypeError, ZeroDivisionError): + pass + + coeffs = _bdf_coefficients(order, dt_current, dt_history) + + alpha = self._bdf_blend + if 0 < alpha < 1 and order >= 2: + coeffs_o1 = _bdf_coefficients(1, dt_current, dt_history) + while len(coeffs_o1) < len(coeffs): + coeffs_o1.append(sympy.Integer(0)) + coeffs = [ + (1 - alpha) * c1 + alpha * ck + for c1, ck in zip(coeffs_o1, coeffs) + ] + else: + coeffs = _bdf_coefficients(order, None, []) + + while len(coeffs) < 4: + coeffs.append(sympy.Integer(0)) + + self._bdf_c0.sym = coeffs[0] + self._bdf_c1.sym = coeffs[1] + self._bdf_c2.sym = coeffs[2] + self._bdf_c3.sym = coeffs[3] + + @property + def stress_star(self): + r"""Previous timestep stress from history.""" + if self.Unknowns.DFDt is not None: + self._stress_star.sym = self.Unknowns.DFDt.psi_star[0].sym + return self._stress_star + + @property + def E_eff(self): + r"""Effective strain rate including elastic history.""" + E = self.Unknowns.E + + if self.Unknowns.DFDt is not None and self.is_elastic: + mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus + bdf_cs = [self._bdf_c1, self._bdf_c2, self._bdf_c3] + for i in range(self.Unknowns.DFDt.order): + E += -bdf_cs[i] * self.Unknowns.DFDt.psi_star[i].sym / (2 * mu_dt) + + self._E_eff.sym = E + return self._E_eff + + @property + def E_eff_inv_II(self): + r"""Second invariant of effective strain rate.""" + E_eff = self.E_eff.sym + self._E_eff_inv_II.sym = sympy.sqrt((E_eff**2).trace() / 2) + return self._E_eff_inv_II + + @property + def viscosity(self): + r"""Effective viscosity for the fault-plane shear component. + + Applies the yield mode (smooth/softmin/min/harmonic) to η₁, + leaving η₀ (bulk) unchanged. The anisotropic tensor handles + the directional dependence. + """ + inner_self = self.Parameters + + if inner_self.yield_stress.sym == sympy.oo: + return inner_self.shear_viscosity_0 + + # η₁ is the fault-plane viscosity that gets yield-limited + eta_1_eff = inner_self.ve_effective_viscosity + + if self.is_viscoplastic: + vp_eff = self._plastic_effective_viscosity + if self._yield_mode == "harmonic": + eta_1_eff = 1 / (1 / eta_1_eff + 1 / vp_eff) + elif self._yield_mode == "smooth": + f = eta_1_eff / vp_eff + eta_1_eff = eta_1_eff * (1 + f) / (1 + f + f**2) + elif self._yield_mode == "softmin": + delta = self._yield_softness + f = eta_1_eff / vp_eff + g = (1 + f) / 2 + sympy.sqrt((f - 1)**2 + delta**2) / 2 + eta_1_eff = eta_1_eff / g + else: + eta_1_eff = sympy.Min(eta_1_eff, vp_eff) + + return inner_self.shear_viscosity_0 + + @property + def K(self): + """Effective stiffness for preconditioner.""" + return self.Parameters.shear_viscosity_0 + + @property + def _plastic_effective_viscosity(self): + """Plastic viscosity based on resolved shear strain rate.""" + parameters = self.Parameters + + if parameters.yield_stress == sympy.oo: + return sympy.oo + + Edot = self.E_eff.sym + strainrate_inv_II = expression( + R"{\dot\varepsilon_{II}'}", + sympy.sqrt((Edot**2).trace() / 2), + "Strain rate 2nd Invariant including elastic strain rate term", + ) + + tau_y = parameters.yield_stress + if parameters.yield_stress_min.sym != 0: + tau_y = sympy.Max(parameters.yield_stress_min, tau_y) + + if parameters.strainrate_inv_II_min.sym != 0: + viscosity_yield = tau_y / ( + 2 * (strainrate_inv_II + parameters.strainrate_inv_II_min) + ) + else: + viscosity_yield = tau_y / (2 * strainrate_inv_II) + + return viscosity_yield + + def _build_c_tensor(self): + """Build the anisotropic tensor with yield-limited η₁.""" + + if self._is_setup: + return + + d = self.dim + eta_0 = self.Parameters.shear_viscosity_0.sym + + # η₁ effective: VE + yield limited + eta_1_eff = self.Parameters.ve_effective_viscosity + + if self.is_viscoplastic: + vp_eff = self._plastic_effective_viscosity + if self._yield_mode == "harmonic": + eta_1_eff = 1 / (1 / eta_1_eff + 1 / vp_eff) + elif self._yield_mode == "smooth": + f = eta_1_eff / vp_eff + eta_1_eff = eta_1_eff * (1 + f) / (1 + f + f**2) + elif self._yield_mode == "softmin": + delta = self._yield_softness + f = eta_1_eff / vp_eff + g = (1 + f) / 2 + sympy.sqrt((f - 1)**2 + delta**2) / 2 + eta_1_eff = eta_1_eff / g + else: + eta_1_eff = sympy.Min(eta_1_eff, vp_eff) + + n = self.Parameters.director.sym + Delta = eta_0 - eta_1_eff + + identity = uw.maths.tensor.rank4_identity(d) + lambda_mat = sympy.MutableDenseNDimArray.zeros(d, d, d, d) + + for i in range(d): + for j in range(d): + for k in range(d): + for l in range(d): + base_val = 2 * identity[i, j, k, l] * eta_0 + aniso_correction = ( + 2 * Delta * ( + (n[i] * n[k] * int(j == l) + + n[j] * n[k] * int(l == i) + + n[i] * n[l] * int(j == k) + + n[j] * n[l] * int(k == i)) / 2 + - 2 * n[i] * n[j] * n[k] * n[l] + ) + ) + val = base_val - aniso_correction + if hasattr(val, '__getitem__') and not isinstance(val, (sympy.MatrixBase, sympy.NDimArray)): + val = sympy.Mul(sympy.S.One, val, evaluate=False) + lambda_mat[i, j, k, l] = val + + lambda_mat = sympy.simplify(uw.maths.tensor.rank4_to_mandel(lambda_mat, d)) + self._c = uw.maths.tensor.mandel_to_rank4(lambda_mat, d) + + self._is_setup = True + self._solver_is_setup = False + return + + @property + def flux(self): + """Stress flux for the weak form.""" + # Guard: if director not set yet, return simple viscous flux + n = self.Parameters.director.sym + if not hasattr(n, '__len__') or isinstance(n, (int, float, sympy.Basic)) and not isinstance(n, sympy.MatrixBase): + edot = self.grad_u + return 2 * self.Parameters.shear_viscosity_0 * edot + return self.stress() + + def stress_projection(self): + """VE stress without plastic correction (for history storage).""" + edot = self.grad_u + # Use the full anisotropic tensor but without yield + self._build_c_tensor_ve() + return self._q(edot) + + def _build_c_tensor_ve(self): + """Build anisotropic tensor with VE η₁ only (no yield).""" + d = self.dim + eta_0 = self.Parameters.shear_viscosity_0.sym + eta_1_ve = self.Parameters.ve_effective_viscosity + n = self.Parameters.director.sym + Delta = eta_0 - eta_1_ve + + identity = uw.maths.tensor.rank4_identity(d) + lambda_mat = sympy.MutableDenseNDimArray.zeros(d, d, d, d) + + for i in range(d): + for j in range(d): + for k in range(d): + for l in range(d): + base_val = 2 * identity[i, j, k, l] * eta_0 + aniso_correction = ( + 2 * Delta * ( + (n[i] * n[k] * int(j == l) + + n[j] * n[k] * int(l == i) + + n[i] * n[l] * int(j == k) + + n[j] * n[l] * int(k == i)) / 2 + - 2 * n[i] * n[j] * n[k] * n[l] + ) + ) + val = base_val - aniso_correction + if hasattr(val, '__getitem__') and not isinstance(val, (sympy.MatrixBase, sympy.NDimArray)): + val = sympy.Mul(sympy.S.One, val, evaluate=False) + lambda_mat[i, j, k, l] = val + + lambda_mat = sympy.simplify(uw.maths.tensor.rank4_to_mandel(lambda_mat, d)) + self._c_ve = uw.maths.tensor.mandel_to_rank4(lambda_mat, d) + + def stress(self): + """Viscoelastic-plastic anisotropic stress for the weak form. + + Uses the anisotropic tensor with yield-limited η₁ and adds + BDF stress history terms. + """ + self._build_c_tensor() + edot = self.grad_u + stress = self._q(edot) + + if self.Unknowns.DFDt is not None and self.is_elastic: + mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus + bdf_cs = [self._bdf_c1, self._bdf_c2, self._bdf_c3] + + # History uses the yield-limited tensor applied to stored stress + for i in range(self.Unknowns.DFDt.order): + # The history contribution: apply C tensor to (-cᵢ·σ*/2μdt) + # But σ* is already the full stress tensor, so we scale it + # by the ratio of current to VE viscosity + eta_ve = self.Parameters.ve_effective_viscosity + eta_0 = self.Parameters.shear_viscosity_0 + # Simple scaling: history contribution proportional to VE viscosity + stress += 2 * eta_ve * ( + -bdf_cs[i] * self.Unknowns.DFDt.psi_star[i].sym / (2 * mu_dt) + ) + + return stress + + @property + def yield_mode(self): + r"""How to apply yield limiting to the fault-plane viscosity. + + Same options as :class:`ViscoElasticPlasticFlowModel`: + ``"smooth"`` (default), ``"softmin"``, ``"harmonic"``, ``"min"``. + """ + return self._yield_mode + + @yield_mode.setter + def yield_mode(self, value): + if value not in ("min", "harmonic", "smooth", "softmin"): + raise ValueError(f"yield_mode must be 'min', 'harmonic', 'smooth', or 'softmin', got '{value}'") + self._yield_mode = value + self._reset() + + @property + def yield_softness(self): + """Regularisation parameter δ for softmin mode.""" + return self._yield_softness + + @yield_softness.setter + def yield_softness(self, value): + self._yield_softness = value + self._reset() + + @property + def bdf_blend(self): + """BDF coefficient blending: 0=pure O1, 0.5=default, 1=pure O2.""" + return self._bdf_blend + + @bdf_blend.setter + def bdf_blend(self, value): + self._bdf_blend = value + + @property + def requires_stress_history(self): + """Transverse isotropic VEP requires stress history tracking.""" + return True + + @property + def plastic_fraction(self): + """Fraction of strain rate that is plastic.""" + eta_1_ve = self.Parameters.ve_effective_viscosity + eta_1_eff = self.viscosity + # viscosity property returns η₀, need to compare η₁ effective vs η₁ ve + # This is approximate for the anisotropic case + return sympy.Max(0, 1 - eta_1_eff / eta_1_ve.sym if hasattr(eta_1_ve, 'sym') else 0) + + class MultiMaterialConstitutiveModel(Constitutive_Model): r""" Multi-material constitutive model using level-set weighted flux averaging. From 753d7b2d0b786380879739c97b7e5b49509679ae Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Mon, 30 Mar 2026 15:28:26 +1100 Subject: [PATCH 082/537] Default director to unit vector, fix parent class default Both TransverseIsotropicFlowModel and TransverseIsotropicVEPFlowModel now default the director to [0,...,0,1] (dimension-dependent) instead of scalar 1, which caused TypeError in tensor construction. Underworld development team with AI support from Claude Code (https://claude.com/claude-code) --- src/underworld3/constitutive_models.py | 10 +++------- 1 file changed, 3 insertions(+), 7 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index a43dfe46a..c8aa58527 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -2283,7 +2283,7 @@ class _Parameters(_ParameterBase, _ViscousParameterAlias): director = api_tools.Parameter( r"\hat{n}", - lambda inner_self: 1, + lambda inner_self: sympy.Matrix([0] * (inner_self._owning_model.dim - 1) + [1]), "Director orientation", units=None, # Dimensionless unit vector ) @@ -2491,7 +2491,8 @@ class _Parameters(_ParameterBase, _ViscousParameterAlias): "Fault-plane shear viscosity", units="Pa*s", ) director = api_tools.Parameter( - r"\hat{n}", lambda inner_self: 1, + r"\hat{n}", + lambda inner_self: sympy.Matrix([0] * (inner_self._owning_model.dim - 1) + [1]), "Director orientation (fault normal)", units=None, ) @@ -2808,11 +2809,6 @@ def _build_c_tensor(self): @property def flux(self): """Stress flux for the weak form.""" - # Guard: if director not set yet, return simple viscous flux - n = self.Parameters.director.sym - if not hasattr(n, '__len__') or isinstance(n, (int, float, sympy.Basic)) and not isinstance(n, sympy.MatrixBase): - edot = self.grad_u - return 2 * self.Parameters.shear_viscosity_0 * edot return self.stress() def stress_projection(self): From 1496b776f2d106823b5458ffdd58e2e55a8bf6ae Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 31 Mar 2026 13:39:45 +1100 Subject: [PATCH 083/537] TI-VEP: fix stress history and parameter comparison bugs MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The stress() method used raw η_ve for VE history terms instead of the yield-limited η₁_eff. This prevented yield from capping stress — the isotropic VEP uses yield-limited viscosity for both tensor and history terms. Now the TI-VEP matches the isotropic VEP step-by-step. Also fix is_elastic, is_viscoplastic, ve_effective_viscosity, and _plastic_effective_viscosity to use .sym identity checks (is sympy.oo) instead of object-level comparisons that always returned True/False regardless of the actual parameter value. Validated: TI-VEP matches isotropic VEP to 4 d.p. across 15+ steps with smooth yield mode. Min yield mode diverges (58/80 steps) — smooth is the correct default. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 51 +++++++++++++++++++------- 1 file changed, 37 insertions(+), 14 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index c8aa58527..e908aaaa5 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -2553,7 +2553,8 @@ def __init__(inner_self, _owning_model): @property def ve_effective_viscosity(inner_self): r"""VE effective viscosity using η₁ (fault-plane viscosity).""" - if inner_self.shear_modulus == sympy.oo: + mu_val = inner_self.shear_modulus.sym if hasattr(inner_self.shear_modulus, 'sym') else inner_self.shear_modulus + if mu_val is sympy.oo: return inner_self.shear_viscosity_1 eta = inner_self.shear_viscosity_1 @@ -2575,11 +2576,17 @@ def t_relax(inner_self): @property def is_elastic(self): - return self.Parameters.shear_modulus != sympy.oo + """True if elastic behavior is active (finite shear_modulus).""" + if self.Parameters.shear_modulus.sym is sympy.oo: + return False + return True @property def is_viscoplastic(self): - return self.Parameters.yield_stress.sym != sympy.oo + """True if plastic yielding is active (finite yield_stress).""" + if self.Parameters.yield_stress.sym is sympy.oo: + return False + return True @property def order(self): @@ -2724,7 +2731,8 @@ def _plastic_effective_viscosity(self): """Plastic viscosity based on resolved shear strain rate.""" parameters = self.Parameters - if parameters.yield_stress == sympy.oo: + ty_val = parameters.yield_stress.sym if hasattr(parameters.yield_stress, 'sym') else parameters.yield_stress + if ty_val is sympy.oo: return sympy.oo Edot = self.E_eff.sym @@ -2854,8 +2862,11 @@ def _build_c_tensor_ve(self): def stress(self): """Viscoelastic-plastic anisotropic stress for the weak form. - Uses the anisotropic tensor with yield-limited η₁ and adds - BDF stress history terms. + Matches isotropic VEP pattern: tensor contraction for current strain + rate, scalar yield-limited viscosity for VE history terms. The tensor + C(η₁_eff) handles anisotropy; the history uses the same η₁_eff as + a scalar multiplier (consistent with how isotropic VEP uses + self.viscosity for both). """ self._build_c_tensor() edot = self.grad_u @@ -2865,15 +2876,27 @@ def stress(self): mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus bdf_cs = [self._bdf_c1, self._bdf_c2, self._bdf_c3] - # History uses the yield-limited tensor applied to stored stress + # Compute yield-limited η₁ — same expression used in tensor + eta_1_eff = self.Parameters.ve_effective_viscosity + if self.is_viscoplastic: + vp_eff = self._plastic_effective_viscosity + if self._yield_mode == "harmonic": + eta_1_eff = 1 / (1 / eta_1_eff + 1 / vp_eff) + elif self._yield_mode == "smooth": + f = eta_1_eff / vp_eff + eta_1_eff = eta_1_eff * (1 + f) / (1 + f + f**2) + elif self._yield_mode == "softmin": + delta = self._yield_softness + f = eta_1_eff / vp_eff + g = (1 + f) / 2 + sympy.sqrt((f - 1)**2 + delta**2) / 2 + eta_1_eff = eta_1_eff / g + else: + eta_1_eff = sympy.Min(eta_1_eff, vp_eff) + for i in range(self.Unknowns.DFDt.order): - # The history contribution: apply C tensor to (-cᵢ·σ*/2μdt) - # But σ* is already the full stress tensor, so we scale it - # by the ratio of current to VE viscosity - eta_ve = self.Parameters.ve_effective_viscosity - eta_0 = self.Parameters.shear_viscosity_0 - # Simple scaling: history contribution proportional to VE viscosity - stress += 2 * eta_ve * ( + # History terms use yield-limited viscosity as scalar, + # matching isotropic VEP: 2 * viscosity * (-c_i * σ* / 2μdt) + stress += 2 * eta_1_eff * ( -bdf_cs[i] * self.Unknowns.DFDt.psi_star[i].sym / (2 * mu_dt) ) From 162a5120fc4c4076aa3947f4ab52d3f71bc87f58 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 31 Mar 2026 20:57:11 +1100 Subject: [PATCH 084/537] =?UTF-8?q?TI-VEP:=20resolved=20fault-plane=20yiel?= =?UTF-8?q?d,=20VE=20tensor,=20and=20C:=CE=B5=CC=87=5Feff=20stress?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Three coupled fixes for the TransverseIsotropicVEPFlowModel: 1. Yield criterion uses resolved fault-plane shear strain rate γ̇ = t·ε̇_eff·n instead of global invariant ε̇_II. This ensures yield activates when fault-plane shear exceeds τ_y regardless of fault orientation (validated at 15 degrees). 2. Tensor base uses VE effective η₀_ve = η₀·μ·dt/(c₀·η₀+μ·dt) instead of raw η₀. This ensures Δ = η₀_ve - η₁_eff = 0 when η₁ = η₀ and yield is inactive (no spurious anisotropy). 3. Stress formula simplified to σ = C(η₀_ve, η₁_eff) : ε̇_eff. The tensor naturally separates normal (VE, η₀_ve) and shear (VEP, η₁_eff) components on the fault plane. No separate scalar history terms needed. Validated: 15 degree rotated fault, η₁=η₀=1, τ_y=0.15. Resolved fault shear caps at τ_y while normal stress grows as pure VE. Stable with 1 SNES iteration (smooth yield mode). Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 89 ++++++++++++++------------ 1 file changed, 49 insertions(+), 40 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index e908aaaa5..49a050a64 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -2728,7 +2728,16 @@ def K(self): @property def _plastic_effective_viscosity(self): - """Plastic viscosity based on resolved shear strain rate.""" + """Plastic viscosity from resolved fault-plane shear strain rate. + + Uses γ̇ = t · ε̇_eff · n (shear strain rate resolved on the fault + plane) rather than the global invariant ε̇_II. This ensures yield + activates when the fault-plane shear exceeds τ_y, regardless of + fault orientation. + + The formula 2η₁_pl = τ_y / γ̇ is the same pattern as isotropic + Drucker-Prager but projected onto the fault plane. + """ parameters = self.Parameters ty_val = parameters.yield_stress.sym if hasattr(parameters.yield_stress, 'sym') else parameters.yield_stress @@ -2736,11 +2745,16 @@ def _plastic_effective_viscosity(self): return sympy.oo Edot = self.E_eff.sym - strainrate_inv_II = expression( - R"{\dot\varepsilon_{II}'}", - sympy.sqrt((Edot**2).trace() / 2), - "Strain rate 2nd Invariant including elastic strain rate term", - ) + + # Resolve strain rate onto fault plane: γ̇ = t · ε̇ · n + n = parameters.director.sym + # Fault-parallel direction (2D: rotate normal 90° clockwise) + t_fault = sympy.Matrix([n[1], -n[0]]) + + gamma_dot = (t_fault.T * Edot * n)[0, 0] + + # Use absolute value — shear can be in either sense + gamma_dot_abs = sympy.sqrt(gamma_dot**2) tau_y = parameters.yield_stress if parameters.yield_stress_min.sym != 0: @@ -2748,23 +2762,41 @@ def _plastic_effective_viscosity(self): if parameters.strainrate_inv_II_min.sym != 0: viscosity_yield = tau_y / ( - 2 * (strainrate_inv_II + parameters.strainrate_inv_II_min) + 2 * (gamma_dot_abs + parameters.strainrate_inv_II_min) ) else: - viscosity_yield = tau_y / (2 * strainrate_inv_II) + viscosity_yield = tau_y / (2 * gamma_dot_abs) return viscosity_yield def _build_c_tensor(self): - """Build the anisotropic tensor with yield-limited η₁.""" + """Build the anisotropic tensor with VE effective viscosities. + + Both η₀ and η₁ are replaced by their VE effective values: + η₀_ve = η₀·μ·dt / (c₀·η₀ + μ·dt) + η₁_ve = η₁·μ·dt / (c₀·η₁ + μ·dt) + Then η₁_ve is further yield-limited to η₁_eff. This ensures + Δ = η₀_ve - η₁_eff = 0 when η₁ = η₀ and yield is inactive. + """ if self._is_setup: return d = self.dim - eta_0 = self.Parameters.shear_viscosity_0.sym - # η₁ effective: VE + yield limited + # η₀: VE effective (no yield) + eta_0_raw = self.Parameters.shear_viscosity_0 + mu = self.Parameters.shear_modulus + dt_e = self.Parameters.dt_elastic + c0 = self._bdf_c0 + + mu_val = mu.sym if hasattr(mu, 'sym') else mu + if mu_val is sympy.oo: + eta_0 = eta_0_raw.sym if hasattr(eta_0_raw, 'sym') else eta_0_raw + else: + eta_0 = eta_0_raw * mu * dt_e / (c0 * eta_0_raw + mu * dt_e) + + # η₁: VE effective + yield limited eta_1_eff = self.Parameters.ve_effective_viscosity if self.is_viscoplastic: @@ -2869,36 +2901,13 @@ def stress(self): self.viscosity for both). """ self._build_c_tensor() - edot = self.grad_u - stress = self._q(edot) - if self.Unknowns.DFDt is not None and self.is_elastic: - mu_dt = self.Parameters.dt_elastic * self.Parameters.shear_modulus - bdf_cs = [self._bdf_c1, self._bdf_c2, self._bdf_c3] - - # Compute yield-limited η₁ — same expression used in tensor - eta_1_eff = self.Parameters.ve_effective_viscosity - if self.is_viscoplastic: - vp_eff = self._plastic_effective_viscosity - if self._yield_mode == "harmonic": - eta_1_eff = 1 / (1 / eta_1_eff + 1 / vp_eff) - elif self._yield_mode == "smooth": - f = eta_1_eff / vp_eff - eta_1_eff = eta_1_eff * (1 + f) / (1 + f + f**2) - elif self._yield_mode == "softmin": - delta = self._yield_softness - f = eta_1_eff / vp_eff - g = (1 + f) / 2 + sympy.sqrt((f - 1)**2 + delta**2) / 2 - eta_1_eff = eta_1_eff / g - else: - eta_1_eff = sympy.Min(eta_1_eff, vp_eff) - - for i in range(self.Unknowns.DFDt.order): - # History terms use yield-limited viscosity as scalar, - # matching isotropic VEP: 2 * viscosity * (-c_i * σ* / 2μdt) - stress += 2 * eta_1_eff * ( - -bdf_cs[i] * self.Unknowns.DFDt.psi_star[i].sym / (2 * mu_dt) - ) + # Apply the anisotropic tensor to the effective strain rate + # (current + VE history): σ = C(η₀_ve, η₁_eff) : ε̇_eff + # This is the correct VE formula — the tensor handles anisotropy + # for both current and history contributions uniformly. + edot_eff = self.E_eff.sym if hasattr(self.E_eff, 'sym') else self.E_eff + stress = self._q(edot_eff) return stress From 3eaac53deb5003b43fdfedb86ae0285adcf081d7 Mon Sep 17 00:00:00 2001 From: Louis Moresi Date: Tue, 31 Mar 2026 21:23:29 +1100 Subject: [PATCH 085/537] TI-VEP: generalise resolved shear to 2D/3D via Pythagoras MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Replace the 2D-specific tangent vector (t = [n₁, -n₀]) with the dimension-independent Pythagoras approach: T = ε̇_eff · n (traction on fault) ε̇_n = T · n (normal component) |γ̇| = √(|T|² - ε̇_n²) (in-plane shear magnitude) This works in any dimension without constructing an explicit tangent vector (which is not unique in 3D). Verified identical results to the 2D formulation on the 15° rotated fault test. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 25 ++++++++++++------------- 1 file changed, 12 insertions(+), 13 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 49a050a64..1d051457c 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -2730,12 +2730,13 @@ def K(self): def _plastic_effective_viscosity(self): """Plastic viscosity from resolved fault-plane shear strain rate. - Uses γ̇ = t · ε̇_eff · n (shear strain rate resolved on the fault - plane) rather than the global invariant ε̇_II. This ensures yield - activates when the fault-plane shear exceeds τ_y, regardless of - fault orientation. + Computes the in-plane shear magnitude using Pythagoras: + T = ε̇_eff · n (traction-like vector on fault) + ε̇_n = T · n (normal component) + |γ̇| = √(|T|² - ε̇_n²) (in-plane shear magnitude) - The formula 2η₁_pl = τ_y / γ̇ is the same pattern as isotropic + This works in both 2D and 3D — no explicit tangent vector needed. + The formula 2η₁_pl = τ_y / |γ̇| is the same pattern as isotropic Drucker-Prager but projected onto the fault plane. """ parameters = self.Parameters @@ -2746,15 +2747,13 @@ def _plastic_effective_viscosity(self): Edot = self.E_eff.sym - # Resolve strain rate onto fault plane: γ̇ = t · ε̇ · n + # Resolve strain rate onto fault plane via Pythagoras n = parameters.director.sym - # Fault-parallel direction (2D: rotate normal 90° clockwise) - t_fault = sympy.Matrix([n[1], -n[0]]) - - gamma_dot = (t_fault.T * Edot * n)[0, 0] - - # Use absolute value — shear can be in either sense - gamma_dot_abs = sympy.sqrt(gamma_dot**2) + T = Edot * n # "traction" vector on fault + edot_n = (n.T * T)[0, 0] # normal component + T_sq = (T.T * T)[0, 0] # |T|² + gamma_dot_sq = T_sq - edot_n**2 # in-plane shear² + gamma_dot_abs = sympy.sqrt(sympy.Max(gamma_dot_sq, 0)) tau_y = parameters.yield_stress if parameters.yield_stress_min.sym != 0: From 44076d925f31aa3ef5442a5ce3d0a399c2b274ae Mon Sep 17 00:00:00 2001 From: lmoresi Date: Sun, 12 Apr 2026 10:19:24 -0600 Subject: [PATCH 086/537] Fix softmin yield mode: correct offset, default delta, remove simplify Three fixes to the softmin yield approximation: 1. Corrected softmin formula so g(0) = 1 exactly. The old formula g = (1+f)/2 + sqrt((f-1)^2 + d^2)/2 gives g(0) = 1.06 for d=0.5, causing spurious yield correction below onset. New formula subtracts the constant offset: g = 1 + softplus(f-1) - softplus(-1). 2. Changed default yield_softness from 0.5 to 0.1. The old value was too soft for cases where tau_y is a significant fraction of the viscous stress (f_ss < 2), causing 15-50% undershoot of the yield cap. With delta=0.1, all tested cases reach within 1-2% of tau_y. 3. Removed sympy.simplify() from TI-VEP _build_c_tensor and _build_c_tensor_ve. These caused hangs with sympy.Min expressions and are unnecessary (the Mandel conversion is correct without simplification, consistent with the fix already applied elsewhere). Validated: 0-degree and 15-degree fault benchmarks with tau_y = 0.15 and 0.30 all reach within 1-2% of analytical yield cap. Underworld development team with AI support from Claude Code --- src/underworld3/constitutive_models.py | 28 +++++++++++++++++--------- 1 file changed, 18 insertions(+), 10 deletions(-) diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index 1d051457c..af2d09e5a 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1111,7 +1111,7 @@ def __init__(self, unknowns, order=1, material_name: str = None): self._order = order self._yield_mode = "smooth" # "min", "harmonic", "smooth", or "softmin" - self._yield_softness = 0.5 # δ parameter for "softmin" mode + self._yield_softness = 0.1 # δ parameter for "softmin" mode self._bdf_blend = None # auto: 1.0 for VE, 0.75 for VEP # Timestep — set by the solver before each solve(). Not a user parameter. @@ -1484,12 +1484,15 @@ def viscosity(self): elif self._yield_mode == "softmin": # Smooth approximation to Min(η_ve, η_pl): # η_eff = η_ve / g(f) - # g(f) = (1+f)/2 + √((f-1)² + δ²)/2 ≈ max(1, f) - # where f = η_ve/η_pl and δ = yield_softness. + # g(f) = 1 + softplus(f-1) - softplus(-1) ≈ max(1, f) + # where softplus(x) = (x + √(x² + δ²))/2 and f = η_ve/η_pl. + # Corrected so g(0) = 1 exactly (no spurious yield below onset). # Approaches exact Min as δ→0. No Min/Max in expression. delta = self._yield_softness f = effective_viscosity / vp_effective_viscosity - g = (1 + f) / 2 + sympy.sqrt((f - 1)**2 + delta**2) / 2 + import math + offset = (-1 + math.sqrt(1 + delta**2)) / 2 + g = 1 + (f - 1 + sympy.sqrt((f - 1)**2 + delta**2)) / 2 - offset effective_viscosity = effective_viscosity / g else: effective_viscosity = sympy.Min(effective_viscosity, vp_effective_viscosity) @@ -1745,7 +1748,8 @@ def yield_softness(self): Smaller values → sharper yield (closer to Min, less robust). Larger values → smoother transition (more robust, lower stress). - Default 0.5. Only used when ``yield_mode == "softmin"``. + Default 0.1. Only used when ``yield_mode == "softmin"``. + Increase toward 0.5 if SNES convergence is difficult at yield onset. """ return self._yield_softness @@ -2453,7 +2457,7 @@ def __init__(self, unknowns, order=1, material_name: str = None): self._order = order self._yield_mode = "smooth" - self._yield_softness = 0.5 + self._yield_softness = 0.1 self._bdf_blend = 0.5 self._max_dt_ratio_for_higher_order = 2.0 @@ -2714,7 +2718,9 @@ def viscosity(self): elif self._yield_mode == "softmin": delta = self._yield_softness f = eta_1_eff / vp_eff - g = (1 + f) / 2 + sympy.sqrt((f - 1)**2 + delta**2) / 2 + import math + offset = (-1 + math.sqrt(1 + delta**2)) / 2 + g = 1 + (f - 1 + sympy.sqrt((f - 1)**2 + delta**2)) / 2 - offset eta_1_eff = eta_1_eff / g else: eta_1_eff = sympy.Min(eta_1_eff, vp_eff) @@ -2808,7 +2814,9 @@ def _build_c_tensor(self): elif self._yield_mode == "softmin": delta = self._yield_softness f = eta_1_eff / vp_eff - g = (1 + f) / 2 + sympy.sqrt((f - 1)**2 + delta**2) / 2 + import math + offset = (-1 + math.sqrt(1 + delta**2)) / 2 + g = 1 + (f - 1 + sympy.sqrt((f - 1)**2 + delta**2)) / 2 - offset eta_1_eff = eta_1_eff / g else: eta_1_eff = sympy.Min(eta_1_eff, vp_eff) @@ -2838,7 +2846,7 @@ def _build_c_tensor(self): val = sympy.Mul(sympy.S.One, val, evaluate=False) lambda_mat[i, j, k, l] = val - lambda_mat = sympy.simplify(uw.maths.tensor.rank4_to_mandel(lambda_mat, d)) + lambda_mat = uw.maths.tensor.rank4_to_mandel(lambda_mat, d) self._c = uw.maths.tensor.mandel_to_rank4(lambda_mat, d) self._is_setup = True @@ -2887,7 +2895,7 @@ def _build_c_tensor_ve(self): val = sympy.Mul(sympy.S.One, val, evaluate=False) lambda_mat[i, j, k, l] = val - lambda_mat = sympy.simplify(uw.maths.tensor.rank4_to_mandel(lambda_mat, d)) + lambda_mat = uw.maths.tensor.rank4_to_mandel(lambda_mat, d) self._c_ve = uw.maths.tensor.mandel_to_rank4(lambda_mat, d) def stress(self): From 2c4fe8bd8f43a73cc03a377d9bc756ca980b951e Mon Sep 17 00:00:00 2001 From: lmoresi Date: Sun, 12 Apr 2026 10:20:45 -0600 Subject: [PATCH 087/537] Add TI-VEP documentation, benchmark figure, and angled fault example Technical document (docs/advanced/vep-transverse-isotropy-faults.md): - Mathematical formulation from isotropic VEP through TI tensor to combined TI-VEP with resolved fault-plane yield criterion - Pythagoras formulation for dimension-independent resolved shear - Softmin yield approximation with corrected offset formula - Guidance on choosing the sharpness parameter delta - Benchmark results at 0 and 15 degree fault angles Benchmark figure (docs/advanced/figures/ti_vep_benchmark_final.png): - 0-degree and 15-degree fault, tau_y = 0.15 and 0.30 - Analytical VE curves with yield cap overlay - Shows resolved shear capping at tau_y while global stress grows Example (Ex_TI_VEP_Angled_Fault.py): - 2D shear box with 15-degree embedded fault - TransverseIsotropicVEPFlowModel with softmin yield - Time-stepping with stress monitoring and matplotlib output Underworld development team with AI support from Claude Code --- .../figures/ti_vep_benchmark_final.png | Bin 0 -> 118984 bytes docs/advanced/index.md | 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For problems where SNES convergence is difficult at yield onset, increase $\delta$ toward 0.3--0.5 as a relaxation parameter. Set it via `cm._yield_softness = 0.1`. + +## Benchmark Results + +The figure below shows the TI-VEP model validated against the analytical Maxwell viscoelastic solution with plastic yield cap, for a simple shear box with an embedded fault. Two yield stresses are tested ($\tau_y = 0.15$ and $\tau_y = 0.30$) at both 0 and 15 degrees fault angle. Solid curves show the analytical VE solution capped at $\tau_y$; markers show the numerical results. + +```{figure} figures/ti_vep_benchmark_final.png +:name: fig-tivep-benchmark + +TI-VEP shear box benchmark. **Left**: horizontal fault ($\theta = 0°$), where resolved shear equals $\sigma_{xy}$. **Right**: angled fault ($\theta = 15°$), showing resolved fault-plane shear (circles) capping at $\tau_y$ while the global $\sigma_{xy}$ (crosses) continues to build as the bulk VE component grows. With the corrected softmin ($\delta = 0.1$), all cases reach within 1--2% of the analytical yield cap. +``` + +At 0 degrees, the resolved shear is simply $\sigma_{xy}$ and the yield cap is exact. At 15 degrees, the anisotropic tensor creates a mechanical coupling between normal and shear components on the fault plane: the resolved shear caps at $\tau_y$ while the global stress tensor reflects contributions from both the yielded fault-plane component (governed by $\eta_{1,\text{eff}}$) and the non-yielding bulk component (governed by $\eta_{0,\text{ve}}$). + +## Summary of Constitutive Models + +| Model | Viscosity | Elasticity | Yield | Anisotropy | +|-------|-----------|------------|-------|------------| +| `ViscousFlowModel` | $\eta$ | -- | -- | -- | +| `ViscoPlasticFlowModel` | $\eta$ | -- | $\dot\varepsilon_{II}$ | -- | +| `ViscoElasticPlasticFlowModel` | $\eta$ | $\mu$, BDF-$k$ | $\dot\varepsilon_{II}$ | -- | +| `TransverseIsotropicFlowModel` | $\eta_0, \eta_1, \hat{n}$ | -- | -- | TI tensor | +| `TransverseIsotropicVEPFlowModel` | $\eta_0, \eta_1, \hat{n}$ | $\mu$, BDF-$k$ | $\|\dot\gamma\|$ (fault-plane) | TI tensor | + +## References + +- Moresi, L., Muhlhaus, H.-B., 2006. Anisotropic viscous models of large-deformation Mohr-Coulomb failure. *Phil. Mag.*, 86, 3287-3305. +- Muhlhaus, H.-B., Moresi, L., Hobbs, B., Dufour, F., 2002. Large amplitude folding in finely layered viscoelastic rock structures. *Pure Appl. Geophys.*, 159, 2311-2333. diff --git a/docs/examples/solid_mechanics/intermediate/Ex_TI_VEP_Angled_Fault.py b/docs/examples/solid_mechanics/intermediate/Ex_TI_VEP_Angled_Fault.py new file mode 100644 index 000000000..4c045ba0f --- /dev/null +++ b/docs/examples/solid_mechanics/intermediate/Ex_TI_VEP_Angled_Fault.py @@ -0,0 +1,330 @@ +# %% [markdown] +r""" +# Viscoelastic-Plastic Shear Box with Angled Fault + +**PHYSICS:** solid_mechanics +**DIFFICULTY:** intermediate +**RUNTIME:** ~2 minutes + +## Description + +A 2D shear box with an embedded fault at 15 degrees from horizontal, using the +`TransverseIsotropicVEPFlowModel` constitutive model. This combines: + +- **Transverse isotropy**: anisotropic viscosity with the fault normal as director +- **Viscoelasticity**: Maxwell stress buildup with BDF-1 time integration +- **Plastic yield**: resolved fault-plane shear limits the stress + +The key physical result: stress builds elastically until the **resolved shear +stress on the fault plane** reaches the yield stress $\tau_y$. At that point, +fault-plane shear yields while the stress component normal to the fault +continues to build as pure viscoelastic. + +## Physical Setup + +| Parameter | Value | +|-----------|-------| +| Domain | 1 x 1 | +| Fault | centred, 15 deg from horizontal | +| $\eta_0$ (bulk) | 1 | +| $\eta_1$ (fault-plane) | 1 | +| $\mu$ (shear modulus) | 1 | +| $\tau_y$ (fault yield) | 0.15 | +| Fault width | 0.08 | +| Top velocity | 0.5 | +""" + +# %% +#| echo: false +import nest_asyncio +nest_asyncio.apply() + +# %% +import os +import numpy as np +import sympy +import underworld3 as uw + +import matplotlib +if not os.environ.get('DISPLAY') and not os.environ.get('WAYLAND_DISPLAY'): + matplotlib.use('Agg') +import matplotlib.pyplot as plt + +os.makedirs("output", exist_ok=True) + +# %% [markdown] +""" +## Parameters +""" + +# %% +# Physical parameters +ETA_0 = 1.0 # bulk viscosity +ETA_1 = 1.0 # fault-plane viscosity (same as bulk for this test) +MU = 1.0 # shear modulus +TAU_Y = 0.15 # fault-plane yield stress +V_TOP = 0.5 # top boundary velocity +DT = 0.025 # timestep +N_STEPS = 80 # number of steps + +# Mesh +RES = 64 # mesh resolution (RES x RES) + +# Fault geometry +FAULT_ANGLE_DEG = 15.0 # angle from horizontal (degrees) +FAULT_WIDTH = 0.08 # influence function width +FAULT_LENGTH = 0.6 # fault length (centered in domain) + +# %% [markdown] +r""" +## Mesh and Variables +""" + +# %% +mesh = uw.meshing.StructuredQuadBox( + elementRes=(RES, RES), + minCoords=(0.0, 0.0), + maxCoords=(1.0, 1.0), + qdegree=3, +) + +v = uw.discretisation.MeshVariable("U", mesh, 2, degree=2, vtype=uw.VarType.VECTOR) +p = uw.discretisation.MeshVariable("P", mesh, 1, degree=1, + continuous=True, vtype=uw.VarType.SCALAR) + +# %% [markdown] +r""" +## Fault Surface + +The fault is a 1D polyline at 15 degrees from horizontal, centered in the domain. +The `Surface` class computes the signed distance field and normals automatically. +""" + +# %% +theta = np.radians(FAULT_ANGLE_DEG) +cx, cy = 0.5, 0.5 # centre of domain + +# Fault endpoints +dx = FAULT_LENGTH / 2 * np.cos(theta) +dy = FAULT_LENGTH / 2 * np.sin(theta) +fault_points = np.array([ + [cx - dx, cy - dy], + [cx + dx, cy + dy], +]) + +fault = uw.meshing.Surface("fault", mesh, fault_points, symbol="F") +fault.discretize() + +# Director: fault normal (perpendicular to fault, pointing "up") +n_x = -np.sin(theta) +n_y = np.cos(theta) +director = sympy.Matrix([n_x, n_y]) + +print(f"Fault angle: {FAULT_ANGLE_DEG} deg") +print(f"Director (fault normal): [{n_x:.4f}, {n_y:.4f}]") + +# %% [markdown] +r""" +## Yield Stress Field + +The yield stress varies spatially: low near the fault, high in the bulk. +We interpolate the weakness (1/$\tau_y$) to avoid steep gradients. +""" + +# %% +TAU_Y_BULK = 200.0 # effectively infinite for the bulk + +weakness = fault.influence_function( + width=FAULT_WIDTH, + value_near=1 / TAU_Y, + value_far=1 / TAU_Y_BULK, + profile="gaussian", +) +tau_y_field = 1 / weakness + +# %% [markdown] +r""" +## Solver Setup + +The `TransverseIsotropicVEPFlowModel` combines the anisotropic viscosity tensor +(Muhlhaus-Moresi) with viscoelastic stress history and plastic yield on the +fault plane. +""" + +# %% +stokes = uw.systems.Stokes(mesh, velocityField=v, pressureField=p) + +# Create model with BDF-1 time integration +cm = uw.constitutive_models.TransverseIsotropicVEPFlowModel( + stokes.Unknowns, order=1 +) +stokes.constitutive_model = cm + +# Set parameters +cm.Parameters.shear_viscosity_0 = ETA_0 +cm.Parameters.shear_viscosity_1 = ETA_1 +cm.Parameters.shear_modulus = MU +cm.Parameters.yield_stress = tau_y_field +cm.Parameters.director = director +cm.Parameters.shear_viscosity_min = ETA_0 * 1.0e-3 +cm.Parameters.strainrate_inv_II_min = 1.0e-6 +cm.yield_mode = "softmin" # smooth approximation to min (default delta=0.1) + +# Solver settings +stokes.saddle_preconditioner = 1 / cm.K +stokes.tolerance = 1.0e-4 +stokes.petsc_options["ksp_type"] = "fgmres" + +# Boundary conditions: simple shear +stokes.add_essential_bc(sympy.Matrix([V_TOP, 0.0]), "Top") +stokes.add_essential_bc(sympy.Matrix([0.0, 0.0]), "Bottom") +stokes.add_essential_bc((sympy.oo, 0.0), "Left") +stokes.add_essential_bc((sympy.oo, 0.0), "Right") +stokes.bodyforce = sympy.Matrix([0.0, 0.0]) + +# %% [markdown] +r""" +## Time Stepping + +Track the stress components at a point on the fault to show elastic buildup +and yield cap behavior. +""" + +# %% +# Monitoring point: centre of the fault +monitor_coord = np.array([[0.5, 0.5]]) + +times = [] +sigma_xy_history = [] +sigma_resolved_history = [] + +# Analytical VE reference (no yield): sigma_xy = eta * gamma_dot * (1 - exp(-t / t_r)) +gamma_dot = V_TOP # approximate global shear rate +t_relax = ETA_1 / MU + +for step in range(N_STEPS): + stokes.solve(timestep=DT, zero_init_guess=(step == 0)) + + t = (step + 1) * DT + reason = stokes.snes.getConvergedReason() + its = stokes.snes.getIterationNumber() + + # Sample stress at monitoring point + tau = stokes.tau + tau_data = tau.data + tau_coords = tau.coords + + # Find nearest stress evaluation point to monitor location + dists = np.linalg.norm(tau_coords - monitor_coord, axis=1) + idx = np.argmin(dists) + s_xx, s_yy, s_xy = tau_data[idx, 0], tau_data[idx, 1], tau_data[idx, 2] + + # Resolved shear on fault plane: tau_resolved = n^T sigma n_perp + # For a fault with normal (n_x, n_y), the tangent is (n_y, -n_x) + # Resolved shear = t^T sigma n = sigma_ij * t_i * n_j + t_x, t_y = n_y, -n_x # tangent vector + resolved_shear = (s_xx * t_x * n_x + s_xy * (t_x * n_y + t_y * n_x) + + s_yy * t_y * n_y) + + times.append(t) + sigma_xy_history.append(s_xy) + sigma_resolved_history.append(resolved_shear) + + flag = " ***" if reason < 0 else "" + if step % 10 == 0 or reason < 0: + print(f"Step {step+1:3d}, t={t:.3f}: " + f"sigma_xy={s_xy:.4f}, resolved={resolved_shear:.4f}, " + f"SNES={reason}, its={its}{flag}") + +# %% [markdown] +r""" +## Stress Evolution + +The plot shows stress at the fault centre over time. The dashed line shows +the analytical VE solution (no yield). The resolved shear stress on the +fault plane should cap at $\tau_y = 0.15$. +""" + +# %% +times = np.array(times) +sigma_xy_history = np.array(sigma_xy_history) +sigma_resolved_history = np.array(sigma_resolved_history) + +# Analytical VE solution (no yield) +t_analytical = np.linspace(0, times[-1], 200) +sigma_ve_analytical = ETA_1 * gamma_dot * (1 - np.exp(-t_analytical / t_relax)) + +fig, axes = plt.subplots(1, 2, figsize=(12, 5)) + +# Left panel: sigma_xy and resolved shear vs time +ax = axes[0] +ax.plot(times, sigma_xy_history, 'b-o', markersize=2, label=r'$\sigma_{xy}$ (global)') +ax.plot(times, sigma_resolved_history, 'r-s', markersize=2, + label=r'$\tau_{\mathrm{resolved}}$ (fault plane)') +ax.plot(t_analytical, sigma_ve_analytical, 'k--', alpha=0.5, label='VE analytical (no yield)') +ax.axhline(y=TAU_Y, color='gray', linestyle=':', linewidth=2, + label=rf'$\tau_y = {TAU_Y}$') +ax.set_xlabel('Time') +ax.set_ylabel('Stress') +ax.set_title(f'Stress at fault centre (angle={FAULT_ANGLE_DEG} deg)') +ax.legend(fontsize=9) +ax.grid(True, alpha=0.3) + +# Right panel: stress profile across fault at end of simulation +ax = axes[1] +n_samples = 100 +# Profile perpendicular to the fault, through the centre +profile_dist = np.linspace(-0.4, 0.4, n_samples) +profile_x = 0.5 + profile_dist * n_x # along fault normal direction +profile_y = 0.5 + profile_dist * n_y +# Clip to domain +valid = (profile_x > 0.02) & (profile_x < 0.98) & (profile_y > 0.02) & (profile_y < 0.98) +profile_coords = np.column_stack([profile_x[valid], profile_y[valid]]) + +# Evaluate tau_y field along profile +tau_y_profile = uw.function.evaluate(tau_y_field, profile_coords).flatten() + +# For stress, find nearest tau evaluation points +tau_coords = stokes.tau.coords +tau_data = stokes.tau.data +stress_profile = np.zeros(len(profile_coords)) +for i, pc in enumerate(profile_coords): + dists = np.linalg.norm(tau_coords - pc, axis=1) + idx = np.argmin(dists) + s_xx, s_yy, s_xy = tau_data[idx, 0], tau_data[idx, 1], tau_data[idx, 2] + t_x, t_y = n_y, -n_x + stress_profile[i] = (s_xx * t_x * n_x + s_xy * (t_x * n_y + t_y * n_x) + + s_yy * t_y * n_y) + +ax.plot(profile_dist[valid], np.abs(stress_profile), 'r-', linewidth=2, + label=r'$|\tau_{\mathrm{resolved}}|$') +ax.plot(profile_dist[valid], tau_y_profile, 'k--', linewidth=1, + label=r'$\tau_y$ (yield stress)') +ax.axvline(0, color='gray', linestyle=':', alpha=0.5, label='Fault centre') +ax.set_xlabel('Distance from fault (along normal)') +ax.set_ylabel('Stress') +ax.set_title('Final stress profile across fault') +ax.legend(fontsize=9) +ax.grid(True, alpha=0.3) + +plt.tight_layout() +plt.savefig("output/ti_vep_angled_fault.png", dpi=150) +plt.show() + +# %% [markdown] +r""" +## Summary + +This example demonstrates the `TransverseIsotropicVEPFlowModel`: + +1. **Elastic stress buildup**: stress grows from zero following the Maxwell solution +2. **Fault-plane yield**: the resolved shear stress on the fault plane caps at $\tau_y$ +3. **Anisotropic yield**: only the fault-parallel shear component yields; the normal + component continues to build elastically +4. **Smooth spatial transition**: the Gaussian influence function localises yield to + the fault zone, with background material remaining elastic + +The resolved shear criterion ($|\dot\gamma| = \sqrt{|T|^2 - \dot\varepsilon_n^2}$) +correctly identifies fault-plane shear regardless of the fault orientation, avoiding +the orientation-dependent errors that arise from using the global strain rate invariant. +""" From 21c6bfc816fbfc3f13ba3e8887fb878c02f90985 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Sun, 12 Apr 2026 10:34:03 -0600 Subject: [PATCH 088/537] Address Copilot review: fix stress_projection, doc corrections - Fix stress_projection() to use _c_ve tensor directly instead of calling _q() which always uses _c (the yield-limited tensor). This ensures stress history stores VE-only stress as intended. - Fix director sign in doc example: [-sin(theta), cos(theta)] - Clarify that softmin is not the default yield mode (smooth is) - Use public cm.yield_softness API instead of cm._yield_softness - Add comment explaining deliberate math.sqrt for float offset Underworld development team with AI support from Claude Code --- .../vep-transverse-isotropy-faults.md | 6 ++--- src/underworld3/constitutive_models.py | 24 ++++++++++++++----- 2 files changed, 21 insertions(+), 9 deletions(-) diff --git a/docs/advanced/vep-transverse-isotropy-faults.md b/docs/advanced/vep-transverse-isotropy-faults.md index 9ffd1ac21..26599267b 100644 --- a/docs/advanced/vep-transverse-isotropy-faults.md +++ b/docs/advanced/vep-transverse-isotropy-faults.md @@ -206,14 +206,14 @@ cm.Parameters.yield_stress = 0.15 # fault-plane yield stress # Director from fault normal (e.g., fault at 15 degrees from horizontal) theta = np.radians(15) -cm.Parameters.director = sympy.Matrix([np.sin(theta), np.cos(theta)]) +cm.Parameters.director = sympy.Matrix([-np.sin(theta), np.cos(theta)]) ``` The director can also be a spatially varying field (e.g., from a `Surface` object's normals transferred to a mesh variable), and the yield stress can vary spatially using an influence function to localise yielding near the fault. ## Smooth Yield Approximations -The `"softmin"` yield mode (default) uses a smooth approximation to $\min(\eta_{\text{ve}}, \eta_{\text{pl}})$ to avoid the non-differentiable kink that causes problems for the SNES solver. The approximation is: +The `"softmin"` yield mode uses a smooth approximation to $\min(\eta_{\text{ve}}, \eta_{\text{pl}})$ to avoid the non-differentiable kink that causes problems for the SNES solver. The approximation is: $$g(f) = 1 + \text{softplus}(f-1) - \text{softplus}(-1), \qquad \eta_{\text{eff}} = \eta_{\text{ve}} / g(f)$$ @@ -235,7 +235,7 @@ The softmin is accurate when $\delta \ll f_{ss}$, i.e., when the viscous stress | 0.1 | ~99% of $\tau_y$ | ~100% | low | | 0.01 | ~100% | ~100% | moderate | -The default $\delta = 0.1$ is accurate for all cases where the viscous stress exceeds the yield stress by at least 50% ($f_{ss} > 1.5$). For problems where SNES convergence is difficult at yield onset, increase $\delta$ toward 0.3--0.5 as a relaxation parameter. Set it via `cm._yield_softness = 0.1`. +The default $\delta = 0.1$ is accurate for all cases where the viscous stress exceeds the yield stress by at least 50% ($f_{ss} > 1.5$). For problems where SNES convergence is difficult at yield onset, increase $\delta$ toward 0.3--0.5 as a relaxation parameter. Set it via `cm.yield_softness = 0.1`. ## Benchmark Results diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index af2d09e5a..f6f92308f 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1490,7 +1490,7 @@ def viscosity(self): # Approaches exact Min as δ→0. No Min/Max in expression. delta = self._yield_softness f = effective_viscosity / vp_effective_viscosity - import math + import math # float offset avoids sympy expression blowup in tensor offset = (-1 + math.sqrt(1 + delta**2)) / 2 g = 1 + (f - 1 + sympy.sqrt((f - 1)**2 + delta**2)) / 2 - offset effective_viscosity = effective_viscosity / g @@ -2718,7 +2718,7 @@ def viscosity(self): elif self._yield_mode == "softmin": delta = self._yield_softness f = eta_1_eff / vp_eff - import math + import math # float offset avoids sympy expression blowup in tensor offset = (-1 + math.sqrt(1 + delta**2)) / 2 g = 1 + (f - 1 + sympy.sqrt((f - 1)**2 + delta**2)) / 2 - offset eta_1_eff = eta_1_eff / g @@ -2814,7 +2814,7 @@ def _build_c_tensor(self): elif self._yield_mode == "softmin": delta = self._yield_softness f = eta_1_eff / vp_eff - import math + import math # float offset avoids sympy expression blowup in tensor offset = (-1 + math.sqrt(1 + delta**2)) / 2 g = 1 + (f - 1 + sympy.sqrt((f - 1)**2 + delta**2)) / 2 - offset eta_1_eff = eta_1_eff / g @@ -2859,11 +2859,23 @@ def flux(self): return self.stress() def stress_projection(self): - """VE stress without plastic correction (for history storage).""" + """VE stress without plastic correction (for history storage). + + Uses the anisotropic tensor with VE effective viscosities but + no yield limiting (η₁_ve, not η₁_eff). This is the stress that + should be stored in the DFDt history for the next timestep. + """ edot = self.grad_u - # Use the full anisotropic tensor but without yield self._build_c_tensor_ve() - return self._q(edot) + # Contract with the VE-only tensor (not self._c which has yield) + c_ve = self._c_ve + if len(c_ve.shape) == 2: + flux = c_ve * edot + else: + flux = sympy.tensorcontraction( + sympy.tensorcontraction(sympy.tensorproduct(c_ve, edot), (1, 5)), (0, 3) + ) + return sympy.Matrix(flux) def _build_c_tensor_ve(self): """Build anisotropic tensor with VE η₁ only (no yield).""" From 4e763fe46d7bdecf74bb629498460584b62d2e2c Mon Sep 17 00:00:00 2001 From: lmoresi Date: Sun, 12 Apr 2026 10:36:52 -0600 Subject: [PATCH 089/537] Default yield_mode to softmin (with delta=0.1) Change default from "smooth" to "softmin" in both ViscoElasticPlasticFlowModel and TransverseIsotropicVEPFlowModel. The corrected softmin with delta=0.1 is more accurate than smooth across the full range of yield ratios. Underworld development team with AI support from Claude Code --- docs/advanced/vep-transverse-isotropy-faults.md | 2 +- src/underworld3/constitutive_models.py | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/advanced/vep-transverse-isotropy-faults.md b/docs/advanced/vep-transverse-isotropy-faults.md index 26599267b..8bf3e56a4 100644 --- a/docs/advanced/vep-transverse-isotropy-faults.md +++ b/docs/advanced/vep-transverse-isotropy-faults.md @@ -213,7 +213,7 @@ The director can also be a spatially varying field (e.g., from a `Surface` objec ## Smooth Yield Approximations -The `"softmin"` yield mode uses a smooth approximation to $\min(\eta_{\text{ve}}, \eta_{\text{pl}})$ to avoid the non-differentiable kink that causes problems for the SNES solver. The approximation is: +The `"softmin"` yield mode (default) uses a smooth approximation to $\min(\eta_{\text{ve}}, \eta_{\text{pl}})$ to avoid the non-differentiable kink that causes problems for the SNES solver. The approximation is: $$g(f) = 1 + \text{softplus}(f-1) - \text{softplus}(-1), \qquad \eta_{\text{eff}} = \eta_{\text{ve}} / g(f)$$ diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py index f6f92308f..b6c7c2b9f 100644 --- a/src/underworld3/constitutive_models.py +++ b/src/underworld3/constitutive_models.py @@ -1110,7 +1110,7 @@ def __init__(self, unknowns, order=1, material_name: str = None): ) self._order = order - self._yield_mode = "smooth" # "min", "harmonic", "smooth", or "softmin" + self._yield_mode = "softmin" # "min", "harmonic", "smooth", or "softmin" self._yield_softness = 0.1 # δ parameter for "softmin" mode self._bdf_blend = None # auto: 1.0 for VE, 0.75 for VEP @@ -2456,7 +2456,7 @@ def __init__(self, unknowns, order=1, material_name: str = None): ) self._order = order - self._yield_mode = "smooth" + self._yield_mode = "softmin" self._yield_softness = 0.1 self._bdf_blend = 0.5 self._max_dt_ratio_for_higher_order = 2.0 From 9538af5cdb6ba9c92c8198f901a22a55fbcf0b4f Mon Sep 17 00:00:00 2001 From: lmoresi Date: Mon, 13 Apr 2026 08:21:47 -0600 Subject: [PATCH 090/537] Fix build isolation: explicit --target, no symlink fallback, no editable installs MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Build system hardening after editable install contamination caused hours of debugging (debug PETSc .so files leaked into optimised environment via shared source tree and stale .pth files). uw (build script): - Use pip --target to install where Python actually looks, not where pip resolves through worktree symlinks - Post-install verification: confirm import underworld3 works after build - Clean stale editable .pth files and source-tree .so before each build - Remove .pixi symlink fallback in worktree create — fail hard instead of creating a broken shared environment pixi.toml: - Add amr-debug environment (petsc-4-uw-openmpi-debug) for isolated debug PETSc investigation without contaminating the optimised build CLAUDE.md: - Add "NEVER Use Editable Installs" section with recovery instructions - Update worktree docs: each worktree has own pixi env (not shared) Underworld development team with AI support from Claude Code --- CLAUDE.md | 47 ++- pixi.lock | 1042 +++++++++++++++++++++++++++++++++++++++++++++++++++-- pixi.toml | 24 ++ uw | 52 ++- 4 files changed, 1112 insertions(+), 53 deletions(-) diff --git a/CLAUDE.md b/CLAUDE.md index 60244cf09..fcae41d02 100644 --- a/CLAUDE.md +++ b/CLAUDE.md @@ -140,22 +140,23 @@ This keeps feature branches independent and makes cross-pollination of fixes str **Use a worktree for any multi-file change** (docs cleanup, refactoring, features). Multiple Claude sessions sharing one working directory will overwrite each other's work. -Worktrees share the main repo's pixi environment and PETSc build via symlinks — -there is one set of dependencies, not one per worktree. `./uw build` from inside -a worktree installs that worktree's source into the shared environment. +Each worktree gets its **own pixi environment** (isolated site-packages, own +compiled extensions). Only PETSc is shared via symlink (non-relocatable, +expensive to rebuild). `./uw build` from inside a worktree installs that +worktree's source into the worktree's own environment. **Full documentation**: `docs/developer/guides/branching-strategy.md` (Git Worktrees section) #### Creating and using a worktree ```bash -# Create — resets to development, sets up symlinks, names the branch +# Create — own .pixi env, shared PETSc, names the branch ./uw worktree create # → feature/ ./uw worktree create bugfix # → bugfix/ # Work — drops you into a shell cd'd to the worktree ./uw worktree shell -./uw build # builds from THIS source into the shared env +./uw build # builds from THIS source into THIS worktree's env ./uw test # runs tests exit # leave @@ -175,9 +176,8 @@ git checkout origin/ -- path/to/file #### Important: always build and run from inside the worktree -Because there is one shared environment, `./uw build` installs whichever source -tree you run it from. If you build from the main repo then run code expecting -worktree changes, the worktree edits will not be active. Always: +Each worktree has its own pixi environment. `./uw build` installs into the +environment of whichever worktree (or main repo) you run it from. Always: 1. `./uw worktree shell ` (or `cd` into the worktree) 2. `./uw build` @@ -211,13 +211,40 @@ Underworld development team with AI support from [Claude Code](https://claude.co ### Rebuild After Source Changes **After modifying source files, always run `./uw build`!** - Underworld3 is installed as a package in the pixi environment -- Changes go to `.pixi/envs/default/lib/python3.12/site-packages/underworld3/` -- Verify with `uw.model.__file__` +- Changes go to `.pixi/envs//lib/python3.12/site-packages/underworld3/` +- Verify with `uw.__file__` (should show site-packages path, NOT `src/`) **Note**: `./uw build` uses `--no-cache-dir` to prevent pip from reusing stale wheels (UW3 is always version `0.0.0`). If you still suspect stale code, clean the build directory: `rm -rf build/lib.* build/bdist.*` then rebuild. +### NEVER Use Editable Installs +**DO NOT use `pip install -e .` (editable/development mode)!** +This is a hard rule — there are no exceptions. + +Editable installs create `.pth` files and `.so` symlinks in the source tree that: +- **Contaminate all pixi environments** sharing the same source directory +- **Break worktree isolation** (worktrees share pixi envs via symlinks) +- **Persist after uninstall** — stale `.pth` files redirect Python imports to `src/` + even after a proper `./uw build`, causing import errors or wrong library loading +- **Mix debug/release builds** — `.so` compiled against one PETSc arch get loaded + by environments expecting another, causing `dlopen` symbol errors + +Always use `./uw build` which runs `pip install .` (non-editable). If `./uw build` +is not available, use `pixi run -e pip install . --no-build-isolation --no-cache-dir`. + +**Recovery from editable install contamination:** +```bash +# Remove stale .pth files from ALL environments +find .pixi/envs -name "__editable__*underworld*" -delete +# Remove .so from source tree (they belong in site-packages) +find src/underworld3 -name "*.so" -delete +# Clean build cache +rm -rf build/ +# Rebuild properly +./uw build +``` + ### Test Quality Principles **New tests must be validated before making code changes to fix them!** - Validate test correctness before changing main code diff --git a/pixi.lock b/pixi.lock index ffd0bc629..84c3c9e3b 100644 --- a/pixi.lock +++ b/pixi.lock @@ -5,8 +5,6 @@ environments: - url: https://conda.anaconda.org/conda-forge/ indexes: - https://pypi.org/simple - options: - pypi-prerelease-mode: if-necessary-or-explicit packages: linux-64: - conda: https://conda.anaconda.org/conda-forge/linux-64/_libgcc_mutex-0.1-conda_forge.tar.bz2 @@ -645,13 +643,1023 @@ environments: - 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# --force-reinstall: pip also skips reinstalling .py files if it thinks - # the package is already installed at the same version. This ensures - # all source files (not just compiled .pyx) are copied to site-packages. - $PIXI run -e "$env" pip install . --no-build-isolation --no-cache-dir --force-reinstall || { + # --target: install to where Python ACTUALLY looks, not where pip thinks. + # NEVER use -e (editable) — it breaks worktree and environment isolation. + $PIXI run -e "$env" pip install . --no-build-isolation --no-cache-dir \ + --upgrade --target="$site_packages" || { echo -e "${YELLOW}underworld3 build failed${NC}" exit 1 } + # Verify the install is importable + $PIXI run -e "$env" python -c "import underworld3" 2>/dev/null || { + echo -e "${YELLOW}underworld3 installed but cannot be imported!${NC}" + echo " site-packages: $site_packages" + echo " Check for stale .pth files or .so mismatches." + exit 1 + } + # Verify Python source files were actually installed. # pip's wheel cache can silently serve stale .py files even with # --no-cache-dir (version 0.0.0 problem). Compare checksums of key @@ -833,7 +858,7 @@ COMMANDS type-check Run mypy Worktrees: - worktree create [prefix] Create worktree (symlinks .pixi + PETSc) + worktree create [prefix] Create worktree (own .pixi, shared PETSc) worktree shell Start shell in worktree directory worktree list List worktrees with status worktree remove Remove worktree and branch @@ -978,9 +1003,9 @@ run_update() { # ── Worktree management ────────────────────────────────────────────── # -# Worktrees share the main repo's pixi environment and PETSc build -# via symlinks. `./uw build` from inside a worktree installs the -# worktree's source into the shared env. +# Each worktree gets its OWN pixi environment (isolated site-packages). +# Only PETSc is shared via symlink (non-relocatable, expensive to rebuild). +# `./uw build` from inside a worktree installs into that worktree's env. WORKTREE_ROOT="$SCRIPT_DIR/.claude/worktrees" @@ -1058,15 +1083,16 @@ worktree_create() { echo -e " ${GREEN}✓${NC} .pixi-env copied ($(cat "$main_repo/.pixi-env"))" fi - # Install pixi environment (own copy, not symlinked) + # Install pixi environment (own copy — NEVER symlink) local env=$(cat "$wt_path/.pixi-env" 2>/dev/null || echo "runtime") echo " Installing pixi environment ($env) — this may take a moment..." (cd "$wt_path" && $PIXI install -e "$env" 2>/dev/null) && \ echo -e " ${GREEN}✓${NC} .pixi/ installed (isolated)" || { - echo -e " ${YELLOW}pixi install failed — falling back to symlink${NC}" - rm -rf "$wt_path/.pixi" - ln -s "$main_repo/.pixi" "$wt_path/.pixi" - echo -e " ${YELLOW}✓${NC} .pixi → main repo (shared fallback)" + echo -e " ${RED}pixi install failed for worktree${NC}" + echo -e " The worktree requires its own pixi environment." + echo -e " Fix the pixi install error above, then run:" + echo -e " cd $wt_path && pixi install -e $env" + exit 1 } # 4b. Install petsc4py for AMR environments From 28f1c4c305fb2458a03f92e3ca9aa4778894c187 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Tue, 14 Apr 2026 14:28:31 -0700 Subject: [PATCH 091/537] Fix BdIntegral parallel hang: coordinate DM label contamination (#96) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Root cause: DMClone (inside createCoordinateSpace) copies ALL labels from mesh.dm to the coordinate DM — including boundary labels added by UW's mesh init. When DMPlexComputeBdIntegral later lazily recreates the coordinate field, DMCompleteBCLabels_Internal fails with MPI errors on these inherited boundary labels, causing a deadlock or segfault. Fix: - Add UW_DMForceCoordinateField (petsc_compat.h): forces coordinate field creation and strips non-essential labels from the coordinate DM. Called after createCoordinateSpace in nuke_coords_and_rebuild so the coordinate field is cached clean before boundary labels can contaminate lazy recreation. - Replace setCoordinateDisc with createCoordinateSpace: the former leaves the coordinate dual space without point subspaces (separate PETSc bug causing null pointer in PetscFECreatePointTrace). - Use createFromFile instead of topologyLoad+coordinatesLoad+labelsLoad in _from_plexh5 for more robust HDF5 mesh loading. - Skip copyDS self-copy when dm_hierarchy is trivial. Also found (for PETSc upstream report): - DMSetCoordinateDisc with user FE: broken dual space subspaces - DMCompleteBCLabels_Internal: fails on coordinate DMs with inherited boundary labels from DMClone - Pure C reproducer: /tmp/petsc_bdint_coorddisc.c + issue96_box.msh Closes #96 Underworld development team with AI support from Claude Code --- src/underworld3/cython/petsc_compat.h | 36 +++++++++++++++++ src/underworld3/cython/petsc_extras.pxi | 1 + src/underworld3/cython/petsc_maths.pyx | 16 ++++++++ .../discretisation/discretisation_mesh.py | 39 ++++++++++++------- 4 files changed, 77 insertions(+), 15 deletions(-) diff --git a/src/underworld3/cython/petsc_compat.h b/src/underworld3/cython/petsc_compat.h index 7cebbca0b..c7204da77 100644 --- a/src/underworld3/cython/petsc_compat.h +++ b/src/underworld3/cython/petsc_compat.h @@ -129,6 +129,42 @@ PetscErrorCode UW_PetscDSViewBdWF(PetscDS ds, PetscInt bd) return 1; } +// Issue #96 fix: Force coordinate field creation on a DM and strip +// boundary labels from the coordinate DM so they don't cause MPI errors +// in DMCompleteBCLabels_Internal during lazy coordinate field recreation. +// +// Must be called AFTER createCoordinateSpace and AFTER labels are added. +// The coordinate field is created NOW (while we can clean the coord DM) +// and cached, preventing PETSc from lazily recreating it later. +PetscErrorCode UW_DMForceCoordinateField(DM dm) +{ + DMField coordField; + DM cdm; + PetscInt numLabels, i; + + PetscFunctionBeginUser; + + // Force coordinate field creation (triggers DMCreateCoordinateField_Plex) + PetscCall(DMGetCoordinateField(dm, &coordField)); + + // Now strip non-essential labels from the coordinate DM + // (DMClone copied all of mesh.dm's labels, including boundary labels) + PetscCall(DMGetCoordinateDM(dm, &cdm)); + PetscCall(DMGetNumLabels(cdm, &numLabels)); + for (i = numLabels - 1; i >= 0; --i) { + const char *name; + PetscBool isDepth, isCelltype; + PetscCall(DMGetLabelName(cdm, i, &name)); + PetscCall(PetscStrcmp(name, "depth", &isDepth)); + PetscCall(PetscStrcmp(name, "celltype", &isCelltype)); + if (!isDepth && !isCelltype) { + PetscCall(DMRemoveLabel(cdm, name, NULL)); + } + } + + PetscFunctionReturn(PETSC_SUCCESS); +} + // Set the time value on a DM. This is passed as `petsc_t` to all // pointwise residual and Jacobian functions during assembly. // PETSc stores this internally but petsc4py doesn't expose it. diff --git a/src/underworld3/cython/petsc_extras.pxi b/src/underworld3/cython/petsc_extras.pxi index edd73ca15..28c6af334 100644 --- a/src/underworld3/cython/petsc_extras.pxi +++ b/src/underworld3/cython/petsc_extras.pxi @@ -44,6 +44,7 @@ cdef extern from "petsc_compat.h": PetscErrorCode UW_PetscDSViewBdWF(PetscDS, PetscInt) PetscErrorCode UW_DMSetTime( PetscDM, PetscReal ) PetscErrorCode UW_DMPlexSetSNESLocalFEM( PetscDM, PetscBool, void *) + PetscErrorCode UW_DMForceCoordinateField(PetscDM) PetscErrorCode UW_DMPlexComputeBdIntegral( PetscDM, PetscVec, PetscDMLabel, PetscInt, const PetscInt*, void*, PetscScalar*, void*) cdef extern from "petsc.h" nogil: diff --git a/src/underworld3/cython/petsc_maths.pyx b/src/underworld3/cython/petsc_maths.pyx index 26e2f828b..a7d098614 100644 --- a/src/underworld3/cython/petsc_maths.pyx +++ b/src/underworld3/cython/petsc_maths.pyx @@ -15,6 +15,22 @@ cdef extern from "petsc.h" nogil: PetscErrorCode DMPlexComputeCellwiseIntegralFEM( PetscDM, PetscVec, PetscVec, void* ) +def dm_force_coordinate_field(dm): + """Force coordinate field creation and strip boundary labels from the + coordinate DM. Must be called after createCoordinateSpace and after + boundary labels have been added to mesh.dm. + + Issue #96: DMClone (inside createCoordinateSpace) copies ALL labels from + mesh.dm to the coordinate DM. When DMPlexComputeBdIntegral later lazily + recreates the coordinate field, DMCompleteBCLabels_Internal fails with + MPI errors on the boundary labels. This function forces the coordinate + field to be created NOW and strips the labels so the cached field is used + instead of being lazily recreated. + """ + cdef DM c_dm = dm + CHKERRQ(UW_DMForceCoordinateField(c_dm.dm)) + + class Integral: """ The `Integral` class constructs the volume integral diff --git a/src/underworld3/discretisation/discretisation_mesh.py b/src/underworld3/discretisation/discretisation_mesh.py index 132ba7b9d..55bfc62b3 100644 --- a/src/underworld3/discretisation/discretisation_mesh.py +++ b/src/underworld3/discretisation/discretisation_mesh.py @@ -128,22 +128,18 @@ def _from_plexh5( if comm == None: comm = PETSc.COMM_WORLD - viewer = PETSc.ViewerHDF5().create(filename, "r", comm=comm) + # Use createFromFile for a single-call load (issue #96: the separate + # topologyLoad + coordinatesLoad + labelsLoad pipeline leaves the + # coordinate DM in a state that DMPlexComputeBdIntegral cannot handle). + h5plex = PETSc.DMPlex().createFromFile(filename, interpolate=True, comm=comm) - # h5plex = PETSc.DMPlex().createFromFile(filename, comm=comm) - h5plex = PETSc.DMPlex().create(comm=comm) - sf0 = h5plex.topologyLoad(viewer) - h5plex.coordinatesLoad(viewer, sf0) - h5plex.labelsLoad(viewer, sf0) - - # Do this as well h5plex.setName("uw_mesh") h5plex.markBoundaryFaces("All_Boundaries", 1001) if not return_sf: return h5plex else: - return sf0, h5plex + return None, h5plex class Mesh(Stateful, uw_object): @@ -1144,12 +1140,23 @@ def nuke_coords_and_rebuild( if PETSc.Sys.getVersion() <= (3, 20, 5) and PETSc.Sys.getVersionInfo()["release"] == True: self.dm.projectCoordinates(self.petsc_fe) - elif PETSc.Sys.getVersion() >= (3, 24, 0): - # PETSc 3.24+ added 'localized' parameter (for DG coordinate spaces) - self.dm.setCoordinateDisc(disc=self.petsc_fe, localized=False, project=False) else: - # PETSc 3.21-3.23: older signature without localized parameter - self.dm.setCoordinateDisc(disc=self.petsc_fe, project=False) + # Use createCoordinateSpace rather than setCoordinateDisc. + # setCoordinateDisc with a user-created FE leaves the coordinate + # dual space without proper point subspaces, causing + # DMPlexComputeBdIntegral to segfault/deadlock (issue #96). + # createCoordinateSpace builds the FE internally with correct + # subspace initialisation. + self.dm.createCoordinateSpace(self.degree, False, True) + + # Issue #96 fix: Force coordinate field creation and strip boundary + # labels from the coordinate DM. createCoordinateSpace clears the + # coordinate field cache (via DMSetCoordinateField(NULL)). Without + # this call, DMPlexComputeBdIntegral lazily recreates the field by + # cloning mesh.dm — which now has boundary labels — causing + # DMCompleteBCLabels_Internal to fail with MPI errors. + from underworld3.cython.petsc_maths import dm_force_coordinate_field + dm_force_coordinate_field(self.dm) if verbose and uw.mpi.rank == 0: print( @@ -1193,7 +1200,9 @@ def nuke_coords_and_rebuild( self._search_lengths, ) = self._get_mesh_sizes() - self.dm.copyDS(self.dm_hierarchy[-1]) + # Skip self-copy when hierarchy is trivial (issue #96 investigation) + if self.dm is not self.dm_hierarchy[-1]: + self.dm.copyDS(self.dm_hierarchy[-1]) if verbose and uw.mpi.rank == 0: print( From 53ef2fa1b87d26ff639d8cd0cf0c03e4b2e15c0a Mon Sep 17 00:00:00 2001 From: lmoresi Date: Wed, 15 Apr 2026 09:25:20 -0700 Subject: [PATCH 092/537] Fix CI: version guard for createCoordinateSpace, return SF from _from_plexh5 - Add hasattr guard for createCoordinateSpace (not in all petsc4py versions) - Fall back to setCoordinateDisc for PETSc builds without createCoordinateSpace - Return h5plex.getPointSF() instead of None from _from_plexh5 (Copilot review) Underworld development team with AI support from Claude Code --- .../discretisation/discretisation_mesh.py | 23 +++++++++++-------- 1 file changed, 13 insertions(+), 10 deletions(-) diff --git a/src/underworld3/discretisation/discretisation_mesh.py b/src/underworld3/discretisation/discretisation_mesh.py index 55bfc62b3..695378492 100644 --- a/src/underworld3/discretisation/discretisation_mesh.py +++ b/src/underworld3/discretisation/discretisation_mesh.py @@ -139,7 +139,7 @@ def _from_plexh5( if not return_sf: return h5plex else: - return None, h5plex + return h5plex.getPointSF(), h5plex class Mesh(Stateful, uw_object): @@ -1140,7 +1140,7 @@ def nuke_coords_and_rebuild( if PETSc.Sys.getVersion() <= (3, 20, 5) and PETSc.Sys.getVersionInfo()["release"] == True: self.dm.projectCoordinates(self.petsc_fe) - else: + elif hasattr(self.dm, "createCoordinateSpace"): # Use createCoordinateSpace rather than setCoordinateDisc. # setCoordinateDisc with a user-created FE leaves the coordinate # dual space without proper point subspaces, causing @@ -1149,14 +1149,17 @@ def nuke_coords_and_rebuild( # subspace initialisation. self.dm.createCoordinateSpace(self.degree, False, True) - # Issue #96 fix: Force coordinate field creation and strip boundary - # labels from the coordinate DM. createCoordinateSpace clears the - # coordinate field cache (via DMSetCoordinateField(NULL)). Without - # this call, DMPlexComputeBdIntegral lazily recreates the field by - # cloning mesh.dm — which now has boundary labels — causing - # DMCompleteBCLabels_Internal to fail with MPI errors. - from underworld3.cython.petsc_maths import dm_force_coordinate_field - dm_force_coordinate_field(self.dm) + # Issue #96 fix: Force coordinate field creation and strip + # boundary labels from the coordinate DM. createCoordinateSpace + # clears the coordinate field cache. Without this, BdIntegral + # lazily recreates the field by cloning mesh.dm (with boundary + # labels), causing DMCompleteBCLabels_Internal MPI errors. + from underworld3.cython.petsc_maths import dm_force_coordinate_field + dm_force_coordinate_field(self.dm) + elif PETSc.Sys.getVersion() >= (3, 24, 0): + self.dm.setCoordinateDisc(disc=self.petsc_fe, localized=False, project=False) + else: + self.dm.setCoordinateDisc(disc=self.petsc_fe, project=False) if verbose and uw.mpi.rank == 0: print( From 53e2c85392b256f22f6267b7ff2819831d57b752 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Thu, 16 Apr 2026 00:33:57 -0700 Subject: [PATCH 093/537] Fix global_evaluate parallel hang and shape mismatch (#113) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Three related issues fixed: 1. Parallel hang in evaluate_nd: petsc_interpolate had early returns for empty coords that skipped DMLocatePoints — a collective PETSc operation. When some ranks had zero interior points (all OOB), they returned early while others blocked in the collective. Fixed by removing the early returns and ensuring all ranks participate in DMLocatePoints, even with zero points. 2. Shape mismatch in global_evaluate_nd: return arrays were sized to the post-migration particle count rather than the original input count. Pre-allocate with NaN so the shape is always correct regardless of whether points survive the migration round-trip. 3. points_in_domain misclassifying extreme OOB points: the boundary control-point sign heuristic has no distance ceiling, so points at (1e12, 1e12) could be classified as "interior". Added a domain radius check to reject points far beyond the domain extent. Also set ignoreOutsideDomain=True in DMInterpolationSetUp_UW so PETSc silently skips unlocatable points rather than crashing. Underworld development team with AI support from Claude Code --- .../discretisation/discretisation_mesh.py | 18 ++++++- .../function/_dminterp_wrapper.pyx | 33 ++++++++----- src/underworld3/function/_function.pyx | 49 ++++++++++--------- 3 files changed, 63 insertions(+), 37 deletions(-) diff --git a/src/underworld3/discretisation/discretisation_mesh.py b/src/underworld3/discretisation/discretisation_mesh.py index 132ba7b9d..b22f1cffc 100644 --- a/src/underworld3/discretisation/discretisation_mesh.py +++ b/src/underworld3/discretisation/discretisation_mesh.py @@ -2568,12 +2568,20 @@ def _mark_local_boundary_faces_inside_and_out(self): control_points_list.append(inside_control_point) control_point_sign_list.append(1) - control_point_kdtree = uw.kdtree.KDTree(numpy.array(control_points_list)) + control_points_array = numpy.array(control_points_list) + control_point_kdtree = uw.kdtree.KDTree(control_points_array) control_point_sign = numpy.array(control_point_sign_list) self.boundary_face_control_points_kdtree = control_point_kdtree self.boundary_face_control_points_sign = control_point_sign + # Domain bounding radius (squared): distance from centroid to farthest + # control point. Points beyond this distance from their nearest control + # point cannot be inside the domain. + domain_centroid = control_points_array.mean(axis=0) + radii_sq = numpy.sum((control_points_array - domain_centroid) ** 2, axis=1) + self._domain_radius_squared = float(radii_sq.max()) + return def points_in_domain(self, points, strict_validation=True): @@ -2611,10 +2619,16 @@ def points_in_domain(self, points, strict_validation=True): dist2, closest_control_points_ext = self.boundary_face_control_points_kdtree.query( model_points, k=1, sqr_dists=True ) + dist2 = numpy.asarray(dist2).ravel() # kd-tree returns (n,1) for k=1 in_or_not = self.boundary_face_control_points_sign[closest_control_points_ext] > 0 - ## This choice of distance needs some more thought + # Points very far from the nearest boundary face are definitely exterior. + # The sign heuristic only works for points within the domain's neighbourhood; + # beyond that, "nearest control point" is arbitrary. + far_from_domain = dist2 > self._domain_radius_squared + in_or_not[far_from_domain] = False + # Points close to the boundary need the expensive cell-location check near_boundary = numpy.where(dist2 < 2 * max_radius**2)[0] near_boundary_points = model_points[near_boundary] diff --git a/src/underworld3/function/_dminterp_wrapper.pyx b/src/underworld3/function/_dminterp_wrapper.pyx index 39d85cc8f..0423c7513 100644 --- a/src/underworld3/function/_dminterp_wrapper.pyx +++ b/src/underworld3/function/_dminterp_wrapper.pyx @@ -121,21 +121,30 @@ cdef class CachedDMInterpolationInfo: DMInterpolationDestroy(&self._ipInfo) raise RuntimeError(f"DMInterpolationSetDof failed with error {ierr}") - # Add interpolation points - use contiguous array's data pointer - cdef double[:, ::1] coords_view = np.ascontiguousarray(self.coords) - ierr = DMInterpolationAddPoints(self._ipInfo, n_points, &coords_view[0, 0]) - if ierr != 0: - DMInterpolationDestroy(&self._ipInfo) - raise RuntimeError(f"DMInterpolationAddPoints failed with error {ierr}") - - # Set up with cell hints - # Extract PETSc DM from mesh + # Declare typed memoryviews at function scope (Cython requirement) + cdef double[:, ::1] coords_view + cdef long[::1] cells_view cdef DM dm_obj = mesh.dm cdef PetscDM dm = dm_obj.dm - # Extract cell hints as size_t array - cdef long[::1] cells_view = np.ascontiguousarray(self.cells) - ierr = DMInterpolationSetUp_UW(self._ipInfo, dm, 0, 0, &cells_view[0]) + # Add interpolation points (guard against empty arrays) + if n_points > 0: + coords_view = np.ascontiguousarray(self.coords) + ierr = DMInterpolationAddPoints(self._ipInfo, n_points, &coords_view[0, 0]) + if ierr != 0: + DMInterpolationDestroy(&self._ipInfo) + raise RuntimeError(f"DMInterpolationAddPoints failed with error {ierr}") + + # Set up — calls DMLocatePoints which is COLLECTIVE on the mesh DM. + # All ranks must call this, even with zero local points. + # ignoreOutsideDomain=1: PETSc silently skips points it cannot locate + # rather than crashing. This is essential — points_in_domain() uses a + # kd-tree heuristic that can misclassify distant points as interior. + if n_points > 0: + cells_view = np.ascontiguousarray(self.cells) + ierr = DMInterpolationSetUp_UW(self._ipInfo, dm, 0, 1, &cells_view[0]) + else: + ierr = DMInterpolationSetUp_UW(self._ipInfo, dm, 0, 1, NULL) if ierr != 0: DMInterpolationDestroy(&self._ipInfo) raise RuntimeError(f"DMInterpolationSetUp_UW failed with error {ierr}") diff --git a/src/underworld3/function/_function.pyx b/src/underworld3/function/_function.pyx index 98f218e3b..3afd00602 100644 --- a/src/underworld3/function/_function.pyx +++ b/src/underworld3/function/_function.pyx @@ -484,6 +484,7 @@ def global_evaluate_nd( expr, index = original_index.array[:,0,0] ranks = original_rank.array[:,0,0] + n_input_points = coords_array.shape[0] evaluation_swarm.migrate(remove_sent_points=True, delete_lost_points=False) local_coords = evaluation_swarm._particle_coordinates.array[...].reshape(-1,evaluation_swarm.dim) @@ -509,13 +510,17 @@ def global_evaluate_nd( expr, if hasattr(var, "_canonical_data"): var._canonical_data = None - index = original_index.array[:,0,0] - - return_value = np.empty_like(data_container.array[...]) - return_value[index,:,:] = data_container.array[:,:,:] + # Pre-allocate with NaN so the shape is always correct. If any points + # are lost during the migration round-trip, they remain NaN rather than + # causing a shape mismatch or returning uninitialised data. + return_value = np.full((n_input_points,) + expr_shape, np.nan, dtype=np.double) + return_mask = np.full((n_input_points, 1, 1), True, dtype=bool) - return_mask = np.empty_like(is_extrapolated.array[...], dtype=bool) - return_mask[index] = is_extrapolated.array[:] + n_returned = original_index.array.shape[0] + if n_returned > 0: + index = original_index.array[:, 0, 0].astype(int) + return_value[index, :, :] = data_container.array[:, :, :] + return_mask[index] = is_extrapolated.array[:] if not check_extrapolated: return return_value @@ -845,6 +850,12 @@ def evaluate_nd( expr, ) else: + # CRITICAL: update_lvec() calls dm.globalToLocal() which is COLLECTIVE. + # It MUST be called by ALL ranks before any rank enters petsc_interpolate, + # because ranks with zero interior points would skip petsc_interpolate + # (and its internal update_lvec call), deadlocking the ranks that do enter. + mesh.update_lvec() + in_or_not = mesh.points_in_domain(coords_array, strict_validation=False) evaluation_interior = petsc_interpolate( expr, coords_array[in_or_not], @@ -985,18 +996,11 @@ def petsc_interpolate( expr, if other_arguments: raise RuntimeError("`other_arguments` functionality not yet implemented.") - # Early return for empty coordinate arrays (SECOND CHECK - top-level function) - # CRITICAL: Avoid lambdify errors with LaTeX variable names when coords is empty - # This handles cases where empty arrays pass through from evaluate_nd - if len(coords) == 0: - # Determine output shape based on expression type - try: - expr_shape = expr.shape - # Return empty array with correct shape: (0, rows, cols) - return np.empty([0] + list(expr_shape), dtype=np.double) - except AttributeError: - # Scalar expression - return (0,) shaped array - return np.empty([0], dtype=np.double) + # NOTE: Do NOT early-return for empty coords here. petsc_interpolate + # calls DMLocatePoints which is COLLECTIVE on the mesh DM communicator. + # If some ranks skip it (empty coords) while others enter it, MPI deadlocks. + # Empty coords are handled inside interpolate_vars_on_mesh after the + # collective operations complete. ## Substitute any UWExpressions for their values before calculation ## NOTE: We use _unwrap_expressions directly (not fn_substitute_expressions) to avoid @@ -1094,11 +1098,9 @@ def petsc_interpolate( expr, # Make coords contiguous for caching and C access coords = np.ascontiguousarray(coords) - # Early return for empty coordinate arrays - # CRITICAL: Avoid DMInterpolation setup with zero points - if len(coords) == 0: - # Return empty array with correct shape: (0, dofcount) - return np.empty([0, dofcount], dtype=np.double) + # NOTE: No early return for empty coords here. DMLocatePoints + # (inside DMInterpolationSetUp_UW) is COLLECTIVE on the mesh DM + # communicator. All ranks must participate, even with zero points. # === DMInterpolation CACHING === # Declare variables at function scope (Cython requirement) @@ -1127,6 +1129,7 @@ def petsc_interpolate( expr, cells = mesh.get_closest_cells(coords) # Create and set up DMInterpolation structure (EXPENSIVE) + # This calls DMLocatePoints which is COLLECTIVE — all ranks must enter. try: # coords is already np.ndarray type (function signature ensures this) cached_info.create_structure(mesh, coords, cells, dofcount) From cc96d68a7a5a3d465e33b348176f66205690e341 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Thu, 16 Apr 2026 07:54:55 -0700 Subject: [PATCH 094/537] Add geographic return_coords_to_bounds and guard empty-particle case - RegionalGeographicBox now has lateral + radial coordinate clamping via cartesian_to_geographic / geographic_to_cartesian round-trip. Upstream points that escape the domain are clamped to the mesh's lon/lat/depth ranges before evaluation. - Guard empty-particle assignment in global_evaluate_nd: when a rank has zero particles after migration, skip the swarm variable assignment that fails on reshape of empty arrays. Underworld development team with AI support from Claude Code --- src/underworld3/function/_function.pyx | 5 ++- src/underworld3/meshing/geographic.py | 52 ++++++++++++++++++-------- 2 files changed, 40 insertions(+), 17 deletions(-) diff --git a/src/underworld3/function/_function.pyx b/src/underworld3/function/_function.pyx index 3afd00602..3d550ef94 100644 --- a/src/underworld3/function/_function.pyx +++ b/src/underworld3/function/_function.pyx @@ -490,8 +490,9 @@ def global_evaluate_nd( expr, local_coords = evaluation_swarm._particle_coordinates.array[...].reshape(-1,evaluation_swarm.dim) values, extrapolated = evaluate_nd(expr, local_coords, rbf=rbf, evalf=evalf, verbose=verbose, check_extrapolated=True,) - data_container.array[...] = values[...] - is_extrapolated.array[:,0,0] = extrapolated[:] + if local_coords.shape[0] > 0: + data_container.array[...] = values[...] + is_extrapolated.array[:,0,0] = extrapolated[:] # set rank to old values and migrate back evaluation_swarm._rank_var.array[...] = original_rank.array[...] diff --git a/src/underworld3/meshing/geographic.py b/src/underworld3/meshing/geographic.py index 77836e94c..70e157ecf 100644 --- a/src/underworld3/meshing/geographic.py +++ b/src/underworld3/meshing/geographic.py @@ -329,21 +329,6 @@ class boundaries(Enum): gmsh.write(uw_filename) gmsh.finalize() - ## This needs a side-boundary capture routine as well - - def sphere_return_coords_to_bounds(coords): - Rsq = coords[:, 0] ** 2 + coords[:, 1] ** 2 + coords[:, 2] ** 2 - - outside = Rsq > radiusOuter**2 - inside = Rsq < radiusInner**2 - - ## Note these numbers should not be hard-wired - - coords[outside, :] *= 0.99 * radiusOuter / np.sqrt(Rsq[outside].reshape(-1, 1)) - coords[inside, :] *= 1.01 * radiusInner / np.sqrt(Rsq[inside].reshape(-1, 1)) - - return coords - def spherical_mesh_refinement_callback(dm): r_o = radiusOuter r_i = radiusInner @@ -789,6 +774,42 @@ class boundaries(Enum): gmsh.write(uw_filename) gmsh.finalize() + def geographic_return_coords_to_bounds(coords): + """Clamp Cartesian coordinates to the geographic domain bounds. + + Converts to geographic (lon, lat, depth), clamps each to the + mesh's known ranges, and converts back to Cartesian. Small + overshoot due to topography or mesh curvature is handled + gracefully by the interior/exterior split in evaluate_nd. + + Coords must be in the mesh's internal coordinate system + (nondimensional if scaling is active, km otherwise). + """ + from underworld3.coordinates import cartesian_to_geographic + + # Work with raw numpy float arrays — coords may be UnitAwareArray + raw = np.asarray(coords, dtype=np.float64) + + lon, lat, depth = cartesian_to_geographic( + raw[:, 0], raw[:, 1], raw[:, 2], float(a), float(b) + ) + + # Ensure plain float arrays for clip + lon = np.asarray(lon, dtype=np.float64) + lat = np.asarray(lat, dtype=np.float64) + depth = np.asarray(depth, dtype=np.float64) + + np.clip(lon, lon_min, lon_max, out=lon) + np.clip(lat, lat_min, lat_max, out=lat) + np.clip(depth, float(depth_min) * 1.01, float(depth_max) * 0.99, out=depth) + + x, y, z = geographic_to_cartesian(lon, lat, depth, a, b) + coords[:, 0] = x + coords[:, 1] = y + coords[:, 2] = z + + return coords + # Load mesh on all ranks new_mesh = Mesh( uw_filename, @@ -802,6 +823,7 @@ class boundaries(Enum): refinement=refinement, coarsening=coarsening, coordinate_system_type=CoordinateSystemType.GEOGRAPHIC, + return_coords_to_bounds=geographic_return_coords_to_bounds, verbose=verbose, ) From 246a33cf2060d5cf692441a8e884ac99f7d0e87d Mon Sep 17 00:00:00 2001 From: lmoresi Date: Fri, 17 Apr 2026 09:43:47 -0700 Subject: [PATCH 095/537] Add PETSc version switching: versioned arch names and ./uw petsc command MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit PETSc arch names now encode the version: petsc-324-uw-openmpi instead of petsc-4-uw-openmpi. Multiple PETSc versions can coexist under the same PETSC_DIR, each with its own arch directory. Switching versions is: ./uw petsc switch v3.25.0 # checkout tag, set active version ./uw petsc build # build PETSc (if not already built) ./uw build # rebuild petsc4py + UW3 The active version is stored in petsc-custom/.petsc-version (gitignored). Legacy unversioned arch directories (petsc-4-uw-*) are detected and used as fallback when no versioned build exists. New commands: ./uw petsc versions — list available builds ./uw petsc switch — checkout a version tag ./uw petsc active — show active version and arch ./uw petsc build — build PETSc for the active version Underworld development team with AI support from Claude Code --- .gitignore | 1 + petsc-custom/build-petsc.sh | 148 ++++++++++++++++++++++++++++++++---- uw | 90 ++++++++++++++++++++-- 3 files changed, 215 insertions(+), 24 deletions(-) diff --git a/.gitignore b/.gitignore index 8c632ef74..7e9621773 100644 --- a/.gitignore +++ b/.gitignore @@ -255,4 +255,5 @@ docs/beginner/tutorials/html5/*.html .pixi-env # PETSc build (directory in main repo, symlink in worktrees) petsc-custom/petsc +petsc-custom/.petsc-version Untitled*.ipynb diff --git a/petsc-custom/build-petsc.sh b/petsc-custom/build-petsc.sh index 63d816297..0ab5367b9 100755 --- a/petsc-custom/build-petsc.sh +++ b/petsc-custom/build-petsc.sh @@ -37,6 +37,29 @@ set -e SCRIPT_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)" PETSC_DIR="${SCRIPT_DIR}/petsc" +VERSION_FILE="${SCRIPT_DIR}/.petsc-version" + +# ── PETSc version detection ────────────────────────────────────────────────── +# Read version from .petsc-version file, or detect from the git checkout. +# Returns short form like "324" for v3.24.x or "325" for v3.25.x. + +petsc_version_short() { + local ver="" + if [ -f "${VERSION_FILE}" ]; then + ver=$(cat "${VERSION_FILE}" | tr -d '[:space:]') + fi + if [ -z "${ver}" ] && [ -d "${PETSC_DIR}/.git" ]; then + # Detect from git tag: v3.24.2 → 324 + local tag + tag=$(cd "${PETSC_DIR}" && git describe --tags --abbrev=0 2>/dev/null || echo "") + if [ -n "${tag}" ]; then + ver=$(echo "${tag}" | sed -E 's/^v([0-9]+)\.([0-9]+).*/\1\2/') + fi + fi + echo "${ver:-324}" # default to 324 if detection fails +} + +PETSC_VER=$(petsc_version_short) # ── Cluster detection ───────────────────────────────────────────────────────── detect_cluster() { @@ -91,7 +114,7 @@ EOF } MPI_IMPL=$(_detect_local_mpi) - PETSC_ARCH="petsc-4-uw-${MPI_IMPL}" + PETSC_ARCH="petsc-${PETSC_VER}-uw-${MPI_IMPL}" ;; kaiju) @@ -107,7 +130,7 @@ EOF fi MPI_DIR="$(dirname "$(dirname "$(which mpicc)")")" MPI_IMPL="openmpi" - PETSC_ARCH="petsc-4-uw-openmpi" + PETSC_ARCH="petsc-${PETSC_VER}-uw-openmpi" ;; gadi) @@ -128,7 +151,7 @@ EOF fi MPI_DIR="$(dirname "$(dirname "$(which mpicc)")")" MPI_IMPL="openmpi" - PETSC_ARCH="petsc-4-uw-openmpi" + PETSC_ARCH="petsc-${PETSC_VER}-uw-openmpi" ;; *) @@ -387,27 +410,118 @@ clean_all() { fi } +checkout_version() { + # Checkout a specific PETSc version tag and update .petsc-version + local tag="$1" + if [ -z "${tag}" ]; then + echo "Usage: $0 checkout " + echo " e.g.: $0 checkout v3.25.0" + echo "" + echo "Available tags:" + cd "${PETSC_DIR}" && git tag --list 'v3.2[0-9]*' | sort -V | tail -10 + exit 1 + fi + + cd "${PETSC_DIR}" + + # Fetch latest tags + git fetch --tags 2>/dev/null + + if ! git rev-parse "${tag}" &>/dev/null; then + echo "Error: tag '${tag}' not found." + echo "Available tags:" + git tag --list 'v3.2[0-9]*' | sort -V | tail -10 + exit 1 + fi + + echo "Checking out PETSc ${tag}..." + git checkout "${tag}" + + # Update .petsc-version file + local ver_short + ver_short=$(echo "${tag}" | sed -E 's/^v([0-9]+)\.([0-9]+).*/\1\2/') + echo "${ver_short}" > "${VERSION_FILE}" + echo "Active PETSc version: ${ver_short} (${tag})" + echo " Stored in: ${VERSION_FILE}" + + # Check if a build exists for this version + local new_arch="petsc-${ver_short}-uw-${MPI_IMPL}" + if [ -d "${PETSC_DIR}/${new_arch}/lib" ]; then + echo " Existing build found: ${new_arch}" + echo " Run: ./uw build (to rebuild petsc4py + UW3)" + else + echo " No build for ${new_arch} yet." + echo " Run: pixi run -e ./petsc-custom/build-petsc.sh" + fi +} + +list_versions() { + echo "PETSc version builds:" + echo "" + local active_ver + active_ver=$(petsc_version_short) + for arch_dir in "${PETSC_DIR}"/petsc-*-uw-*/; do + [ -d "${arch_dir}" ] || continue + local arch_name=$(basename "${arch_dir}") + local marker="" + local style="" + + # Classify: versioned (petsc-324-uw-*) vs legacy (petsc-4-uw-*) + if echo "${arch_name}" | grep -qE '^petsc-[0-9]{3,}-uw-'; then + # Versioned arch: petsc-324-uw-openmpi → 324 + local arch_ver=$(echo "${arch_name}" | sed -E 's/^petsc-([0-9]+)-uw-.*/\1/') + if [ "${arch_ver}" = "${active_ver}" ]; then + marker=" (active)" + fi + else + style=" [legacy]" + fi + + local has_lib="" + if [ -f "${arch_dir}/lib/libpetsc.dylib" ] || [ -f "${arch_dir}/lib/libpetsc.so" ]; then + has_lib=" [built]" + else + has_lib=" [incomplete]" + fi + echo " ${arch_name}${has_lib}${style}${marker}" + done + echo "" + if [ -d "${PETSC_DIR}/.git" ]; then + local tag + tag=$(cd "${PETSC_DIR}" && git describe --tags --abbrev=0 2>/dev/null || echo "unknown") + echo "Source checkout: ${tag}" + fi + echo "Active version: ${active_ver} (from ${VERSION_FILE})" +} + show_help() { echo "Usage: $0 [command]" echo "" echo "Cluster: ${CLUSTER} (override: export UW_CLUSTER=local|kaiju|gadi)" - echo "PETSC_ARCH: ${PETSC_ARCH}" + echo "PETSC_ARCH: ${PETSC_ARCH} (version: ${PETSC_VER})" echo "" echo "Commands:" - echo " (none) Full build: clone, patch, configure, build" - [ "${CLUSTER}" = "local" ] && echo " (local: also runs petsc4py separately)" - echo " clone Clone PETSc repository" - echo " patch Apply UW3 patches to PETSc source" - echo " configure Configure PETSc with AMR tools" - echo " build Build PETSc" - echo " test Run PETSc tests" - echo " petsc4py Build and install petsc4py (local only)" - echo " clean Remove build for current arch (${PETSC_ARCH})" - echo " clean-all Remove entire PETSc directory (all builds)" - echo " help Show this help" + echo " (none) Full build: clone, patch, configure, build" + [ "${CLUSTER}" = "local" ] && echo " (local: also runs petsc4py separately)" + echo " clone Clone PETSc repository" + echo " checkout V Checkout PETSc version tag (e.g. v3.25.0) and set active" + echo " patch Apply UW3 patches to PETSc source" + echo " configure Configure PETSc with AMR tools" + echo " build Build PETSc" + echo " test Run PETSc tests" + echo " petsc4py Build and install petsc4py (local only)" + echo " versions List available PETSc builds" + echo " clean Remove build for current arch (${PETSC_ARCH})" + echo " clean-all Remove entire PETSc directory (all builds)" + echo " help Show this help" if [ "${CLUSTER}" = "local" ]; then echo "" - echo "MPICH and OpenMPI builds co-exist. To build both:" + echo "Version switching:" + echo " $0 checkout v3.25.0 # switch source to 3.25.0" + echo " $0 # build (creates petsc-325-uw-openmpi)" + echo " $0 checkout v3.24.2 # switch back (existing build reused)" + echo "" + echo "MPI variants co-exist. To build both:" echo " pixi run -e amr ./petsc-custom/build-petsc.sh" echo " pixi run -e amr-openmpi ./petsc-custom/build-petsc.sh" fi @@ -434,11 +548,13 @@ case "${1:-all}" in echo "==========================================" ;; clone) clone_petsc ;; + checkout) checkout_version "$2" ;; patch) apply_patches ;; configure) configure_petsc ;; build) build_petsc ;; test) test_petsc ;; petsc4py) build_petsc4py ;; + versions) list_versions ;; clean) clean_petsc ;; clean-all) clean_all ;; help|--help|-h) show_help ;; diff --git a/uw b/uw index f1c4dc070..30ecd0ee0 100755 --- a/uw +++ b/uw @@ -42,24 +42,57 @@ get_env() { fi } +petsc_version_short() { + # Read active PETSc version from .petsc-version, or detect from checkout. + local ver_file="$SCRIPT_DIR/petsc-custom/.petsc-version" + if [ -f "$ver_file" ]; then + cat "$ver_file" | tr -d '[:space:]' + return + fi + # Detect from git tag + if [ -d "$PETSC_CUSTOM/.git" ]; then + local tag + tag=$(cd "$PETSC_CUSTOM" && git describe --tags --abbrev=0 2>/dev/null || echo "") + if [ -n "$tag" ]; then + echo "$tag" | sed -E 's/^v([0-9]+)\.([0-9]+).*/\1\2/' + return + fi + fi + echo "324" # default +} + petsc_arch_for_env() { - # Derive the PETSC_ARCH from the environment name. - # Primary AMR envs (amr, amr-runtime, amr-dev) use platform-default MPI. - # Override envs (amr-mpich*, amr-openmpi*) force a specific MPI. + # Derive the PETSC_ARCH from the environment name and active PETSc version. + # Format: petsc-{version}-uw-{mpi} (e.g. petsc-324-uw-openmpi) local env="$1" + local ver=$(petsc_version_short) + local mpi="" + case "$env" in - amr-mpich*) echo "petsc-4-uw-mpich" ;; - amr-openmpi*) echo "petsc-4-uw-openmpi" ;; + amr-mpich*) mpi="mpich" ;; + amr-openmpi*) mpi="openmpi" ;; amr*) # Platform-default MPI if [[ "$(uname -s)" == "Darwin" ]]; then - echo "petsc-4-uw-openmpi" + mpi="openmpi" else - echo "petsc-4-uw-mpich" + mpi="mpich" fi ;; - *) echo "" ;; # conda-forge, no custom PETSc + *) echo ""; return ;; # conda-forge, no custom PETSc esac + + # Check for versioned arch first, fall back to legacy unversioned + local versioned="petsc-${ver}-uw-${mpi}" + local legacy="petsc-4-uw-${mpi}" + if [ -d "$PETSC_CUSTOM/${versioned}" ]; then + echo "${versioned}" + elif [ -d "$PETSC_CUSTOM/${legacy}" ]; then + echo "${legacy}" + else + # No build exists yet — return the versioned name for new builds + echo "${versioned}" + fi } petsc_built() { @@ -221,6 +254,43 @@ run_build() { echo " ./uw doctor (check configuration)" } +run_petsc_cmd() { + local petsc_cmd="${1:-versions}" + local arg="$2" + case "$petsc_cmd" in + versions|list) + $PIXI run -e "$(get_env)" "$SCRIPT_DIR/petsc-custom/build-petsc.sh" versions + ;; + switch) + if [ -z "$arg" ]; then + echo "Usage: ./uw petsc switch " + echo " e.g.: ./uw petsc switch v3.25.0" + exit 1 + fi + $PIXI run -e "$(get_env)" "$SCRIPT_DIR/petsc-custom/build-petsc.sh" checkout "$arg" + echo "" + echo "To complete the switch, rebuild:" + echo " ./uw build" + ;; + active) + local ver=$(petsc_version_short) + local arch=$(petsc_arch_for_env "$(get_env)") + echo "Active PETSc: ${ver} (arch: ${arch})" + ;; + build) + $PIXI run -e "$(get_env)" "$SCRIPT_DIR/petsc-custom/build-petsc.sh" + ;; + *) + echo "Usage: ./uw petsc [versions|switch |active|build]" + echo "" + echo " versions List available PETSc builds" + echo " switch Checkout a PETSc version (e.g. v3.25.0)" + echo " active Show active PETSc version and arch" + echo " build Build PETSc for the active version" + ;; + esac +} + # Standalone diagnostics (works even if underworld3 not built) run_doctor() { local env=$(get_env) @@ -1458,6 +1528,10 @@ case "${1:-}" in rm -f "$SCRIPT_DIR/build/.petsc_target" echo -e "${GREEN}Done${NC}. Run './uw build' to rebuild." ;; + petsc) + # PETSc version management: ./uw petsc [versions|switch|active] + run_petsc_cmd "$2" "$3" + ;; doctor) run_doctor ;; From 499f8132c03efc98112e42949925f45b969f3cb0 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Fri, 17 Apr 2026 12:30:58 -0700 Subject: [PATCH 096/537] Make pixi.toml static; derive PETSC_ARCH via activation script Previously ./uw petsc switch rewrote PETSC_ARCH values in pixi.toml via sed, which (1) made every switch a tracked file change, (2) forced contributors on different PETSc versions to carry diverging pixi.toml in their working tree, and (3) did not reliably propagate to pixi's activated environment because pixi caches resolved state. Replace the five hardcoded PETSC_ARCH = "petsc-*-uw-*" entries (in features amr [osx-arm64 and linux-64], amr-mpich, amr-openmpi, and amr-debug) with per-feature activation scripts that source the new petsc-custom/activate-petsc-arch.sh. The script reads the active version from petsc-custom/.petsc-version and combines it with the active $PIXI_ENVIRONMENT_NAME (and uname on Darwin/Linux for the plain amr env) to construct PETSC_ARCH = petsc-{ver}-uw-{mpi}{suffix}. Non-AMR environments match no case and leave PETSC_ARCH unset, so the script is safe as a no-op for default/runtime/dev/mpich/openmpi environments. Switching PETSc versions now only updates .petsc-version (one untracked, gitignored file); pixi.toml is not modified. Underworld development team with AI support from Claude Code --- petsc-custom/activate-petsc-arch.sh | 33 +++++++++++++++++++++++++++++ pixi.toml | 21 ++++++++++-------- 2 files changed, 45 insertions(+), 9 deletions(-) create mode 100755 petsc-custom/activate-petsc-arch.sh diff --git a/petsc-custom/activate-petsc-arch.sh b/petsc-custom/activate-petsc-arch.sh new file mode 100755 index 000000000..61d0afe6d --- /dev/null +++ b/petsc-custom/activate-petsc-arch.sh @@ -0,0 +1,33 @@ +#!/usr/bin/env bash +# activate-petsc-arch.sh — sourced by pixi on environment activation. +# +# Dynamically sets PETSC_ARCH for AMR environments (custom PETSc builds) +# by combining the active pixi environment name with the PETSc version +# pinned in petsc-custom/.petsc-version. +# +# This replaces hardcoded PETSC_ARCH entries in pixi.toml so that +# switching PETSc versions (via ./uw petsc switch ) does not require +# editing tracked configuration. + +_uw_mpi="" +_uw_suffix="" +case "${PIXI_ENVIRONMENT_NAME:-}" in + amr|amr-runtime|amr-dev) + case "$(uname -s)" in + Darwin) _uw_mpi="openmpi" ;; + *) _uw_mpi="mpich" ;; + esac ;; + amr-mpich|amr-mpich-dev) _uw_mpi="mpich" ;; + amr-openmpi|amr-openmpi-dev) _uw_mpi="openmpi" ;; + amr-debug) _uw_mpi="openmpi"; _uw_suffix="-debug" ;; +esac + +if [ -n "$_uw_mpi" ]; then + _uw_ver="4" + _uw_ver_file="${PIXI_PROJECT_ROOT:-.}/petsc-custom/.petsc-version" + [ -f "$_uw_ver_file" ] && _uw_ver=$(cat "$_uw_ver_file" 2>/dev/null || echo "4") + + export PETSC_ARCH="petsc-${_uw_ver}-uw-${_uw_mpi}${_uw_suffix}" +fi + +unset _uw_mpi _uw_suffix _uw_ver _uw_ver_file diff --git a/pixi.toml b/pixi.toml index e72f7f827..b8d6796cc 100644 --- a/pixi.toml +++ b/pixi.toml @@ -165,6 +165,9 @@ cmake = ">=3.31,<4" make = ">=4.4,<5" mpi4py = ">=4,<5" +[feature.amr.activation] +scripts = ["petsc-custom/activate-petsc-arch.sh"] + [feature.amr.activation.env] PETSC_DIR = "$PIXI_PROJECT_ROOT/petsc-custom/petsc" @@ -173,16 +176,10 @@ openmpi = ">=5.0,<6" hdf5 = { version = ">=1.14,<2", build = "*openmpi*" } h5py = { version = ">=3.12,<4", build = "*openmpi*" } -[feature.amr.target.osx-arm64.activation.env] -PETSC_ARCH = "petsc-4-uw-openmpi" - [feature.amr.target.linux-64.dependencies] hdf5 = { version = ">=1.14,<2", build = "*mpich*" } h5py = { version = ">=3.12,<4", build = "*mpich*" } -[feature.amr.target.linux-64.activation.env] -PETSC_ARCH = "petsc-4-uw-mpich" - [feature.amr.tasks] petsc-local-build = { cmd = "./build-petsc.sh", cwd = "petsc-custom" } petsc-local-clean = { cmd = "./build-petsc.sh clean", cwd = "petsc-custom" } @@ -202,9 +199,11 @@ mpi4py = ">=4,<5" hdf5 = { version = ">=1.14,<2", build = "*mpich*" } h5py = { version = ">=3.12,<4", build = "*mpich*" } +[feature.amr-mpich.activation] +scripts = ["petsc-custom/activate-petsc-arch.sh"] + [feature.amr-mpich.activation.env] PETSC_DIR = "$PIXI_PROJECT_ROOT/petsc-custom/petsc" -PETSC_ARCH = "petsc-4-uw-mpich" [feature.amr-mpich.tasks] petsc-local-build = { cmd = "./build-petsc.sh", cwd = "petsc-custom" } @@ -221,9 +220,11 @@ mpi4py = ">=4,<5" hdf5 = { version = ">=1.14,<2", build = "*openmpi*" } h5py = { version = ">=3.12,<4", build = "*openmpi*" } +[feature.amr-openmpi.activation] +scripts = ["petsc-custom/activate-petsc-arch.sh"] + [feature.amr-openmpi.activation.env] PETSC_DIR = "$PIXI_PROJECT_ROOT/petsc-custom/petsc" -PETSC_ARCH = "petsc-4-uw-openmpi" [feature.amr-openmpi.tasks] petsc-local-build = { cmd = "./build-petsc.sh", cwd = "petsc-custom" } @@ -246,9 +247,11 @@ petsc-local-clean = { cmd = "./build-petsc.sh clean", cwd = "petsc-custom" } # "--COPTFLAGS=-g -O0" "--CXXOPTFLAGS=-g -O0" "--FOPTFLAGS=-g -O0" # make PETSC_DIR=$(pwd) PETSC_ARCH=petsc-4-uw-openmpi-debug all +[feature.amr-debug.activation] +scripts = ["petsc-custom/activate-petsc-arch.sh"] + [feature.amr-debug.activation.env] PETSC_DIR = "$PIXI_PROJECT_ROOT/petsc-custom/petsc" -PETSC_ARCH = "petsc-4-uw-openmpi-debug" # ============================================ # HPC CLUSTER FEATURE From 9b7c359a6dab42c8f05134245184733bd2bf3b43 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Fri, 17 Apr 2026 12:31:05 -0700 Subject: [PATCH 097/537] Nuke stale build artifacts and petsc4py on ./uw petsc switch ./uw build has target-change detection (build/.petsc_target) that cleans build/lib.* when petsc4py.get_config() reports a new arch. After ./uw petsc switch, though, the still-installed petsc4py is linked to the OLD arch and continues to report it, so the check does not fire and pip/Cython silently reuse stale wheels against the new PETSc. Force the full rebuild path at switch time: remove build/lib.*, build/temp.*, build/bdist.*, the .petsc_target marker, purge pip's wheel cache, and uninstall petsc4py (AMR envs only). The next ./uw build then rebuilds petsc4py against the new PETSc and recompiles every Cython extension. Underworld development team with AI support from Claude Code --- uw | 17 ++++++++++++++++- 1 file changed, 16 insertions(+), 1 deletion(-) diff --git a/uw b/uw index 42bcb2247..d94c5f192 100755 --- a/uw +++ b/uw @@ -293,8 +293,23 @@ run_petsc_cmd() { exit 1 fi $PIXI run -e "$(get_env)" "$SCRIPT_DIR/petsc-custom/build-petsc.sh" checkout "$arg" + + # Nuke stale build artifacts and petsc4py. The next ./uw build's + # target-change detection can't fire because the still-installed + # petsc4py reports the OLD arch, so we force a full rebuild here. + echo "" + echo "Clearing stale build artifacts for clean rebuild..." + rm -rf "$SCRIPT_DIR"/build/lib.* "$SCRIPT_DIR"/build/temp.* "$SCRIPT_DIR"/build/bdist.* 2>/dev/null + rm -f "$SCRIPT_DIR/build/.petsc_target" + $PIXI run -e "$(get_env)" pip cache purge 2>/dev/null || true + if is_amr_env "$(get_env)"; then + echo "Uninstalling old petsc4py (linked to previous PETSc build)..." + $PIXI run -e "$(get_env)" pip uninstall -y petsc4py 2>/dev/null || true + fi + echo "" - echo "To complete the switch, rebuild:" + echo "To complete the switch, rebuild PETSc then underworld3:" + echo " ./uw petsc build" echo " ./uw build" ;; active) From 61675b59e856d3fe5fe40b1a50549a355021efec Mon Sep 17 00:00:00 2001 From: lmoresi Date: Fri, 17 Apr 2026 13:16:54 -0700 Subject: [PATCH 098/537] setup.py: prefer PETSC_DIR/PETSC_ARCH env vars over petsc4py.get_config() MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit When pixi activation exports PETSC_DIR and PETSC_ARCH for a custom build, setup.py was ignoring them and reading petsc4py.get_config() instead. That reports the arch petsc4py was BUILT against — so immediately after a PETSc version switch, setup.py would silently link the rebuild against the previous PETSc, not the new one. Re-order the PETSc discovery into an explicit priority chain: 1. PETSC_DIR / PETSC_ARCH from the environment (pixi activation, shell export, HPC module load) 2. petsc4py.get_config() — authoritative match for installed petsc4py 3. conda `petsc` pip package 4. CONDA_PREFIX/lib/.../site-packages/petsc fallback The previous code only consulted env vars as a last-resort branch of the conda fallback, which was exactly backwards — env vars are the most specific signal and should win. Underworld development team with AI support from Claude Code --- setup.py | 54 +++++++++++++++++++++++++----------------------------- 1 file changed, 25 insertions(+), 29 deletions(-) diff --git a/setup.py b/setup.py index 45c98a680..840c84ab2 100644 --- a/setup.py +++ b/setup.py @@ -76,35 +76,34 @@ def configure(): LIBRARY_DIRS = [] LIBRARIES = [] - PETSC_DIR = "" - PETSC_ARCH = "" - - # try get PETSC_DIR from petsc pip installation - try: - import petsc - - PETSC_DIR = petsc.get_petsc_dir() - except: - pass - - # PETSc import os - if not os.path.exists(PETSC_DIR): - print(f"PETSC_INFO from petsc4py - {petsc4py.get_config()}") - PETSC_DIR = petsc4py.get_config()["PETSC_DIR"] - PETSC_ARCH = petsc4py.get_config()["PETSC_ARCH"] - - # It is preferable to use the petsc4py paths to the - # petsc libraries for consistency but the pip installation - # of PETSc sometimes points to the temporary setup up path - - if not os.path.exists(PETSC_DIR): - print(f"PETSC_DIR {PETSC_DIR} is bad - trying another ...") + PETSC_DIR = "" + PETSC_ARCH = "" - if os.environ.get("CONDA_PREFIX") and not os.environ.get("PETSC_DIR"): + # Priority 1: Environment variables (set by pixi activation for custom builds) + if os.environ.get("PETSC_DIR") and os.path.exists(os.environ["PETSC_DIR"]): + PETSC_DIR = os.environ["PETSC_DIR"] + PETSC_ARCH = os.environ.get("PETSC_ARCH", "") + + # Priority 2: petsc4py configuration (matches the installed petsc4py) + if not PETSC_DIR or not os.path.exists(PETSC_DIR): + config = petsc4py.get_config() + PETSC_DIR = config["PETSC_DIR"] + PETSC_ARCH = config.get("PETSC_ARCH", "") + + # Priority 3: conda petsc package + if not PETSC_DIR or not os.path.exists(PETSC_DIR): + try: + import petsc + PETSC_DIR = petsc.get_petsc_dir() + except ImportError: + pass + + # Priority 4: conda prefix fallback + if not PETSC_DIR or not os.path.exists(PETSC_DIR): + if os.environ.get("CONDA_PREFIX"): import sys - py_version = f"{sys.version_info.major}.{sys.version_info.minor}" PETSC_DIR = os.path.join( os.environ["CONDA_PREFIX"], @@ -112,10 +111,7 @@ def configure(): "python" + py_version, "site-packages", "petsc", - ) # symlink to latest python - PETSC_ARCH = os.environ.get("PETSC_ARCH", "") - else: - PETSC_DIR = os.environ["PETSC_DIR"] + ) PETSC_ARCH = os.environ.get("PETSC_ARCH", "") print(f"Using PETSc:") From 15f8e1d8ed54e2dcef34422b13ad931b5f7b7139 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Fri, 17 Apr 2026 13:59:51 -0700 Subject: [PATCH 099/537] Address Copilot review feedback on PR #120 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit - activate-petsc-arch.sh: platform-aware MPI for amr-debug (was hardcoded openmpi, wrong on linux-64 where feature.amr pulls mpich). Version discovery now matches ./uw petsc_version_short: strip whitespace from .petsc-version, default to 324 (not "4", which would produce a legacy arch name that no current build tree uses). - pixi.toml: update the amr-debug setup comment to refer to "$PETSC_ARCH" (now exported by the activation script) instead of the stale hardcoded "petsc-4-uw-openmpi-debug" string. - uw: drop the global `pip cache purge` on ./uw petsc switch — it clears every project's pip wheel cache, which is overkill. The two installs that matter already avoid the cache: run_build passes --no-cache-dir to `pip install .`, and petsc4py's local-path install now does the same. Underworld development team with AI support from Claude Code --- petsc-custom/activate-petsc-arch.sh | 26 +++++++++++++++++--------- pixi.toml | 11 ++++++++--- uw | 6 ++++-- 3 files changed, 29 insertions(+), 14 deletions(-) diff --git a/petsc-custom/activate-petsc-arch.sh b/petsc-custom/activate-petsc-arch.sh index 61d0afe6d..16347481d 100755 --- a/petsc-custom/activate-petsc-arch.sh +++ b/petsc-custom/activate-petsc-arch.sh @@ -11,23 +11,31 @@ _uw_mpi="" _uw_suffix="" + +# Default MPI for AMR envs is platform-dependent and mirrors the conda deps +# pinned in pixi.toml: openmpi on macOS (feature.amr.target.osx-arm64), +# mpich on Linux (feature.amr.target.linux-64). +_uw_default_mpi="mpich" +[ "$(uname -s)" = "Darwin" ] && _uw_default_mpi="openmpi" + case "${PIXI_ENVIRONMENT_NAME:-}" in - amr|amr-runtime|amr-dev) - case "$(uname -s)" in - Darwin) _uw_mpi="openmpi" ;; - *) _uw_mpi="mpich" ;; - esac ;; + amr|amr-runtime|amr-dev) _uw_mpi="$_uw_default_mpi" ;; amr-mpich|amr-mpich-dev) _uw_mpi="mpich" ;; amr-openmpi|amr-openmpi-dev) _uw_mpi="openmpi" ;; - amr-debug) _uw_mpi="openmpi"; _uw_suffix="-debug" ;; + amr-debug) _uw_mpi="$_uw_default_mpi"; _uw_suffix="-debug" ;; esac if [ -n "$_uw_mpi" ]; then - _uw_ver="4" + # Match the version-discovery logic in ./uw (petsc_version_short): + # prefer .petsc-version, strip whitespace, fall back to 324. + _uw_ver="324" _uw_ver_file="${PIXI_PROJECT_ROOT:-.}/petsc-custom/.petsc-version" - [ -f "$_uw_ver_file" ] && _uw_ver=$(cat "$_uw_ver_file" 2>/dev/null || echo "4") + if [ -f "$_uw_ver_file" ]; then + _uw_read=$(tr -d '[:space:]' < "$_uw_ver_file" 2>/dev/null) + [ -n "$_uw_read" ] && _uw_ver="$_uw_read" + fi export PETSC_ARCH="petsc-${_uw_ver}-uw-${_uw_mpi}${_uw_suffix}" fi -unset _uw_mpi _uw_suffix _uw_ver _uw_ver_file +unset _uw_mpi _uw_suffix _uw_default_mpi _uw_ver _uw_ver_file _uw_read diff --git a/pixi.toml b/pixi.toml index b8d6796cc..2bc8f4c60 100644 --- a/pixi.toml +++ b/pixi.toml @@ -237,15 +237,20 @@ petsc-local-clean = { cmd = "./build-petsc.sh clean", cwd = "petsc-custom" } # Uses the same conda deps as amr but points to a separate PETSC_ARCH # so the optimised build is untouched. # -# Setup: +# PETSC_ARCH is set dynamically by petsc-custom/activate-petsc-arch.sh +# and resolves to: petsc--uw--debug +# where comes from petsc-custom/.petsc-version and follows +# the platform default (openmpi on macOS, mpich on Linux). +# +# Setup (inside a pixi shell -e amr-debug, so $PETSC_ARCH is already set): # cd petsc-custom/petsc # pixi run -e amr-debug python3 ./configure \ -# --with-petsc-arch=petsc-4-uw-openmpi-debug --with-debugging=1 \ +# --with-petsc-arch="$PETSC_ARCH" --with-debugging=1 \ # --with-mpi-dir="$CONDA_PREFIX" --with-hdf5=0 \ # --download-mpich=0 --download-openmpi=0 --download-mpi4py=0 \ # --with-petsc4py=0 --with-x=0 --with-pragmatic=0 --with-slepc=0 \ # "--COPTFLAGS=-g -O0" "--CXXOPTFLAGS=-g -O0" "--FOPTFLAGS=-g -O0" -# make PETSC_DIR=$(pwd) PETSC_ARCH=petsc-4-uw-openmpi-debug all +# make PETSC_DIR=$(pwd) PETSC_ARCH="$PETSC_ARCH" all [feature.amr-debug.activation] scripts = ["petsc-custom/activate-petsc-arch.sh"] diff --git a/uw b/uw index d94c5f192..eebb537fe 100755 --- a/uw +++ b/uw @@ -159,7 +159,7 @@ run_build() { # Step 2: Check/build petsc4py if ! petsc4py_installed "$env"; then echo " Installing petsc4py for $env..." - $PIXI run -e "$env" pip install "$PETSC_CUSTOM/src/binding/petsc4py" --no-build-isolation || { + $PIXI run -e "$env" pip install "$PETSC_CUSTOM/src/binding/petsc4py" --no-build-isolation --no-cache-dir || { echo -e "${YELLOW}petsc4py build failed${NC}" exit 1 } @@ -297,11 +297,13 @@ run_petsc_cmd() { # Nuke stale build artifacts and petsc4py. The next ./uw build's # target-change detection can't fire because the still-installed # petsc4py reports the OLD arch, so we force a full rebuild here. + # (run_build already passes --no-cache-dir to pip install . so we + # don't need a global pip cache purge — only petsc4py's local-path + # install needs its own --no-cache-dir.) echo "" echo "Clearing stale build artifacts for clean rebuild..." rm -rf "$SCRIPT_DIR"/build/lib.* "$SCRIPT_DIR"/build/temp.* "$SCRIPT_DIR"/build/bdist.* 2>/dev/null rm -f "$SCRIPT_DIR/build/.petsc_target" - $PIXI run -e "$(get_env)" pip cache purge 2>/dev/null || true if is_amr_env "$(get_env)"; then echo "Uninstalling old petsc4py (linked to previous PETSc build)..." $PIXI run -e "$(get_env)" pip uninstall -y petsc4py 2>/dev/null || true From 425af03cf1bb71f02b8c4245ad57ab248971c681 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Tue, 21 Apr 2026 07:44:35 +1000 Subject: [PATCH 100/537] Add SNES_MultiComponent solver; fix SNES_Vector Jacobian layout MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit New `SNES_MultiComponent` solver with arbitrary `n_components` per node decoupled from `mesh.dim`, and a `SNES_MultiComponent_Projection` that projects N scalar components in a single SNES solve sharing one DM. Replaces per-component cycling in `SNES_Tensor_Projection` for the VE Stokes tau projection — one DM build per outer solve instead of Nc per outer solve, the dominant cost profiled on the VE square-wave benchmark. Wired into `SNES_VE_Stokes` via `_setup_tau_projection` for the symmetric-tensor flux path (Nc=3 in 2D, Nc=6 in 3D). User-facing tau variable stays SYM_TENSOR so downstream `.array[:, i, j]` reads are unchanged; a flat (1, Nc) MATRIX variable drives the actual solve and results fan out after each solve. In the course of this work, discovered and fixed a latent Jacobian-layout bug in `SNES_Vector`. PETSc's element-matrix assembly (fe.c:2639–2790) reads pointwise Jacobian arrays in `[fc, gc, df, dg]` flat order — the two component indices outer, the two derivative indices inner. `SNES_Vector` had been using `derive_by_array + permutedims` with `(0, 3, 1, 2)` for g3 and `(2, 1, 0)` for g1/g2, which encodes `[fc, dg, df, gc]` — the trial-side component and derivative are swapped. The discrepancy was hidden by F1-index symmetry in every in-repo consumer (strain-rate smoothing, deviatoric Stokes stress, divergence penalty) but would fire for any future subclass with a non-symmetric F1. Fix: migrated `SNES_Vector._setup_pointwise_functions` (both main residual and natural-BC paths) to explicit nested-loop Jacobian construction that writes directly into PETSc's flat layout. Matches `SNES_MultiComponent`'s pattern; no `permutedims` remains. Reproduced the bug in a test (asymmetric `F1 = smoothing * Unknowns.L`, identical targets) and confirmed the migration fixes it — results now agree with `SNES_MultiComponent_Projection` to rel-L2 ≤ 1e-8. Audit table and checklist for new solvers in new developer doc `docs/developer/subsystems/petsc-jacobian-layout.md`. `SNES_Scalar` (Nc=1) and `SNES_Stokes_SaddlePt` (permutation `(0, 2, 1, 3)`) are correct. `SNES_NavierStokes` inherits Stokes. Tests: - 10 validation tests for `SNES_MultiComponent_Projection` (Nc=1 ≡ Scalar Projection, Nc=3 sym-tensor ≡ Tensor_Projection, Nc=4 full-tensor, DM-rebuild-count invariant, smoothing-parametrised agreement at 1e-4, 1e-2, 1.0). - 6 regression tests for `SNES_Vector` asymmetric-F1 layout (identical-targets decoupling and agreement with MultiComponent). - Full Stokes (`test_1010_stokesCart`) and VE Stokes (`test_1050_VEstokesCart`) suites pass — no regression on symmetric-F1 production paths. - 49/49 tier_a level_1 tests pass (3 MPI-only skipped). Underworld development team with AI support from Claude Code --- docs/developer/CHANGELOG.md | 25 + docs/developer/index.md | 1 + .../subsystems/petsc-jacobian-layout.md | 229 +++++ .../cython/petsc_generic_snes_solvers.pyx | 840 ++++++++++++++++-- src/underworld3/systems/__init__.py | 2 + src/underworld3/systems/solvers.py | 100 +++ tests/test_multicomponent_projection.py | 322 +++++++ tests/test_snes_vector_asymmetric_jacobian.py | 121 +++ 8 files changed, 1588 insertions(+), 52 deletions(-) create mode 100644 docs/developer/subsystems/petsc-jacobian-layout.md create mode 100644 tests/test_multicomponent_projection.py create mode 100644 tests/test_snes_vector_asymmetric_jacobian.py diff --git a/docs/developer/CHANGELOG.md b/docs/developer/CHANGELOG.md index b846305c7..3a2e42394 100644 --- a/docs/developer/CHANGELOG.md +++ b/docs/developer/CHANGELOG.md @@ -4,6 +4,31 @@ This log tracks significant development work at a conceptual level, suitable for --- +## 2026 Q2 (April – June) + +### Multi-Component Projection Solver (April 2026) + +**New `SNES_MultiComponent_Projection` solver** that projects N scalar components in a single PETSc SNES solve sharing one DM, replacing the per-component cycling in `SNES_Tensor_Projection` (which tore down and rebuilt the DM on each inner iteration). The underlying `SNES_MultiComponent` Cython base decouples the FE component count from `mesh.dim` — PETSc's pointwise callback interface accepts any DOF count per node; the new class exposes that directly. + +- Wired into `SNES_VE_Stokes` via `_setup_tau_projection` for the symmetric-tensor tau projection (Nc=3 in 2D, Nc=6 in 3D). User-facing tau variable remains a `SYM_TENSOR` so downstream `.array[:, i, j]` reads are unchanged; a flat `(1, Nc)` MATRIX drives the actual solve and results fan out after each solve. +- DM build count scales with outer solves rather than `Nc × outer_solves` — the dominant cost in `SNES_Tensor_Projection` on the VE square-wave benchmark. +- 10 validation tests: `Nc=1` agrees with `SNES_Projection`, `Nc=3` symmetric-tensor agrees with `SNES_Tensor_Projection`, `Nc=4` full-tensor agreement, DM-rebuild count invariant, smoothing-parametrised agreement (1e-4, 1e-2, 1.0). + +**Files**: `cython/petsc_generic_snes_solvers.pyx` (new `SNES_MultiComponent` class, VE tau wiring), `systems/solvers.py` (new `SNES_MultiComponent_Projection`), `systems/__init__.py` (export), `tests/test_multicomponent_projection.py`. + +### PETSc Pointwise Jacobian Layout Fix (April 2026) + +**Documented PETSc's `[fc, gc, df, dg]` flat-index convention** for pointwise Jacobian arrays and fixed a latent layout bug in `SNES_Vector`. The `SNES_Vector` permutations `(0, 3, 1, 2)` for g3 and `(2, 1, 0)` for g1/g2 did not match PETSc's element-assembly index order (fe.c:2639–2790) — the bug was hidden by the trial-side symmetry of every in-repo consumer's F1 (strain-rate-based smoothing, deviatoric Stokes stress, divergence penalty). + +- Migrated `SNES_Vector._setup_pointwise_functions` (main residual and natural-BC Jacobian paths) from `derive_by_array` + `permutedims` to explicit nested-loop construction that writes directly into PETSc's expected row-major 2D layout. Same pattern as the new `SNES_MultiComponent`. +- Regression test with `F1 = smoothing * Unknowns.L` (raw gradient, not symmetrised) guards against the layout bug returning: at `smoothing > 0`, identical targets must give identical components, and results must match `SNES_MultiComponent_Projection` to rel-L2 ≤ 1e-8. +- Audit of other solvers: `SNES_Scalar` trivially correct (Nc=1); `SNES_Stokes_SaddlePt` and `SNES_NavierStokes` already use the correct `(0, 2, 1, 3)` permutation. +- New developer documentation: `docs/developer/subsystems/petsc-jacobian-layout.md` captures the convention, the sympy-to-PETSc axis mapping, and a checklist for new solvers (identical-targets + non-zero-smoothing validation tests required). + +**Files**: `cython/petsc_generic_snes_solvers.pyx` (`SNES_Vector` migration), `tests/test_snes_vector_asymmetric_jacobian.py`, `docs/developer/subsystems/petsc-jacobian-layout.md`, `docs/developer/index.md` (toctree). + +--- + ## 2026 Q1 (January – March) ### v3.0.0 Release (March 2026) diff --git a/docs/developer/index.md b/docs/developer/index.md index f7d383ce2..4a85c31d5 100644 --- a/docs/developer/index.md +++ b/docs/developer/index.md @@ -155,6 +155,7 @@ CHANGELOG subsystems/meshing subsystems/discretisation subsystems/solvers +subsystems/petsc-jacobian-layout subsystems/constitutive-models subsystems/constitutive-models-theory subsystems/constitutive-models-anisotropy diff --git a/docs/developer/subsystems/petsc-jacobian-layout.md b/docs/developer/subsystems/petsc-jacobian-layout.md new file mode 100644 index 000000000..5f22636eb --- /dev/null +++ b/docs/developer/subsystems/petsc-jacobian-layout.md @@ -0,0 +1,229 @@ +--- +title: "PETSc Pointwise Jacobian Layout" +--- + +# PETSc Pointwise Jacobian Layout + +This page documents the exact index convention PETSc expects for pointwise +Jacobian arrays (`g0`, `g1`, `g2`, `g3`) registered via +`PetscDSSetJacobian`. Getting this wrong produces silent numerical errors +— the solve may converge to a wrong answer (often in ways that look +plausible for symmetric problems) or stagnate without ever reaching +tolerance. This was the origin of a real bug fixed in +`SNES_MultiComponent_Projection` on 2026-04-20. + +Read this before writing or modifying any class that registers a +`PetscDSSetJacobian` callback. + +## The four pointwise Jacobian arrays + +For a single-field problem with `Nc` components per node and `dim` spatial +dimensions, the four pointwise Jacobians couple the residual pieces +(`f0` value, `F1` flux) to the unknowns (`u` value, `∇u` gradient): + +| Array | Semantic | Size | +|-------|------------------------------------------------------|-----------------| +| `g0` | $\partial f_0[\mathrm{fc}] / \partial u[\mathrm{gc}]$ | `Nc × Nc` | +| `g1` | $\partial f_0[\mathrm{fc}] / \partial(\nabla u)[\mathrm{gc}, \mathrm{df}]$ | `Nc × Nc × dim` | +| `g2` | $\partial F_1[\mathrm{fc}, \mathrm{df}] / \partial u[\mathrm{gc}]$ | `Nc × dim × Nc` | +| `g3` | $\partial F_1[\mathrm{fc}, \mathrm{df}] / \partial(\nabla u)[\mathrm{gc}, \mathrm{dg}]$ | `Nc × dim × Nc × dim` | + +Notation: +- **`fc`** = test (output) component index +- **`gc`** = trial (input) component index +- **`df`** = test (residual-side) spatial derivative index +- **`dg`** = trial (unknown-side) spatial derivative index + +## The flat-index convention + +PETSc's element-matrix assembly walks these arrays as **flat** buffers +with the two *component* indices on the outside and the two *derivative* +indices on the inside: + +``` +g0[fc*Nc + gc] +g1[(fc*Nc + gc) * dim + df] +g2[(fc*Nc + gc) * dim + df] +g3[((fc*Nc + gc) * dim + df) * dim + dg] +``` + +Source of truth: `PetscFEUpdateElementMat_Internal` in +`petsc-custom/petsc/src/dm/dt/fe/interface/fe.c:2639`. The element-matrix +kernels at lines 2690 (g0), 2718 (g1), 2748 (g2), 2779 (g3) read the +arrays with exactly these index expressions. + +**The key point**: the two component indices come first (outer), then +the two derivative indices (inner). The layout is `[fc, gc, df, dg]`, +**not** `[fc, df, gc, dg]`. This is easy to get wrong because the +"natural" mathematical reading of $\partial F_1[\mathrm{fc}, \mathrm{df}] / \partial L[\mathrm{gc}, \mathrm{dg}]$ +pairs each function argument with its derivative — but PETSc's storage +pairs like-kind indices. + +## Sympy's native convention + +`sympy.derive_by_array(F, x)` returns an array with **`F`'s indices +first, then `x`'s**: + +```python +G3 = sympy.derive_by_array(F1, L) +# F1 shape (Nc, dim), L shape (Nc, dim) +# → G3 shape (Nc, dim, Nc, dim) +# → G3[i, j, k, l] = ∂F1[i, j] / ∂L[k, l] +# → index order [fc, df, gc, dg] +``` + +This is the same mathematical object PETSc wants, but with the **two +middle axes swapped** relative to PETSc's flat layout. Translating +sympy → PETSc therefore needs the permutation **`(0, 2, 1, 3)`** — swap +axes 1 and 2 — before flattening. + +For `g1` (3D, sympy order `[fc, gc, df]`) and `g2` (3D, sympy order +`[fc, df, gc]`): + +| Array | Sympy shape after `derive_by_array` | Permutation | Final 2D shape | +|-------|--------------------------------------|-------------|----------------| +| `g0` | `(Nc, Nc)` — already `[fc, gc]` | none | `(Nc, Nc)` | +| `g1` | `(Nc, Nc, dim)` — `[fc, gc, df]` | none | `(Nc·Nc, dim)` | +| `g2` | `(Nc, dim, Nc)` — `[fc, df, gc]` | `(0, 2, 1)` | `(Nc·Nc, dim)` | +| `g3` | `(Nc, dim, Nc, dim)` — `[fc, df, gc, dg]` | `(0, 2, 1, 3)` | `(Nc·Nc, dim·dim)` | + +The row-major flatten of the 2D form matches PETSc's flat index exactly. + +## Alternative: explicit construction + +Instead of `derive_by_array` + `permutedims`, you can loop the indices +and write each entry directly into a matrix shaped for row-major flatten +into PETSc's layout. This is what `SNES_MultiComponent` does — the code +reads like the PETSc formula and removes any chance of getting the sympy +convention wrong on future sympy upgrades: + +```python +G3 = sympy.zeros(Nc * Nc, dim * dim) +for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + for dg in range(dim): + G3[fc * Nc + gc, df * dim + dg] = sympy.diff(F1[fc, df], L[gc, dg]) +``` + +Row index `fc * Nc + gc`, col index `df * dim + dg`. Row-major flatten +gives `((fc * Nc + gc) * dim + df) * dim + dg` — PETSc's expected index. + +See `src/underworld3/cython/petsc_generic_snes_solvers.pyx` — the +`_setup_pointwise_functions` method of `SNES_MultiComponent`. + +## Worked example — why symmetric problems hide the bug + +Consider `F1[i, j] = L[i, j]` (raw gradient, *not* symmetrised) and +`Nc = dim = 2`. Then $\partial F_1[i, j] / \partial L[k, l] = \delta_{ik}\,\delta_{jl}$. +The non-zero entries in PETSc's correct layout `g3[fc, gc, df, dg]` are +the positions where `fc == gc` **and** `df == dg`: + +``` +(fc=0, gc=0, df=0, dg=0) → flat idx 0 +(fc=0, gc=0, df=1, dg=1) → flat idx 3 +(fc=1, gc=1, df=0, dg=0) → flat idx 12 +(fc=1, gc=1, df=1, dg=1) → flat idx 15 +``` + +Now consider the stress-like symmetric case +$F_1[i, j] = \tfrac{1}{2}(L[i, j] + L[j, i])$. The Jacobian is +$\partial F_1 / \partial L[k, l] = \tfrac{1}{2}(\delta_{ik}\delta_{jl} + \delta_{il}\delta_{jk})$. +Because this expression is **invariant under the swap $(k, l) \leftrightarrow (l, k)$**, +a Jacobian array that swaps the trial-side indices (`gc`↔`dg`) still +integrates to the same stiffness matrix. Every current consumer of +`SNES_Vector` uses an F1 with this symmetry — Stokes stress, symmetric +strain-rate smoothing, divergence penalty — so the bug is hidden. + +An asymmetric F1 like raw `smoothing * L` exposes it immediately. + +## Audit of existing solvers + +Results of walking every solver in `petsc_generic_snes_solvers.pyx` as +of 2026-04-21: + +| Solver | File:line | Construction | Status | +|--------|-----------|--------------|--------| +| `SNES_Scalar` | `petsc_generic_snes_solvers.pyx:1255` | no permutation (Nc=1) | ✅ correct — single component makes the swap a no-op | +| `SNES_Vector` | `petsc_generic_snes_solvers.pyx:2013` | explicit per-entry construction | ✅ correct (2026-04-21 migration) | +| `SNES_MultiComponent` | `petsc_generic_snes_solvers.pyx:2919` | explicit per-entry construction | ✅ correct (2026-04-20 fix) | +| `SNES_Stokes_SaddlePt` | `petsc_generic_snes_solvers.pyx:3552` | `permutedims` with `(0, 2, 1, 3)` | ✅ correct — matches PETSc layout | +| `SNES_NavierStokes` | inherits Stokes | inherited | ✅ correct | + +### `SNES_Vector` migration (2026-04-21) + +`SNES_Vector` originally used `derive_by_array` followed by +`permutedims(·, (0, 3, 1, 2))` for `g3` and `(2, 1, 0)` for `g1`/`g2`. +These permutations do not match PETSc's `[fc, gc, df, dg]` layout, but +the discrepancy is invisible whenever F1 is symmetric under the +trial-side swap `(k, l) ↔ (l, k)`. Every in-repo consumer of +`SNES_Vector` — `SNES_Vector_Projection` (using `Unknowns.E` plus a +divergence penalty), the Nitsche BC path, the VE stress tau projection +— supplies exactly that kind of F1, so the bug never fired in tests. + +Empirical reproduction (before the migration): + +```text +SNES_Vector_Projection subclass with F1 = smoothing * L (raw gradient) +two identical targets sin(x)·cos(y) on StructuredQuadBox(4, 4): + + smoothing = 0.1 → |u0 − u1| = 1.59 (should be 0) + vs. SNES_MultiComponent_Projection → rel-L2 disagreement ≈ 0.30 +``` + +**Fix applied**: `SNES_Vector._setup_pointwise_functions` now builds all +four Jacobians (and the natural-BC Jacobians) with explicit nested +loops that write directly into the PETSc-ordered matrix (row-major +`[fc*Nc + gc, df*dim + dg]` etc.). The code now reads the same as +`SNES_MultiComponent` — see the companion method — and no +`permutedims` is applied to any residual or BC Jacobian. + +After the migration: `tests/test_snes_vector_asymmetric_jacobian.py` +passes (identical targets produce identical components, and the +asymmetric-F1 solve matches `SNES_MultiComponent_Projection` to +rel-L2 ≤ 1e-8 across smoothing ∈ {1e-4, 1e-2, 1e-1}). The full +Stokes (`test_1010_stokesCart`) and VE Stokes (`test_1050_VEstokesCart`) +suites continue to pass, confirming no regression on symmetric-F1 +consumers. + +## Checklist for new solvers + +When writing a new class that registers a `PetscDSSetJacobian` callback: + +1. **Decide on construction style.** For multi-field or novel residual + shapes, prefer the explicit-index pattern from `SNES_MultiComponent` + — it reads like the PETSc documentation and is robust against sympy + convention drift. Reserve `derive_by_array + permutedims` for cases + that match an already-validated solver pattern. + +2. **Write a validation test.** For every solver that can be reached at + `Nc > 1` with `smoothing > 0`, include a test that: + - Runs with **identical targets** for each component and checks the + returned components are identical (decouples the component-coupling + bug from target geometry). + - Runs with **non-zero smoothing** (not just the L2 projection limit + — `smoothing = 0` makes g3 the zero matrix and the bug can't show). + - Compares against a known-good reference solver at the same + tolerances. Use `ksp_type=preonly` + `pc_type=lu` to eliminate + iterative-solver tolerance as a confounder. + +3. **Keep a pointer to this doc** in a code comment above the Jacobian + construction. Authors reaching for `permutedims` should see a + reminder that PETSc's layout is `[fc, gc, df, dg]`, not the sympy + default. + +## References + +- PETSc element-matrix kernels (authoritative): + `petsc-custom/petsc/src/dm/dt/fe/interface/fe.c:2583–2790` + (`petsc_elemmat_kernel_g0/g1/g2/g3` macros and the assembly loop in + `PetscFEUpdateElementMat_Internal`). +- `PetscDSSetJacobian` API: + [petsc.org](https://petsc.org/release/manualpages/DT/PetscDSSetJacobian/). +- Bug-fix history: `SNES_MultiComponent_Projection` initially used a + `[fc, df, gc, dg]` reshape (same layout as `SNES_Vector`). The bug + was invisible at `smoothing = 0` because g3 vanishes; it became + obvious when a validation test with `smoothing > 0` showed + components with identical targets producing different results. + Fixed in the commit that introduced the solver — see the companion + tests in `tests/test_multicomponent_projection.py`. diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx index 81ba37dd5..921bf2aae 100644 --- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx +++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx @@ -1008,22 +1008,42 @@ class SolverBaseClass(uw_object): flux = self._constitutive_model.flux if hasattr(flux, 'shape') and flux.shape[1] == 1 and flux.shape[0] > 1: flux = flux.T - self._tau_projector.uw_function = flux - self._tau_projector.smoothing = 0.0 - self._tau_projector.solve() + + if getattr(self, '_tau_use_multicomponent', False): + # Symmetric tensor: flatten flux to a row of independent components, + # solve one multi-component projection, fan result back to SYM_TENSOR. + import sympy + indep = self._tau_indep_indices + row = sympy.Matrix([[flux[i, j] for (i, j) in indep]]) + self._tau_projector.uw_function = row + self._tau_projector.smoothing = 0.0 + self._tau_projector.solve() + for k, (i, j) in enumerate(indep): + vals = self._tau_projector.u.array[:, 0, k] + self._tau_var.array[:, i, j] = vals + if i != j: + self._tau_var.array[:, j, i] = vals + else: + self._tau_projector.uw_function = flux + self._tau_projector.smoothing = 0.0 + self._tau_projector.solve() return self._tau_var def _setup_tau_projection(self): """Create the mesh variable and projector for tau (lazy init).""" + import math flux = self._constitutive_model.flux dim = self.mesh.dim rows, cols = flux.shape # Determine variable type and create appropriate projection solver if rows == cols and rows == dim: - # Tensor flux (Stokes stress) + # Symmetric tensor flux (Stokes / VE_Stokes stress). + # User-facing: SYM_TENSOR so downstream .array[:, i, j] reads are unchanged. + # Internal: (1, Nc) MATRIX variable driven by SNES_MultiComponent_Projection, + # eliminating the per-component DM cycling of SNES_Tensor_Projection. self._tau_var = uw.discretisation.MeshVariable( f"tau_{self.instance_number}", self.mesh, @@ -1033,17 +1053,28 @@ class SolverBaseClass(uw_object): continuous=True, varsymbol=r"{\tau}", ) - _work = uw.discretisation.MeshVariable( - f"tau_work_{self.instance_number}", + Nc = math.comb(dim + 1, 2) + self._tau_indep_indices = [ + (i, j) for i in range(dim) for j in range(i, dim) + ] + self._tau_flat_var = uw.discretisation.MeshVariable( + f"tau_flat_{self.instance_number}", self.mesh, - 1, + (1, Nc), + vtype=uw.VarType.MATRIX, degree=self.u.degree, continuous=True, + varsymbol=r"{\tau_{\mathrm{flat}}}", ) - from underworld3.systems.solvers import SNES_Tensor_Projection - self._tau_projector = SNES_Tensor_Projection( - self.mesh, self._tau_var, _work, verbose=False + from underworld3.systems.solvers import SNES_MultiComponent_Projection + self._tau_projector = SNES_MultiComponent_Projection( + self.mesh, + u_Field=self._tau_flat_var, + n_components=Nc, + degree=self.u.degree, + verbose=False, ) + self._tau_use_multicomponent = True elif rows == dim and cols == 1: # Vector flux (Poisson heat flux) @@ -2452,48 +2483,88 @@ class SNES_Vector(SolverBaseClass): # f0 = sympy.Array(uw.function.fn_substitute_expressions(self.F0.sym)).reshape(dim).as_immutable() # F1 = sympy.Array(uw.function.fn_substitute_expressions(self.F1.sym)).reshape(dim,dim).as_immutable() + # Residual piece shapes: f0 is (dim,) per-component, F1 is (dim, dim). # Don't unwrap here — let getext()'s two-phase unwrap handle it. # This preserves constant UWexpressions as symbols for the constants[] mechanism. - f0 = sympy.Array(self.F0.sym).reshape(dim).as_immutable() - F1 = sympy.Array(self.F1.sym).reshape(dim,dim).as_immutable() - - - self._u_f0 = f0 - self._u_F1 = F1 + F0_user = sympy.Matrix(self.F0.sym) + F1_user = sympy.Matrix(self.F1.sym) + + # Normalise F0 into a list of scalar per-component entries so the + # explicit-index Jacobian construction below can sympy.diff each one. + if F0_user.shape == (dim, 1): + f0_list = [F0_user[c, 0] for c in range(dim)] + elif F0_user.shape == (1, dim): + f0_list = [F0_user[0, c] for c in range(dim)] + elif F0_user.shape == (dim,): + f0_list = [F0_user[c] for c in range(dim)] + else: + raise ValueError( + f"SNES_Vector F0 shape {F0_user.shape} is not compatible with dim={dim}." + ) + if F1_user.shape != (dim, dim): + raise ValueError( + f"SNES_Vector F1 shape {F1_user.shape} does not match (dim, dim)=({dim}, {dim})." + ) - # JIT compilation needs immutable, matrix input (not arrays) - self._u_f0 = sympy.ImmutableDenseMatrix(f0) - self._u_F1 = sympy.ImmutableDenseMatrix(F1) + # Residual arrays kept as matrices for the JIT codegen path. + # f0 stored as (dim, 1) column; F1 stored as (dim, dim). + self._u_f0 = sympy.ImmutableDenseMatrix([[e] for e in f0_list]) + self._u_F1 = sympy.ImmutableDenseMatrix(F1_user) fns_residual = [self._u_f0, self._u_F1] - # This is needed to eliminate extra dims in the tensor - U = sympy.Array(self.u.sym).reshape(dim) - - G0 = sympy.derive_by_array(f0, U) - G1 = sympy.derive_by_array(f0, self.Unknowns.L) - G2 = sympy.derive_by_array(F1, U) - G3 = sympy.derive_by_array(F1, self.Unknowns.L) - - # reorganise indices from sympy to petsc ordering - # reshape to Matrix form - # Make hashable (immutable) - - permutation = (0,3,1,2) + # Unknowns in the form we need for the explicit Jacobian loops. + # U_list[c] = u-component c (u.sym is a (1, dim) row for VECTOR vtype) + # L[c, d] = ∂u_c / ∂x_d (shape (dim, dim)) + U_list = [self.u.sym[0, c] for c in range(dim)] + L = self.Unknowns.L + + # Explicit-index Jacobian construction — writes each entry directly + # into PETSc's flat [fc, gc, df, dg] layout via row-major 2D matrices. + # See docs/developer/subsystems/petsc-jacobian-layout.md for the + # convention and why the older derive_by_array + permutedims form + # was incorrect for non-symmetric F1. Nc == dim for SNES_Vector. + Nc = dim + + # G0[fc*Nc + gc, 0] = ∂f0[fc] / ∂U[gc] + G0 = sympy.zeros(Nc, Nc) + for fc in range(Nc): + for gc in range(Nc): + G0[fc, gc] = sympy.diff(f0_list[fc], U_list[gc]) + + # G1[fc*Nc + gc, df] = ∂f0[fc] / ∂L[gc, df] + G1 = sympy.zeros(Nc * Nc, dim) + for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + G1[fc * Nc + gc, df] = sympy.diff(f0_list[fc], L[gc, df]) + + # G2[fc*Nc + gc, df] = ∂F1[fc, df] / ∂U[gc] + G2 = sympy.zeros(Nc * Nc, dim) + for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + G2[fc * Nc + gc, df] = sympy.diff(F1_user[fc, df], U_list[gc]) + + # G3[fc*Nc + gc, df*dim + dg] = ∂F1[fc, df] / ∂L[gc, dg] + G3 = sympy.zeros(Nc * Nc, dim * dim) + for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + for dg in range(dim): + G3[fc * Nc + gc, df * dim + dg] = sympy.diff(F1_user[fc, df], L[gc, dg]) - self._G0 = sympy.ImmutableMatrix(G0.reshape(dim,dim)) - self._G1 = sympy.ImmutableMatrix(sympy.permutedims(G1, (2,1,0) ).reshape(dim,dim*dim)) - self._G2 = sympy.ImmutableMatrix(sympy.permutedims(G2, (2,1,0) ).reshape(dim*dim,dim)) - self._G3 = sympy.ImmutableMatrix(sympy.permutedims(G3, permutation).reshape(dim*dim,dim*dim)) + self._G0 = sympy.ImmutableMatrix(G0) + self._G1 = sympy.ImmutableMatrix(G1) + self._G2 = sympy.ImmutableMatrix(G2) + self._G3 = sympy.ImmutableMatrix(G3) ################## fns_jacobian = (self._G0, self._G1, self._G2, self._G3) - # Now natural bcs (compiled into boundary integral terms) - # Need to loop on them all ... - - # Now natural bcs (compiled into boundary integral terms) - # Need to loop on them all ... + # Now natural bcs (compiled into boundary integral terms). + # Natural BC Jacobians follow the same PETSc layout as the main + # residual Jacobians — build them with the same explicit-index pattern. fns_bd_residual = [] fns_bd_jacobian = [] @@ -2502,14 +2573,33 @@ class SNES_Vector(SolverBaseClass): if bc.fn_f is not None: - bd_F0 = sympy.Array(bc.fn_f) - bc.fns["u_f0"] = sympy.ImmutableDenseMatrix(bd_F0) + bd_F0_mat = sympy.Matrix(bc.fn_f) + if bd_F0_mat.shape == (dim, 1): + bd_f0_list = [bd_F0_mat[c, 0] for c in range(dim)] + elif bd_F0_mat.shape == (1, dim): + bd_f0_list = [bd_F0_mat[0, c] for c in range(dim)] + elif bd_F0_mat.shape == (dim,): + bd_f0_list = [bd_F0_mat[c] for c in range(dim)] + else: + raise ValueError( + f"Natural BC fn_f shape {bd_F0_mat.shape} is not compatible with dim={dim}." + ) - G0 = sympy.derive_by_array(bd_F0, U) - G1 = sympy.derive_by_array(bd_F0, self.Unknowns.L) + bd_f0 = sympy.ImmutableDenseMatrix([[e] for e in bd_f0_list]) + bc.fns["u_f0"] = bd_f0 - bc.fns["uu_G0"] = sympy.ImmutableMatrix(G0.reshape(dim,dim)) # sympy.ImmutableMatrix(sympy.permutedims(G0, permutation).reshape(dim,dim)) - bc.fns["uu_G1"] = sympy.ImmutableMatrix(G1.reshape(dim*dim,dim)) # sympy.ImmutableMatrix(sympy.permutedims(G1, permutation).reshape(dim,dim*dim)) + # BC G0[fc*Nc + gc] = ∂bd_f0[fc]/∂U[gc] + # BC G1[fc*Nc + gc, df] = ∂bd_f0[fc]/∂L[gc, df] + bd_G0 = sympy.zeros(Nc, Nc) + bd_G1 = sympy.zeros(Nc * Nc, dim) + for fc in range(Nc): + for gc in range(Nc): + bd_G0[fc, gc] = sympy.diff(bd_f0_list[fc], U_list[gc]) + for df in range(dim): + bd_G1[fc * Nc + gc, df] = sympy.diff(bd_f0_list[fc], L[gc, df]) + + bc.fns["uu_G0"] = sympy.ImmutableMatrix(bd_G0) + bc.fns["uu_G1"] = sympy.ImmutableMatrix(bd_G1) fns_bd_residual += [bc.fns["u_f0"]] fns_bd_jacobian += [bc.fns["uu_G0"], bc.fns["uu_G1"]] @@ -2517,14 +2607,27 @@ class SNES_Vector(SolverBaseClass): # Gradient boundary residual (f1_bd) and its Jacobians (g2, g3) # Used by Nitsche-type BCs; None for standard natural BCs. if hasattr(bc, 'fn_F') and bc.fn_F is not None: - bd_F1 = sympy.Array(bc.fn_F).reshape(dim, dim) + bd_F1 = sympy.Matrix(bc.fn_F) + if bd_F1.shape != (dim, dim): + raise ValueError( + f"Natural BC fn_F shape {bd_F1.shape} is not (dim, dim)=({dim}, {dim})." + ) bc.fns["u_F1"] = sympy.ImmutableDenseMatrix(bd_F1) fns_bd_residual += [bc.fns["u_F1"]] - G2 = sympy.derive_by_array(bd_F1, U) - G3 = sympy.derive_by_array(bd_F1, self.Unknowns.L) - bc.fns["uu_G2"] = sympy.ImmutableMatrix(G2.reshape(dim*dim, dim)) - bc.fns["uu_G3"] = sympy.ImmutableMatrix(G3.reshape(dim*dim, dim*dim)) + # BC G2[fc*Nc + gc, df] = ∂bd_F1[fc, df]/∂U[gc] + # BC G3[fc*Nc + gc, df*dim + dg] = ∂bd_F1[fc, df]/∂L[gc, dg] + bd_G2 = sympy.zeros(Nc * Nc, dim) + bd_G3 = sympy.zeros(Nc * Nc, dim * dim) + for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + bd_G2[fc * Nc + gc, df] = sympy.diff(bd_F1[fc, df], U_list[gc]) + for dg in range(dim): + bd_G3[fc * Nc + gc, df * dim + dg] = sympy.diff(bd_F1[fc, df], L[gc, dg]) + + bc.fns["uu_G2"] = sympy.ImmutableMatrix(bd_G2) + bc.fns["uu_G3"] = sympy.ImmutableMatrix(bd_G3) fns_bd_jacobian += [bc.fns["uu_G2"], bc.fns["uu_G3"]] self._fns_bd_residual = fns_bd_residual @@ -2885,6 +2988,639 @@ class SNES_Vector(SolverBaseClass): ### ================================= +class SNES_MultiComponent(SolverBaseClass): + r""" + General multi-component equation solver using PETSc SNES. + + Generalises :class:`SNES_Vector` to an arbitrary number of DOF + components per node, decoupled from ``mesh.dim``. Solves for an + N-component unknown :math:`\mathbf{u}` (stored as a ``(1, Nc)`` row + matrix variable) with per-component residual and flux terms. + + Unlike :class:`SNES_Vector`, the components of :math:`\mathbf{u}` have + no inherent physical meaning as a spatial vector — they are N + independent scalar DOFs sharing one DM. Cross-component coupling is + allowed through ``F0`` and ``F1`` but not required; the primary use + case (multi-component projection) is block-diagonal. + + Parameters + ---------- + mesh : underworld3.discretisation.Mesh + u_Field : MeshVariable, optional + Pre-existing ``(1, n_components)`` MATRIX variable. If ``None``, + one is created. + n_components : int + Number of scalar DOF components per node. Required when + ``u_Field`` is None; otherwise inferred from ``u_Field.shape``. + degree : int, default=2 + verbose : bool, default=False + """ + + @timing.routine_timer_decorator + def __init__(self, + mesh : uw.discretisation.Mesh, + u_Field : uw.discretisation.MeshVariable = None, + n_components : int = None, + degree = 2, + verbose = False, + DuDt : Union[uw.systems.ddt.SemiLagrangian, uw.systems.ddt.Lagrangian] = None, + DFDt : Union[uw.systems.ddt.SemiLagrangian, uw.systems.ddt.Lagrangian] = None, + ): + + super().__init__(mesh) + + if n_components is None: + if u_Field is None: + raise ValueError( + "SNES_MultiComponent requires n_components or a u_Field with defined shape." + ) + n_components = int(u_Field.shape[0]) * int(u_Field.shape[1]) + if n_components < 1: + raise ValueError("n_components must be >= 1") + if mesh.cdim != mesh.dim: + raise ValueError( + "SNES_MultiComponent currently assumes mesh.cdim == mesh.dim." + ) + + self._n_components = int(n_components) + + if u_Field is None: + self.Unknowns.u = uw.discretisation.MeshVariable( + mesh=mesh, + num_components=(1, self._n_components), + varname="Umc{}".format(SNES_MultiComponent._obj_count), + vtype=uw.VarType.MATRIX, + degree=degree, + ) + else: + self.Unknowns.u = u_Field + + self.Unknowns.DuDt = DuDt + self.Unknowns.DFDt = DFDt + + self.verbose = verbose + self._tolerance = 1.0e-4 + + # PETSc options — mirror SNES_Vector defaults + self.petsc_options["snes_type"] = "newtonls" + self.petsc_options["ksp_rtol"] = 1.0e-3 + self.petsc_options["ksp_type"] = "gmres" + self.petsc_options["pc_type"] = "gamg" + self.petsc_options["pc_gamg_type"] = "agg" + self.petsc_options["pc_gamg_repartition"] = True + self.petsc_options["pc_mg_type"] = "additive" + self.petsc_options["pc_gamg_agg_nsmooths"] = 2 + self.petsc_options["snes_rtol"] = 1.0e-3 + self.petsc_options["mg_levels_ksp_max_it"] = 3 + self.petsc_options["mg_levels_ksp_converged_maxits"] = None + + if self.verbose == True: + self.petsc_options["ksp_monitor"] = None + self.petsc_options["snes_converged_reason"] = None + self.petsc_options["snes_monitor_short"] = None + else: + self.petsc_options.delValue("ksp_monitor") + self.petsc_options.delValue("snes_monitor") + self.petsc_options.delValue("snes_monitor_short") + self.petsc_options.delValue("snes_converged_reason") + + self.dm = None + self._U = self.Unknowns.u.sym + + self.essential_bcs = [] + self.natural_bcs = [] + self.bcs = self.essential_bcs + self.boundary_conditions = False + + self.is_setup = False + self._rebuild_after_mesh_update = self._build + self.mesh._equation_systems_register.append(self) + + # Counter used by tests to assert single-DM-build behaviour. + self._dm_build_count = 0 + + @property + def n_components(self): + """Number of scalar DOF components per node.""" + return self._n_components + + @property + def tolerance(self): + return self._tolerance + + @tolerance.setter + def tolerance(self, value): + self._tolerance = value + self.petsc_options["snes_rtol"] = self._tolerance + self.petsc_options["ksp_rtol"] = self._tolerance * 1.0e-1 + self.petsc_options["ksp_atol"] = self._tolerance * 1.0e-6 + + @timing.routine_timer_decorator + def _setup_discretisation(self, verbose=False): + mesh = self.mesh + + import xxhash + import numpy as np + + xxh = xxhash.xxh64() + xxh.update(np.ascontiguousarray(mesh.X.coords)) + mesh_dm_coord_hash = xxh.intdigest() + + if self.dm is not None and self.mesh_dm_coordinate_hash == mesh_dm_coord_hash: + if verbose and uw.mpi.rank == 0: + print(f"SNES_MultiComponent ({self.name}): Discretisation does not need to be rebuilt", flush=True) + return + + self.mesh_dm_coordinate_hash = mesh_dm_coord_hash + + cdef PtrContainer ext = self.compiled_extensions + + mesh = self.mesh + u_degree = self.u.degree + + if mesh.qdegree < u_degree: + print(f"Caution - the mesh quadrature ({mesh.qdegree})is lower") + print(f"than {u_degree} which is required by the {self.name} solver") + + self.dm_hierarchy = mesh.clone_dm_hierarchy() + self.dm = self.dm_hierarchy[-1] + + options = PETSc.Options() + options.setValue("private_{}_u_petscspace_degree".format(self.petsc_options_prefix), u_degree) + options.setValue("private_{}_u_petscdualspace_lagrange_continuity".format(self.petsc_options_prefix), self.u.continuous) + options.setValue("private_{}_u_petscdualspace_lagrange_node_endpoints".format(self.petsc_options_prefix), False) + + # KEY DIFFERENCE from SNES_Vector: n_components, not mesh.dim. + self.petsc_fe_u = PETSc.FE().createDefault( + mesh.dim, self._n_components, mesh.isSimplex, mesh.qdegree, + "private_{}_u_".format(self.petsc_options_prefix), PETSc.COMM_SELF, + ) + self.petsc_fe_u_id = self.dm.getNumFields() + self.dm.setField(self.petsc_fe_u_id, self.petsc_fe_u) + self.petsc_fe_u.setName("_multicomponent_unknown_") + + self.dm.createDS() + + cdef int ind=1 + cdef int [::1] comps_view + cdef DM cdm = self.dm + + for index, bc in enumerate(self.natural_bcs): + + if uw.mpi.rank == 0 and self.verbose: + print("Setting bc {} ({})".format(index, bc.type)) + print(" - field: {}".format(bc.f_id)) + print(" - component: {}".format(bc.components)) + print(" - boundary: {}".format(bc.boundary)) + print(" - fn: {} ".format(bc.fn_f)) + + boundary = bc.boundary + value = mesh.boundaries[bc.boundary].value + ind = value + + bc_label = self.dm.getLabel(boundary) + bc_is = bc_label.getStratumIS(value) + self.natural_bcs[index] = self.natural_bcs[index]._replace(boundary_label_val=value) + + bc_type = 6 + num_constrained_components = bc.components.shape[0] + comps_view = bc.components + bc = PetscDSAddBoundary_UW(cdm.dm, + bc_type, + str(boundary+f"{bc.components}").encode('utf8'), + "UW_Boundaries".encode('utf8'), + bc.f_id, + num_constrained_components, + &comps_view[0], + NULL, + NULL, + 1, + &ind, + NULL, ) + + self.natural_bcs[index] = self.natural_bcs[index]._replace(PETScID=bc, boundary_label_val=ind) + + for index, bc in enumerate(self.essential_bcs): + if uw.mpi.rank == 0 and self.verbose: + print("Setting bc {} ({})".format(index, bc.type)) + print(" - field: {}".format(bc.f_id)) + print(" - component: {}".format(bc.components)) + print(" - boundary: {}".format(bc.boundary)) + print(" - fn: {} ".format(bc.fn)) + + boundary = bc.boundary + value = mesh.boundaries[bc.boundary].value + ind = value + + bc_type = 5 + fn_index = self.ext_dict.ebc[sympy.Matrix([[bc.fn]]).as_immutable()] + num_constrained_components = bc.components.shape[0] + comps_view = bc.components + bc = PetscDSAddBoundary_UW(cdm.dm, + bc_type, + str(boundary+f"{bc.components}").encode('utf8'), + "UW_Boundaries".encode('utf8'), + bc.f_id, + num_constrained_components, + &comps_view[0], + ext.fns_bcs[fn_index], + NULL, + 1, + &ind, + NULL, ) + + self.essential_bcs[index] = self.essential_bcs[index]._replace(PETScID=bc, boundary_label_val=value) + + for coarse_dm in self.dm_hierarchy: + self.dm.copyFields(coarse_dm) + self.dm.copyDS(coarse_dm) + + self.is_setup = False + self._dm_build_count += 1 + + return + + @timing.routine_timer_decorator + def _setup_pointwise_functions(self, verbose=False, debug=False, debug_name=None): + import sympy + + if self.is_setup: + if verbose and uw.mpi.rank == 0: + print(f"SNES_MultiComponent ({self.name}): Pointwise functions do not need to be rebuilt", flush=True) + return + else: + if verbose and uw.mpi.rank == 0: + print(f"SNES_MultiComponent ({self.name}): Pointwise functions need to be built", flush=True) + + N = self.mesh.N + dim = self.mesh.dim + Nc = self._n_components + + sympy.core.cache.clear_cache() + + # User-provided expressions. + # F0 shape: (1, Nc) row matrix — per-component residual + # F1 shape: (Nc, dim) — per-component flux + F0_user = sympy.Matrix(self.F0.sym) + F1_user = sympy.Matrix(self.F1.sym) + + # Normalise F0 into an (Nc, 1) column for PETSc layout. + if F0_user.shape == (1, Nc): + f0_list = [F0_user[0, c] for c in range(Nc)] + elif F0_user.shape == (Nc, 1): + f0_list = [F0_user[c, 0] for c in range(Nc)] + elif F0_user.shape == (Nc,): + f0_list = [F0_user[c] for c in range(Nc)] + else: + raise ValueError( + f"F0 shape {F0_user.shape} does not match n_components={Nc}; " + "expected (1, Nc), (Nc, 1) or (Nc,)." + ) + + if F1_user.shape != (Nc, dim): + raise ValueError( + f"F1 shape {F1_user.shape} does not match (n_components, dim)=({Nc}, {dim})." + ) + + # Residuals: f0 as (Nc, 1) column, F1 as (Nc, dim). + # The JIT generator reads matrix shape to size the output buffer. + self._u_f0 = sympy.ImmutableDenseMatrix([[e] for e in f0_list]) + self._u_F1 = sympy.ImmutableDenseMatrix(F1_user) + fns_residual = [self._u_f0, self._u_F1] + + # Unknowns in PETSc-friendly flat form. + # U_list[c] = u-component c + # L[c, d] = ∂u_c / ∂x_d (already shape (Nc, dim) from Unknowns.u setter) + U_list = [self.u.sym[0, c] for c in range(Nc)] + L = self.Unknowns.L + + # ----- Explicit-differentiation Jacobian construction ----- + # PETSc's element-matrix assembly walks the Jacobian arrays in the + # order [test_component, trial_component, test_deriv, trial_deriv]. + # From `PetscFEUpdateElementMat_Internal` in fe.c: + # g0[fc * Nc + gc] + # g1[(fc * Nc + gc) * dim + df] + # g2[(fc * Nc + gc) * dim + df] + # g3[((fc * Nc + gc) * dim + df) * dim + dg] + # i.e. fc and gc are the two outer indices; df/dg are the derivative + # indices inside. Construct each Jacobian as a 2D sympy matrix with + # row = fc*Nc + gc and col = (df) or (df*dim + dg), then row-major + # flatten naturally matches PETSc's layout. + + # G0[fc*Nc + gc, 0] = ∂f0[fc] / ∂U[gc] + G0 = sympy.zeros(Nc, Nc) + for fc in range(Nc): + for gc in range(Nc): + G0[fc, gc] = sympy.diff(f0_list[fc], U_list[gc]) + + # G1[fc*Nc + gc, df] = ∂f0[fc] / ∂L[gc, df] + G1 = sympy.zeros(Nc * Nc, dim) + for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + G1[fc * Nc + gc, df] = sympy.diff(f0_list[fc], L[gc, df]) + + # G2[fc*Nc + gc, df] = ∂F1[fc, df] / ∂U[gc] + G2 = sympy.zeros(Nc * Nc, dim) + for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + G2[fc * Nc + gc, df] = sympy.diff(F1_user[fc, df], U_list[gc]) + + # G3[fc*Nc + gc, df*dim + dg] = ∂F1[fc, df] / ∂L[gc, dg] + G3 = sympy.zeros(Nc * Nc, dim * dim) + for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + for dg in range(dim): + G3[fc * Nc + gc, df * dim + dg] = sympy.diff(F1_user[fc, df], L[gc, dg]) + + self._G0 = sympy.ImmutableMatrix(G0) + self._G1 = sympy.ImmutableMatrix(G1) + self._G2 = sympy.ImmutableMatrix(G2) + self._G3 = sympy.ImmutableMatrix(G3) + + fns_jacobian = (self._G0, self._G1, self._G2, self._G3) + + fns_bd_residual = [] + fns_bd_jacobian = [] + + # Natural BCs. Expected shapes: fn_f is (Nc, 1) or (1, Nc) or (Nc,); + # fn_F (gradient term) is (Nc, dim) if provided. + for index, bc in enumerate(self.natural_bcs): + + if bc.fn_f is not None: + bd_F0_mat = sympy.Matrix(bc.fn_f) + if bd_F0_mat.shape == (1, Nc): + bd_f0_list = [bd_F0_mat[0, c] for c in range(Nc)] + elif bd_F0_mat.shape == (Nc, 1): + bd_f0_list = [bd_F0_mat[c, 0] for c in range(Nc)] + elif bd_F0_mat.shape == (Nc,): + bd_f0_list = [bd_F0_mat[c] for c in range(Nc)] + else: + raise ValueError( + f"Natural BC fn_f shape {bd_F0_mat.shape} != n_components={Nc}." + ) + + bd_f0 = sympy.ImmutableDenseMatrix([[e] for e in bd_f0_list]) + bc.fns["u_f0"] = bd_f0 + + bd_G0 = sympy.zeros(Nc, Nc) + bd_G1 = sympy.zeros(Nc * Nc, dim) + for fc in range(Nc): + for gc in range(Nc): + bd_G0[fc, gc] = sympy.diff(bd_f0_list[fc], U_list[gc]) + for df in range(dim): + bd_G1[fc * Nc + gc, df] = sympy.diff(bd_f0_list[fc], L[gc, df]) + + bc.fns["uu_G0"] = sympy.ImmutableMatrix(bd_G0) + bc.fns["uu_G1"] = sympy.ImmutableMatrix(bd_G1) + + fns_bd_residual += [bc.fns["u_f0"]] + fns_bd_jacobian += [bc.fns["uu_G0"], bc.fns["uu_G1"]] + + if hasattr(bc, 'fn_F') and bc.fn_F is not None: + bd_F1 = sympy.Matrix(bc.fn_F) + if bd_F1.shape != (Nc, dim): + raise ValueError( + f"Natural BC fn_F shape {bd_F1.shape} != (n_components, dim)=({Nc}, {dim})." + ) + bc.fns["u_F1"] = sympy.ImmutableDenseMatrix(bd_F1) + fns_bd_residual += [bc.fns["u_F1"]] + + bd_G2 = sympy.zeros(Nc * Nc, dim) + bd_G3 = sympy.zeros(Nc * Nc, dim * dim) + for fc in range(Nc): + for gc in range(Nc): + for df in range(dim): + bd_G2[fc * Nc + gc, df] = sympy.diff(bd_F1[fc, df], U_list[gc]) + for dg in range(dim): + bd_G3[fc * Nc + gc, df * dim + dg] = sympy.diff(bd_F1[fc, df], L[gc, dg]) + + bc.fns["uu_G2"] = sympy.ImmutableMatrix(bd_G2) + bc.fns["uu_G3"] = sympy.ImmutableMatrix(bd_G3) + fns_bd_jacobian += [bc.fns["uu_G2"], bc.fns["uu_G3"]] + + self._fns_bd_residual = fns_bd_residual + self._fns_bd_jacobian = fns_bd_jacobian + + prim_field_list = [self.u,] + _getext_result = getext( + self.mesh, + JITCallbackSet( + residual=tuple(fns_residual), + bcs=tuple(x.fn for x in self.essential_bcs), + jacobian=tuple(fns_jacobian), + bd_residual=tuple(fns_bd_residual), + bd_jacobian=tuple(fns_bd_jacobian), + ), + prim_field_list, + verbose=verbose, + debug=debug, + ) + self.compiled_extensions = _getext_result.ptrobj + self.ext_dict = _getext_result.fn_dicts + self.constants_manifest = _getext_result.constants_manifest + + cdef PtrContainer ext = self.compiled_extensions + + return + + @timing.routine_timer_decorator + def _setup_solver(self, verbose=False): + + if self.is_setup == True: + if verbose and uw.mpi.rank == 0: + print(f"SNES_MultiComponent ({self.name}): SNES solver does not need to be rebuilt", flush=True) + return + + cdef int ind=1 + cdef int [::1] comps_view + cdef DM cdm = self.dm + cdef DS ds = self.dm.getDS() + cdef PtrContainer ext = self.compiled_extensions + + i_res = self.ext_dict.res + + PetscDSSetResidual(ds.ds, 0, ext.fns_residual[i_res[self._u_f0]], ext.fns_residual[i_res[self._u_F1]]) + + i_jac = self.ext_dict.jac + PetscDSSetJacobian(ds.ds, 0, 0, + ext.fns_jacobian[i_jac[self._G0]], + ext.fns_jacobian[i_jac[self._G1]], + ext.fns_jacobian[i_jac[self._G2]], + ext.fns_jacobian[i_jac[self._G3]], + ) + + cdef DMLabel c_label + + for bc in self.natural_bcs: + boundary = bc.boundary + boundary_id = bc.PETScID + + value = self.mesh.boundaries[bc.boundary].value + bc_label = self.dm.getLabel("UW_Boundaries") + label_val = value + + i_bd_res = self.ext_dict.bd_res + i_bd_jac = self.ext_dict.bd_jac + + c_label = bc_label + + if bc.fn_f is not None: + _has_f1 = "u_F1" in bc.fns + + if _has_f1: + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, + ext.fns_bd_residual[i_bd_res[bc.fns["u_f0"]]], + ext.fns_bd_residual[i_bd_res[bc.fns["u_F1"]]], + ) + else: + UW_PetscDSSetBdResidual(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, + ext.fns_bd_residual[i_bd_res[bc.fns["u_f0"]]], + NULL, + ) + + if _has_f1: + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]], + ) + else: + UW_PetscDSSetBdJacobian(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + NULL, NULL, + ) + + if _has_f1: + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G2"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G3"]]], + ) + else: + UW_PetscDSSetBdJacobianPreconditioner(ds.ds, c_label.dmlabel, label_val, boundary_id, + 0, 0, 0, + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G0"]]], + ext.fns_bd_jacobian[i_bd_jac[bc.fns["uu_G1"]]], + NULL, NULL, + ) + + if verbose: + print(f"Weak form (DS)", flush=True) + UW_PetscDSViewWF(ds.ds) + print(f"=============", flush=True) + + print(f"Weak form(s) (Natural Boundaries)", flush=True) + for boundary in self.natural_bcs: + UW_PetscDSViewBdWF(ds.ds, boundary.PETScID) + + self._set_constants_on_ds(ds) + + for coarse_dm in self.dm_hierarchy: + self.dm.copyFields(coarse_dm) + self.dm.copyDS(coarse_dm) + + for coarse_dm in self.dm_hierarchy: + coarse_dm.createClosureIndex(None) + + self.dm.setUp() + + self.snes = PETSc.SNES().create(PETSc.COMM_WORLD) + self.snes.setDM(self.dm) + self.snes.setOptionsPrefix(self.petsc_options_prefix) + self.snes.setFromOptions() + + cdef DM dm = self.dm + UW_DMPlexSetSNESLocalFEM(dm.dm, PETSC_FALSE, NULL) + + self.is_setup = True + self.constitutive_model._solver_is_setup = True + + @timing.routine_timer_decorator + def solve(self, + zero_init_guess: bool = True, + _force_setup: bool = False, + verbose=False, + debug=False, + debug_name=None, + ): + """Solve the multi-component SNES problem. + + Collective across all MPI ranks. The solution is written back to + ``self.u.vec`` and made available through ``self.u.array``. + """ + + if _force_setup or not self.constitutive_model._solver_is_setup: + self.is_setup = False + + self._build(verbose, debug, debug_name) + + gvec = self.dm.getGlobalVec() + + if not zero_init_guess: + self.dm.localToGlobal(self.u.vec, gvec) + else: + gvec.array[:] = 0. + + self.mesh.update_lvec() + cdef DM dm = self.dm + cdef Vec cmesh_lvec + cmesh_lvec = self.mesh.lvec + ierr = DMSetAuxiliaryVec_UW(dm.dm, NULL, 0, 0, cmesh_lvec.vec); CHKERRQ(ierr) + + self._update_constants() + + self.snes.solve(None, gvec) + + lvec = self.dm.getLocalVec() + cdef Vec clvec = lvec + self.dm.globalToLocal(gvec, lvec) + if verbose: + print(f"{uw.mpi.rank}: Copy solution / bcs to user variables", flush=True) + + ierr = DMPlexSNESComputeBoundaryFEM(dm.dm, clvec.vec, NULL); CHKERRQ(ierr) + self.u.vec.array[:] = lvec.array[:] + self.mesh._stale_lvec = True + + target_var = getattr(self.u, "_base_var", self.u) + target_var._sync_lvec_to_gvec() + if hasattr(target_var, "_canonical_data"): + target_var._canonical_data = None + + self.dm.restoreLocalVec(lvec) + self.dm.restoreGlobalVec(gvec) + + self._warn_on_divergence() + + return + + def _object_viewer(self): + from IPython.display import Latex, Markdown, display + + f0 = self.F0.sym + F1 = self.F1.sym + + eqF1 = "$\\tiny \\quad \\nabla \\cdot \\color{Blue}" + sympy.latex(F1) + "$ + " + eqf0 = "$\\tiny \\phantom{ \\quad \\nabla \\cdot} \\color{DarkRed}" + sympy.latex(f0) + "\\color{Black} = 0 $" + + display( + Markdown(f"# Underworld / PETSc General Multi-Component Solver ({self._n_components} components)"), + Markdown(f"Primary problem: "), + Latex(eqF1), Latex(eqf0), + ) + +### ================================= + class SNES_Stokes_SaddlePt(SolverBaseClass): r""" Saddle point equation solver for constrained problems using PETSc SNES. diff --git a/src/underworld3/systems/__init__.py b/src/underworld3/systems/__init__.py index fa0160ba0..0c66d57cc 100644 --- a/src/underworld3/systems/__init__.py +++ b/src/underworld3/systems/__init__.py @@ -42,6 +42,7 @@ SNES_Scalar, SNES_Vector, SNES_Stokes_SaddlePt, + SNES_MultiComponent, ) from .solvers import SNES_Poisson as Poisson @@ -51,6 +52,7 @@ from .solvers import SNES_Projection as Projection from .solvers import SNES_Vector_Projection as Vector_Projection from .solvers import SNES_Tensor_Projection as Tensor_Projection +from .solvers import SNES_MultiComponent_Projection as MultiComponent_Projection # from .solvers import SNES_Solenoidal_Vector_Projection as Solenoidal_Vector_Projection ## WIP / maybe some issues # from .solvers import ( diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index 3f55c6447..ab18b4838 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -59,6 +59,7 @@ import underworld3 as uw from underworld3.systems import SNES_Scalar, SNES_Vector, SNES_Stokes_SaddlePt +from underworld3.cython.generic_solvers import SNES_MultiComponent from underworld3 import VarType import underworld3.timing as timing from underworld3.utilities._api_tools import ( @@ -2204,6 +2205,105 @@ def uw_scalar_function(self, user_uw_function): self._uw_scalar_function = user_uw_function +class SNES_MultiComponent_Projection(SNES_MultiComponent): + r""" + Multi-component projection solver. + + Projects an N-component row-matrix expression onto an N-component + mesh variable in a **single** SNES solve, sharing one DM across all + components. Replaces the per-component cycling used by + :class:`SNES_Tensor_Projection`, which tears down and rebuilds the + PETSc DM on every inner iteration. + + The projection is block-diagonal across components: each component + satisfies the scalar problem + + .. math:: + + -\nabla \cdot \left[ \alpha \nabla u_k \right] + - \left[ u_k - \tilde f_k \right] = 0 + + with no cross-component coupling. Setting :math:`\alpha = 0` gives a + pure L2 projection per component. + + Parameters + ---------- + mesh : Mesh + u_Field : MeshVariable, optional + Target ``(1, n_components)`` MATRIX variable. If ``None``, one is + created. + n_components : int, optional + Number of scalar components; required if ``u_Field`` is ``None``. + degree : int, default=2 + verbose : bool, default=False + + See Also + -------- + SNES_Projection : Scalar projection (Nc=1). + SNES_Tensor_Projection : Legacy per-component cycling projector. + """ + + @timing.routine_timer_decorator + def __init__( + self, + mesh: uw.discretisation.Mesh, + u_Field: uw.discretisation.MeshVariable = None, + n_components: int = None, + degree=2, + verbose=False, + ): + super().__init__( + mesh, + u_Field=u_Field, + n_components=n_components, + degree=degree, + verbose=verbose, + ) + + self.is_setup = False + self._smoothing = sympify(0) + self._uw_weighting_function = sympify(1) + self._uw_function = sympy.zeros(1, self._n_components) + self._constitutive_model = uw.constitutive_models.Constitutive_Model(self.Unknowns) + + F0 = Template( + r"f_0 \left( \mathbf{u} \right)", + lambda self: (self.u.sym - self.uw_function) * self.uw_weighting_function, + "Per-component projection misfit (row matrix shape (1, Nc)).", + ) + + F1 = Template( + r"\mathbf{F}_1 \left( \mathbf{u} \right)", + lambda self: self.smoothing * self.Unknowns.L, + "Per-component block-diagonal Laplacian smoothing (shape (Nc, dim)).", + ) + + uw_function = SymbolicProperty( + matrix_wrap=True, + doc="Row matrix (1, n_components) of expressions to project.", + ) + + @property + def smoothing(self): + """Smoothing regularisation parameter.""" + return self._smoothing + + @smoothing.setter + def smoothing(self, value): + self.is_setup = False + self._smoothing = sympify(value) + + @property + def uw_weighting_function(self): + """Weighting function applied during projection.""" + return self._uw_weighting_function + + @uw_weighting_function.setter + def uw_weighting_function(self, value): + self.is_setup = False + self._uw_weighting_function = value + + # ################################################# # # Swarm-based advection-diffusion # # solver based on SNES_Poisson and swarm-variable diff --git a/tests/test_multicomponent_projection.py b/tests/test_multicomponent_projection.py new file mode 100644 index 000000000..27674604b --- /dev/null +++ b/tests/test_multicomponent_projection.py @@ -0,0 +1,322 @@ +"""Validation tests for SNES_MultiComponent_Projection. + +The multi-component projector solves all N components in a single SNES +solve sharing one DM, replacing the per-component cycling of +SNES_Tensor_Projection. These tests confirm equivalence with the legacy +solvers and check the DM-rebuild economics. +""" + +import math + +import numpy as np +import pytest +import sympy + +import underworld3 as uw + + +# --- helpers ---------------------------------------------------------------- + + +def _structured_box(res=(8, 8)): + return uw.meshing.StructuredQuadBox(elementRes=res) + + +# --- tests ------------------------------------------------------------------ + + +@pytest.mark.level_1 +@pytest.mark.tier_a +def test_multicomponent_matches_scalar_at_nc_one(): + """Nc=1 multi-component projection agrees with SNES_Projection.""" + mesh = _structured_box() + x, y = mesh.X + + # Scalar reference. + scalar_var = uw.discretisation.MeshVariable( + "scalar_ref", mesh, 1, vtype=uw.VarType.SCALAR, degree=2, continuous=True + ) + ref = uw.systems.Projection(mesh, u_Field=scalar_var, degree=2) + ref.tolerance = 1e-10 + ref.uw_function = sympy.sin(x) * sympy.cos(y) + ref.smoothing = 0.0 + ref.solve() + + # N=1 multi-component. + mc = uw.systems.MultiComponent_Projection(mesh, n_components=1, degree=2) + mc.tolerance = 1e-10 + mc.uw_function = sympy.Matrix([[sympy.sin(x) * sympy.cos(y)]]) + mc.smoothing = 0.0 + mc.solve() + + ref_vals = ref.u.array[:, 0, 0] + mc_vals = mc.u.array[:, 0, 0] + + assert ref_vals.shape == mc_vals.shape + diff = np.linalg.norm(ref_vals - mc_vals) / np.linalg.norm(ref_vals) + assert diff < 1e-7, ( + f"Nc=1 multi-component differs from SNES_Projection by rel-L2 {diff:.3e}" + ) + + +@pytest.mark.level_1 +@pytest.mark.tier_a +def test_multicomponent_matches_tensor_projection_sym2d(): + """Nc=3 multi-component projection agrees with SNES_Tensor_Projection (2D sym).""" + mesh = _structured_box() + x, y = mesh.X + + # Legacy: SYM_TENSOR + cycling tensor projector. + tensor_var = uw.discretisation.MeshVariable( + "tensor_ref", + mesh, + (mesh.dim, mesh.dim), + vtype=uw.VarType.SYM_TENSOR, + degree=2, + continuous=True, + ) + work_var = uw.discretisation.MeshVariable( + "tensor_work", mesh, 1, degree=2, continuous=True + ) + flux_xx = x * y + 1 + flux_xy = x - y + flux_yy = sympy.sin(x) * sympy.cos(y) + flux_full = sympy.Matrix([[flux_xx, flux_xy], [flux_xy, flux_yy]]) + + legacy = uw.systems.Tensor_Projection( + mesh, tensor_Field=tensor_var, scalar_Field=work_var, degree=2 + ) + legacy.tolerance = 1e-10 + legacy.uw_function = flux_full + legacy.smoothing = 0.0 + legacy.solve() + + # New: 3-component multi-component projection (unpacked sym-tensor). + mc = uw.systems.MultiComponent_Projection(mesh, n_components=3, degree=2) + mc.tolerance = 1e-10 + mc.uw_function = sympy.Matrix([[flux_xx, flux_xy, flux_yy]]) + mc.smoothing = 0.0 + mc.solve() + + # Compare legacy [i,j] against mc[0,k] for the three indep indices. + indep = [(0, 0), (0, 1), (1, 1)] + for k, (i, j) in enumerate(indep): + legacy_vals = tensor_var.array[:, i, j] + mc_vals = mc.u.array[:, 0, k] + rel = np.linalg.norm(legacy_vals - mc_vals) / max( + np.linalg.norm(legacy_vals), 1e-30 + ) + assert rel < 1e-7, ( + f"Component ({i},{j}) differs rel-L2 {rel:.3e} between " + f"Tensor_Projection and MultiComponent_Projection" + ) + + +@pytest.mark.level_1 +@pytest.mark.tier_a +def test_multicomponent_dm_builds_scale_with_outer_solves(): + """DM build count scales with outer solves, not Nc × outer solves. + + The legacy SNES_Tensor_Projection performs Nc DM rebuilds per outer + call (one per scalar component). SNES_MultiComponent_Projection should + rebuild the DM *at most once* per outer call. + """ + mesh = _structured_box() + x, y = mesh.X + + mc = uw.systems.MultiComponent_Projection(mesh, n_components=3, degree=2) + + n_solves = 5 + for k in range(n_solves): + mc.uw_function = sympy.Matrix( + [[k * x, k * y, sympy.sin(x + k)]] + ) + mc.smoothing = 0.0 + mc.solve() + + # Exactly n_solves rebuilds is the current behaviour (is_setup=False on + # uw_function change). The important invariant is: not Nc × n_solves. + assert mc._dm_build_count <= n_solves, ( + f"Expected at most {n_solves} DM builds across {n_solves} solves " + f"(n_components=3), got {mc._dm_build_count}." + ) + + +@pytest.mark.level_1 +@pytest.mark.tier_a +def test_multicomponent_matches_tensor_projection_full2d(): + """Nc=4 multi-component projection agrees with Tensor_Projection (2D non-sym). + + The legacy SNES_Tensor_Projection will cycle all four (i,j) entries — + the new solver projects them together in a single DM. + """ + mesh = _structured_box() + x, y = mesh.X + + tensor_var = uw.discretisation.MeshVariable( + "tensor_full", + mesh, + (mesh.dim, mesh.dim), + vtype=uw.VarType.TENSOR, + degree=2, + continuous=True, + ) + work_var = uw.discretisation.MeshVariable( + "tensor_full_work", mesh, 1, degree=2, continuous=True + ) + flux_full = sympy.Matrix( + [[x * y, x - y], [sympy.sin(x), sympy.cos(y)]] + ) + + legacy = uw.systems.Tensor_Projection( + mesh, tensor_Field=tensor_var, scalar_Field=work_var, degree=2 + ) + legacy.tolerance = 1e-10 + legacy.uw_function = flux_full + legacy.smoothing = 0.0 + legacy.solve() + + mc = uw.systems.MultiComponent_Projection(mesh, n_components=4, degree=2) + mc.tolerance = 1e-10 + mc.uw_function = sympy.Matrix( + [[flux_full[0, 0], flux_full[0, 1], flux_full[1, 0], flux_full[1, 1]]] + ) + mc.smoothing = 0.0 + mc.solve() + + index_map = [(0, 0), (0, 1), (1, 0), (1, 1)] + for k, (i, j) in enumerate(index_map): + legacy_vals = tensor_var.array[:, i, j] + mc_vals = mc.u.array[:, 0, k] + rel = np.linalg.norm(legacy_vals - mc_vals) / max( + np.linalg.norm(legacy_vals), 1e-30 + ) + assert rel < 1e-7, ( + f"Full-tensor component ({i},{j}) differs rel-L2 {rel:.3e}" + ) + + +@pytest.mark.level_1 +@pytest.mark.tier_a +@pytest.mark.parametrize("smoothing", [1e-4, 1e-2, 1.0]) +def test_multicomponent_matches_scalar_with_smoothing(smoothing): + """Non-zero smoothing: Nc=1 multi-component matches SNES_Projection. + + Exercises the F1 (Laplacian) pathway and the G2/G3 Jacobian blocks + that `smoothing=0` skips entirely. + """ + mesh = _structured_box() + x, y = mesh.X + target = sympy.sin(2 * x) * sympy.cos(2 * y) + x * y + + scalar_var = uw.discretisation.MeshVariable( + f"scalar_ref_sm_{int(smoothing*1e6)}", mesh, 1, + vtype=uw.VarType.SCALAR, degree=2, continuous=True, + ) + ref = uw.systems.Projection(mesh, u_Field=scalar_var, degree=2) + ref.tolerance = 1e-10 + ref.uw_function = target + ref.smoothing = smoothing + ref.solve() + + mc = uw.systems.MultiComponent_Projection(mesh, n_components=1, degree=2) + mc.tolerance = 1e-10 + mc.uw_function = sympy.Matrix([[target]]) + mc.smoothing = smoothing + mc.solve() + + ref_vals = ref.u.array[:, 0, 0] + mc_vals = mc.u.array[:, 0, 0] + rel = np.linalg.norm(ref_vals - mc_vals) / np.linalg.norm(ref_vals) + assert rel < 1e-6, ( + f"Nc=1 differs from SNES_Projection at smoothing={smoothing}: " + f"rel-L2 {rel:.3e}" + ) + + +@pytest.mark.level_1 +@pytest.mark.tier_a +@pytest.mark.parametrize("smoothing", [1e-4, 1e-2]) +def test_multicomponent_matches_tensor_sym2d_with_smoothing(smoothing): + """Non-zero smoothing: Nc=3 sym-tensor matches SNES_Tensor_Projection. + + SNES_Tensor_Projection also applies per-component scalar smoothing, + so this is a direct apples-to-apples check of the Laplacian blocks + for multiple components. + """ + mesh = _structured_box() + x, y = mesh.X + flux_xx = x * y + 1 + flux_xy = sympy.sin(x) - y + flux_yy = sympy.cos(x) + x * y + flux_full = sympy.Matrix([[flux_xx, flux_xy], [flux_xy, flux_yy]]) + + tag = int(smoothing * 1e6) + tensor_var = uw.discretisation.MeshVariable( + f"tensor_ref_sm_{tag}", mesh, (mesh.dim, mesh.dim), + vtype=uw.VarType.SYM_TENSOR, degree=2, continuous=True, + ) + work_var = uw.discretisation.MeshVariable( + f"tensor_ref_sm_work_{tag}", mesh, 1, degree=2, continuous=True, + ) + + legacy = uw.systems.Tensor_Projection( + mesh, tensor_Field=tensor_var, scalar_Field=work_var, degree=2, + ) + legacy.tolerance = 1e-10 + legacy.uw_function = flux_full + legacy.smoothing = smoothing + legacy.solve() + + mc = uw.systems.MultiComponent_Projection(mesh, n_components=3, degree=2) + mc.tolerance = 1e-10 + mc.uw_function = sympy.Matrix([[flux_xx, flux_xy, flux_yy]]) + mc.smoothing = smoothing + mc.solve() + + indep = [(0, 0), (0, 1), (1, 1)] + for k, (i, j) in enumerate(indep): + legacy_vals = tensor_var.array[:, i, j] + mc_vals = mc.u.array[:, 0, k] + rel = np.linalg.norm(legacy_vals - mc_vals) / max( + np.linalg.norm(legacy_vals), 1e-30 + ) + assert rel < 1e-6, ( + f"smoothing={smoothing}, ({i},{j}): rel-L2 {rel:.3e}" + ) + + +@pytest.mark.level_1 +@pytest.mark.tier_a +def test_multicomponent_smoothing_reduces_high_frequencies(): + """Smoking test: large smoothing damps high-frequency content, as expected. + + Projects a high-wavenumber target; the smoothed projection should + have strictly smaller L2 norm than the unsmoothed one. This is a + qualitative sanity check that the smoothing term is active (not + silently dropped). + """ + mesh = _structured_box(res=(16, 16)) + x, y = mesh.X + high_freq = sympy.sin(10 * x) * sympy.cos(10 * y) + target = sympy.Matrix([[high_freq, 2 * high_freq, 0.5 * high_freq]]) + + mc_smooth = uw.systems.MultiComponent_Projection(mesh, n_components=3, degree=2) + mc_smooth.tolerance = 1e-10 + mc_smooth.uw_function = target + mc_smooth.smoothing = 1e-1 + mc_smooth.solve() + + mc_raw = uw.systems.MultiComponent_Projection(mesh, n_components=3, degree=2) + mc_raw.tolerance = 1e-10 + mc_raw.uw_function = target + mc_raw.smoothing = 0.0 + mc_raw.solve() + + for k in range(3): + norm_smooth = np.linalg.norm(mc_smooth.u.array[:, 0, k]) + norm_raw = np.linalg.norm(mc_raw.u.array[:, 0, k]) + assert norm_smooth < norm_raw, ( + f"Component {k}: smoothed norm {norm_smooth:.4e} is not less " + f"than unsmoothed {norm_raw:.4e} — smoothing appears inactive." + ) diff --git a/tests/test_snes_vector_asymmetric_jacobian.py b/tests/test_snes_vector_asymmetric_jacobian.py new file mode 100644 index 000000000..0cd74d56e --- /dev/null +++ b/tests/test_snes_vector_asymmetric_jacobian.py @@ -0,0 +1,121 @@ +"""SNES_Vector Jacobian regression test — asymmetric F1. + +Guards against the `[fc, df, gc, dg]` vs `[fc, gc, df, dg]` layout bug +documented in `docs/developer/subsystems/petsc-jacobian-layout.md`. + +Every current production consumer of `SNES_Vector` uses an F1 that is +symmetric under the trial-index swap `(gc, dg) ↔ (dg, gc)` — e.g. +strain-rate-based smoothing `Unknowns.E`, or deviatoric Stokes stress — +which hides a Jacobian-layout bug. This test constructs a consumer +whose F1 is *asymmetric* (raw gradient `Unknowns.L`, not symmetrised) +so the bug, if present, shows up immediately. + +With the explicit-index construction in place, components given +identical targets should produce identical solutions. +""" + +import numpy as np +import pytest +import sympy + +import underworld3 as uw +from underworld3.utilities._api_tools import Template + + +class _RawLSmoothingProjection(uw.systems.Vector_Projection): + """SNES_Vector_Projection subclass with non-symmetric L-based smoothing. + + Standard ``Vector_Projection.F1`` uses ``self.Unknowns.E`` (symmetric + strain rate) which hides Jacobian-layout bugs. Here we use the raw + Jacobian ``L`` directly — no symmetrisation — so the Jacobian + ``∂F1[i,j]/∂L[k,l] = smoothing·δ_ik·δ_jl`` has no `(k,l)↔(l,k)` + symmetry, and an incorrect `[fc, df, gc, dg]` layout shows up as + spurious cross-component coupling. + """ + + F1 = Template( + r"F1_{\mathrm{raw}-L}", + lambda self: self.smoothing * self.Unknowns.L, + "Raw gradient smoothing, not symmetrised.", + ) + + +@pytest.mark.level_1 +@pytest.mark.tier_a +@pytest.mark.parametrize("smoothing", [1e-4, 1e-2, 1e-1]) +def test_snes_vector_asymmetric_f1_components_decouple(smoothing): + """Identical targets in each component must give identical solutions. + + Cross-component coupling introduced by an incorrect Jacobian layout + would show up as different component values at non-zero smoothing. + """ + mesh = uw.meshing.StructuredQuadBox(elementRes=(8, 8)) + x, y = mesh.X + same_target = sympy.sin(x) * sympy.cos(y) + + vp = _RawLSmoothingProjection(mesh, degree=2) + vp.tolerance = 1e-10 + vp.petsc_options["snes_type"] = "ksponly" + vp.petsc_options["ksp_type"] = "preonly" + vp.petsc_options["pc_type"] = "lu" + vp.uw_function = sympy.Matrix([[same_target, same_target]]) + vp.smoothing = smoothing + vp.solve() + + arr = np.asarray(vp.u.array) + u0 = arr[:, 0, 0] + u1 = arr[:, 0, 1] + rel = np.linalg.norm(u0 - u1) / max(np.linalg.norm(u0), 1e-30) + assert rel < 1e-8, ( + f"Asymmetric-F1 SNES_Vector at smoothing={smoothing}: components " + f"with identical targets differ by rel-L2 {rel:.3e} — suggests a " + f"Jacobian layout bug. See docs/developer/subsystems/" + f"petsc-jacobian-layout.md." + ) + + +@pytest.mark.level_1 +@pytest.mark.tier_a +@pytest.mark.parametrize("smoothing", [1e-4, 1e-2, 1e-1]) +def test_snes_vector_asymmetric_f1_matches_multicomponent(smoothing): + """SNES_Vector with raw-L F1 must agree with SNES_MultiComponent_Projection. + + The multi-component projector builds its Jacobians by explicit + per-entry construction and is independently tested. If SNES_Vector's + layout is wrong, the two will disagree. + """ + mesh = uw.meshing.StructuredQuadBox(elementRes=(8, 8)) + x, y = mesh.X + + # Two *different* targets — more sensitive than identical targets. + target_0 = sympy.sin(x) * sympy.cos(y) + target_1 = sympy.cos(x) - 2 * y + + vp = _RawLSmoothingProjection(mesh, degree=2) + vp.tolerance = 1e-10 + vp.petsc_options["snes_type"] = "ksponly" + vp.petsc_options["ksp_type"] = "preonly" + vp.petsc_options["pc_type"] = "lu" + vp.uw_function = sympy.Matrix([[target_0, target_1]]) + vp.smoothing = smoothing + vp.solve() + vp_arr = np.asarray(vp.u.array) + + mc = uw.systems.MultiComponent_Projection(mesh, n_components=2, degree=2) + mc.tolerance = 1e-10 + mc.petsc_options["snes_type"] = "ksponly" + mc.petsc_options["ksp_type"] = "preonly" + mc.petsc_options["pc_type"] = "lu" + mc.uw_function = sympy.Matrix([[target_0, target_1]]) + mc.smoothing = smoothing + mc.solve() + mc_arr = np.asarray(mc.u.array) + + for k in range(2): + rel = np.linalg.norm(vp_arr[:, 0, k] - mc_arr[:, 0, k]) / max( + np.linalg.norm(mc_arr[:, 0, k]), 1e-30 + ) + assert rel < 1e-8, ( + f"smoothing={smoothing}, component {k}: SNES_Vector differs " + f"from SNES_MultiComponent_Projection by rel-L2 {rel:.3e}." + ) From 112881ba09316af83992c0fa96da5745e7ba2f45 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Tue, 21 Apr 2026 09:40:37 +1000 Subject: [PATCH 101/537] Wire SNES_MultiComponent_Projection into DDt stress projection MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The VE Stokes solver's stress projection was still using the per-component SNES_Tensor_Projection via the DDt's _psi_star_projection_solver, even though the base class tau property was updated in #124. The VE solve path goes through: VE_Stokes.solve() → DFDt._psi_star_projection_solver → SNES_Tensor_Projection This bypasses the base class SolverBaseClass.tau which had the multicomponent projector. Fixed by: 1. Both Lagrangian_DDt._setup_projections and SemiLagrangian.__init__ now create SNES_MultiComponent_Projection for SYM_TENSOR/TENSOR types 2. VE_Stokes.solve() flattens the flux to (1, Nc) and fans results back 3. All uw_function assignment points (psi_fn setter, initialise_history fallback) flatten tensors for the multicomponent solver Result: 99-step VE benchmark drops from 515s to 206s (2.5x speedup). Projection rebuilds: 300 → 100 (one per step instead of three). Numerical result identical (L2 = 1.89e-3). Underworld development team with AI support from Claude Code --- src/underworld3/systems/ddt.py | 110 ++++++++++++++++++++++++----- src/underworld3/systems/solvers.py | 23 +++++- 2 files changed, 111 insertions(+), 22 deletions(-) diff --git a/src/underworld3/systems/ddt.py b/src/underworld3/systems/ddt.py index 64c10b255..289c47584 100644 --- a/src/underworld3/systems/ddt.py +++ b/src/underworld3/systems/ddt.py @@ -746,19 +746,45 @@ def _setup_projections(self): self.mesh, self.psi_star[0], verbose=False ) elif self.vtype == uw.VarType.SYM_TENSOR or self.vtype == uw.VarType.TENSOR: - self._WorkVar = uw.discretisation.MeshVariable( - f"W_star_Eulerian_{self.instance_number}", + import math + dim = self.mesh.dim + if self.vtype == uw.VarType.SYM_TENSOR: + Nc = math.comb(dim + 1, 2) # 3 in 2D, 6 in 3D + self._psi_star_indep_indices = [ + (i, j) for i in range(dim) for j in range(i, dim) + ] + else: + Nc = dim * dim + self._psi_star_indep_indices = [ + (i, j) for i in range(dim) for j in range(dim) + ] + + self._psi_star_flat_var = uw.discretisation.MeshVariable( + f"psi_star_flat_{self.instance_number}", self.mesh, - vtype=uw.VarType.SCALAR, + (1, Nc), + vtype=uw.VarType.MATRIX, degree=self.degree, continuous=self.continuous, - varsymbol=r"W^{*}", + varsymbol=r"{\psi^{*}_{\mathrm{flat}}}", ) - self._psi_star_projection_solver = uw.systems.solvers.SNES_Tensor_Projection( - self.mesh, self.psi_star[0], self._WorkVar, verbose=False + self._psi_star_projection_solver = uw.systems.solvers.SNES_MultiComponent_Projection( + self.mesh, + u_Field=self._psi_star_flat_var, + n_components=Nc, + degree=self.degree, + verbose=False, ) - - self._psi_star_projection_solver.uw_function = self.psi_fn + self._psi_star_use_multicomponent = True + + if getattr(self, '_psi_star_use_multicomponent', False): + # Flatten tensor to (1, Nc) row for multicomponent solver + import sympy + indep = self._psi_star_indep_indices + row = sympy.Matrix([[self.psi_fn[i, j] for (i, j) in indep]]) + self._psi_star_projection_solver.uw_function = row + else: + self._psi_star_projection_solver.uw_function = self.psi_fn self._psi_star_projection_solver.bcs = self.bcs self._psi_star_projection_solver.smoothing = self.smoothing @@ -1120,22 +1146,48 @@ def __init__( ) elif vtype == uw.VarType.SYM_TENSOR or vtype == uw.VarType.TENSOR: - self._WorkVarTP = uw.discretisation.MeshVariable( - f"W_star_slcn_{self.instance_number}", + import math + dim = self.mesh.dim + if vtype == uw.VarType.SYM_TENSOR: + Nc = math.comb(dim + 1, 2) + self._psi_star_indep_indices = [ + (i, j) for i in range(dim) for j in range(i, dim) + ] + else: + Nc = dim * dim + self._psi_star_indep_indices = [ + (i, j) for i in range(dim) for j in range(dim) + ] + + self._psi_star_flat_var = uw.discretisation.MeshVariable( + f"psi_star_flat_slcn_{self.instance_number}", self.mesh, - vtype=uw.VarType.SCALAR, + (1, Nc), + vtype=uw.VarType.MATRIX, degree=degree, continuous=continuous, - varsymbol=r"W^{*}", + varsymbol=r"{\psi^{*}_{\mathrm{flat}}}", ) - self._psi_star_projection_solver = uw.systems.solvers.SNES_Tensor_Projection( - self.mesh, self.psi_star[0], self._WorkVarTP, verbose=False + self._psi_star_projection_solver = uw.systems.solvers.SNES_MultiComponent_Projection( + self.mesh, + u_Field=self._psi_star_flat_var, + n_components=Nc, + degree=degree, + verbose=False, ) + self._psi_star_use_multicomponent = True # We should find a way to add natural bcs here # (self.Unknowns.u carried as a symbol from solver to solver) - self._psi_star_projection_solver.uw_function = self._workVar.sym + if getattr(self, '_psi_star_use_multicomponent', False): + import sympy + indep = self._psi_star_indep_indices + fn = self._workVar.sym + row = sympy.Matrix([[fn[i, j] for (i, j) in indep]]) + self._psi_star_projection_solver.uw_function = row + else: + self._psi_star_projection_solver.uw_function = self._workVar.sym self._psi_star_projection_solver.bcs = bcs self._psi_star_projection_solver.smoothing = smoothing @@ -1154,7 +1206,13 @@ def psi_fn(self): def psi_fn(self, new_fn): """Set the tracked expression.""" self._psi_fn = new_fn - self._psi_star_projection_solver.uw_function = self._psi_fn + if getattr(self, '_psi_star_use_multicomponent', False): + import sympy + indep = self._psi_star_indep_indices + row = sympy.Matrix([[new_fn[i, j] for (i, j) in indep]]) + self._psi_star_projection_solver.uw_function = row + else: + self._psi_star_projection_solver.uw_function = self._psi_fn return def _object_viewer(self): @@ -1202,9 +1260,23 @@ def initialise_history(self): eval_result = UnitAwareArray(eval_result, units=psi_units) self.psi_star[0].array[...] = eval_result except Exception: - self._psi_star_projection_solver.uw_function = self.psi_fn - self._psi_star_projection_solver.smoothing = 0.0 - self._psi_star_projection_solver.solve() + if getattr(self, '_psi_star_use_multicomponent', False): + import sympy + indep = self._psi_star_indep_indices + row = sympy.Matrix([[self.psi_fn[i, j] for (i, j) in indep]]) + self._psi_star_projection_solver.uw_function = row + self._psi_star_projection_solver.smoothing = 0.0 + self._psi_star_projection_solver.solve() + # Fan out flat result to tensor psi_star[0] + for k, (i, j) in enumerate(indep): + vals = self._psi_star_flat_var.array[:, 0, k] + self.psi_star[0].array[:, i, j] = vals + if i != j: + self.psi_star[0].array[:, j, i] = vals + else: + self._psi_star_projection_solver.uw_function = self.psi_fn + self._psi_star_projection_solver.smoothing = 0.0 + self._psi_star_projection_solver.solve() # Copy to all other history slots for i in range(1, self.order): diff --git a/src/underworld3/systems/solvers.py b/src/underworld3/systems/solvers.py index ab18b4838..d8f915dd3 100644 --- a/src/underworld3/systems/solvers.py +++ b/src/underworld3/systems/solvers.py @@ -1267,9 +1267,26 @@ def solve( _advected_sigma_star = np.copy(self.DFDt.psi_star[0].array[...]) - self.DFDt._psi_star_projection_solver.uw_function = self.constitutive_model.flux - self.DFDt._psi_star_projection_solver.smoothing = 0.0 - self.DFDt._psi_star_projection_solver.solve(verbose=verbose) + if getattr(self.DFDt, '_psi_star_use_multicomponent', False): + # Multi-component projection: flatten flux to (1, Nc) row, + # solve all components at once, fan results back to tensor. + import sympy + flux = self.constitutive_model.flux + indep = self.DFDt._psi_star_indep_indices + row = sympy.Matrix([[flux[i, j] for (i, j) in indep]]) + self.DFDt._psi_star_projection_solver.uw_function = row + self.DFDt._psi_star_projection_solver.smoothing = 0.0 + self.DFDt._psi_star_projection_solver.solve(verbose=verbose) + # Fan flat result back to psi_star[0] tensor variable + for k, (i, j) in enumerate(indep): + vals = self.DFDt._psi_star_flat_var.array[:, 0, k] + self.DFDt.psi_star[0].array[:, i, j] = vals + if i != j: + self.DFDt.psi_star[0].array[:, j, i] = vals + else: + self.DFDt._psi_star_projection_solver.uw_function = self.constitutive_model.flux + self.DFDt._psi_star_projection_solver.smoothing = 0.0 + self.DFDt._psi_star_projection_solver.solve(verbose=verbose) for i in range(self.DFDt.order - 1, 0, -1): if i == 1: From 64c4a17fcca567a238813acdf611f2931e45c7e8 Mon Sep 17 00:00:00 2001 From: lmoresi Date: Tue, 21 Apr 2026 10:52:30 +1000 Subject: [PATCH 102/537] Skip redundant uw_function reassignment in projection solvers MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The tau/stress projector was reassigning uw_function = flux on every step, triggering SymbolicProperty.__set__ → is_setup = False → full DM rebuild. The flux expression is structurally identical across timesteps — only constant values (dt_elastic, BDF coeffs) change, which flow through PetscDS constants[] automatically. Set uw_function once at initialisation. Re-set only when the constitutive model changes (_solver_is_setup becomes False). Result: VE benchmark 99 steps drops from 206s to 56s (3.7x on top of the multicomponent 2.5x, total 9.2x vs original 515s). Underworld development team with AI support from Claude Code --- .../figures/cuboid-3d/cuboid-3d-data.json | 264 + .../figures/cuboid-3d/cuboid-faces.png | Bin 0 -> 93053 bytes .../figures/cuboid-3d/cuboid-faces.typ | 177 + .../cuboid-3d/generate-cuboid-3d-data.py | 197 + .../figures/curved-bc/curved-bc-data.json | 652 ++ .../curved-bc/facet-vs-true-normals.png | Bin 0 -> 68940 bytes .../curved-bc/facet-vs-true-normals.typ | 119 + .../curved-bc/generate-curved-bc-data.py | 127 + petsc-custom/bug-reports/README.md | 70 + .../petsc_issue_dmsetcoordinatedisc.c | 135 + .../blog-posts/constitutive-models.md | 240 + .../finding-particles/boundary-demo-data.json | 8858 +++++++++++++++++ .../finding-particles/boundary-demo.png | Bin 0 -> 897297 bytes .../finding-particles/boundary-demo.typ | 229 + .../finding-particles/domain-demo-data.json | 6275 ++++++++++++ .../figures/finding-particles/domain-demo.png | Bin 0 -> 577753 bytes .../figures/finding-particles/domain-demo.typ | 128 + .../generate-boundary-demo-data.py | 230 + .../generate-domain-demo-data.py | 154 + .../finding-particles/generate-mesh-data.py | 107 + .../figures/finding-particles/mesh-data.json | 252 + .../figures/finding-particles/mesh-demo.png | Bin 0 -> 64363 bytes .../figures/finding-particles/mesh-demo.typ | 204 + publications/blog-posts/finding-particles.md | 140 + .../blog-posts/particles-as-symbols.md | 120 + publications/blog-posts/physical-units.md | 221 + publications/blog-posts/time-derivatives.md | 188 + .../cython/petsc_generic_snes_solvers.pyx | 15 +- src/underworld3/systems/solvers.py | 21 +- tests/plot_ve_combined.py | 248 + tests/ve_benchmarks_combined.png | Bin 0 -> 227373 bytes tests/ve_oscillatory_order1_checkpoint.npz | Bin 0 -> 6316 bytes tests/ve_oscillatory_order1_final.npz | Bin 0 -> 6506 bytes tests/ve_oscillatory_order2_checkpoint.npz | Bin 0 -> 6316 bytes tests/ve_oscillatory_order2_final.npz | Bin 0 -> 6506 bytes tests/ve_oscillatory_validation.png | Bin 0 -> 143003 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─────────────────────────────────────────────────────────── +// Each opposite-face pair is coloured by its coordinate axis (RGB-axes +// convention): x-pair (Left/Right) = rust, y-pair (Front/Back) = green, +// z-pair (Upper/Lower) = blue. Hidden faces use the same hue at lower +// alpha so the pairing is legible regardless of visibility. +#let face-fill(name, visible) = { + let (r, g, b) = if name == "Upper" or name == "Lower" { + (85, 130, 195) // blue — z-axis pair + } else if name == "Front" or name == "Back" { + (90, 160, 110) // green — y-axis pair + } else { + (200, 110, 85) // rust — x-axis pair + } + let a = if visible { 140 } else { 30 } + rgb(r, g, b, a) +} +#let visible-edge = 0.9pt + black +#let hidden-edge = (paint: rgb("#808080"), thickness: 0.7pt, dash: "dashed") +#let arrow-colour = rgb("#1f3a6b") +#let arrow-stroke = 0.9pt + arrow-colour + +#let v(i) = (data.vertices_2d.at(i).at(0), data.vertices_2d.at(i).at(1)) + +// ── Face label layout ───────────────────────────────────────────────── +// Two vertical columns at x = ±2, three labels each. Each label is +// paired with a face whose centroid lies on the same side of the +// figure, which prevents line crossings. Lines are bare (no arrow- +// heads) — labels, not symmetry axes. +#let label-overrides = ( + Upper: (pos: (-2.0, +1.5), anchor: "east"), + Left: (pos: (-2.0, 0.0), anchor: "east"), + Back: (pos: (-2.0, -1.5), anchor: "east"), + Front: (pos: (+2.0, +1.5), anchor: "west"), + Right: (pos: (+2.0, 0.0), anchor: "west"), + Lower: (pos: (+2.0, -1.5), anchor: "west"), +) + +// ── Axis triad at V6 (the cuboid corner nearest the viewer) ────────── +// The cube projection itself is unchanged (so the face labels Left/Right +// stay where they were). Only the triad's +y arrow is flipped from the +// projected-y direction so the triad reads as right-handed — pointing +// the +y axis away from the viewer instead of toward. +#let TRIAD-LEN = 0.45 +#let AXIS-X-2D = (0.86603, -0.5) // projected +x direction +#let AXIS-Y-2D = (0.86603, 0.5) // triad-only: flipped from (-0.866, -0.5) +#let AXIS-Z-2D = (0.0, 1.0) // projected +z direction + +#align(center + horizon, cetz.canvas(length: 1.5cm, { + import cetz.draw: * + + // Split back-to-front order into hidden and visible groups, preserving + // each group's internal painter-order for correct translucency stacking. + let hidden-names = data.faces_back_to_front.filter( + n => not data.faces.at(n).visible) + let visible-names = data.faces_back_to_front.filter( + n => data.faces.at(n).visible) + + let draw-face(name) = { + let face = data.faces.at(name) + let idxs = face.vertex_indices + line( + v(idxs.at(0)), v(idxs.at(1)), + v(idxs.at(2)), v(idxs.at(3)), + close: true, fill: face-fill(name, face.visible), stroke: none, + ) + } + + let draw-face-line(name) = { + // Bare line from the (column-aligned) label position to the face + // centroid — no arrowhead. Hidden-face lines are drawn before the + // visible face fills, so their inner segments fade behind the + // translucent fronts. + let face = data.faces.at(name) + let lbl-pos = label-overrides.at(name).pos + let tip = (face.arrow_to.at(0), face.arrow_to.at(1)) + line(lbl-pos, tip, stroke: arrow-stroke) + } + + // Small 3D "badge" at the end of each label line: a shrunken copy of + // the face's projected shape, sharing its axis-pair colour. + let draw-face-marker(name) = { + let face = data.faces.at(name) + let idxs = face.vertex_indices + let c = (face.arrow_to.at(0), face.arrow_to.at(1)) + let shrink-by = 0.18 + let shrunk(idx) = { + let vi = v(idx) + (c.at(0) + (vi.at(0) - c.at(0)) * shrink-by, + c.at(1) + (vi.at(1) - c.at(1)) * shrink-by) + } + let fill-col = { + let (r, g, b) = if name == "Upper" or name == "Lower" { + (85, 130, 195) + } else if name == "Front" or name == "Back" { + (90, 160, 110) + } else { + (200, 110, 85) + } + rgb(r, g, b, 230) + } + line(shrunk(idxs.at(0)), shrunk(idxs.at(1)), + shrunk(idxs.at(2)), shrunk(idxs.at(3)), + close: true, fill: fill-col, stroke: 0.7pt + arrow-colour) + } + + // 1. Hidden face fills (farthest-first painter order within group). + for name in hidden-names { draw-face(name) } + + // 2. Hidden-face label lines + markers — drawn BEFORE the visible + // face fills so their inner segments (and the small badges that + // sit at the face centroid) fade behind the translucent fronts. + for name in hidden-names { draw-face-line(name); draw-face-marker(name) } + + // 3. Hidden edges (dashed) — same "behind the translucent front" idea. + for edge in data.edges { + if not edge.visible { + let v0 = v(edge.vertices.at(0)) + let v1 = v(edge.vertices.at(1)) + line(v0, v1, stroke: hidden-edge) + } + } + + // 4. Visible face fills on top — translucently cover the hidden arrows + // and edges that lie inside the cube silhouette. + for name in visible-names { draw-face(name) } + + // 5. Visible-face label lines + markers — fully in front of everything. + for name in visible-names { draw-face-line(name); draw-face-marker(name) } + + // 6. Visible edges — solid black on top of everything structural. + for edge in data.edges { + if edge.visible { + let v0 = v(edge.vertices.at(0)) + let v1 = v(edge.vertices.at(1)) + line(v0, v1, stroke: visible-edge) + } + } + + // 7. Axis triad at V6 — the corner nearest the viewer. Short arrows + // in the projected +x, +y, +z directions, with italic-math labels. + let triad-origin = v(6) + let triad-stroke = 0.9pt + arrow-colour + let triad-mark = (end: ">", fill: arrow-colour) + let triad-arrow(dir-2d, label-offset-factor, lbl, lbl-anchor) = { + let tip = ( + triad-origin.at(0) + TRIAD-LEN * dir-2d.at(0), + triad-origin.at(1) + TRIAD-LEN * dir-2d.at(1), + ) + line(triad-origin, tip, stroke: triad-stroke, mark: triad-mark) + let lbl-pos = ( + triad-origin.at(0) + label-offset-factor * TRIAD-LEN * dir-2d.at(0), + triad-origin.at(1) + label-offset-factor * TRIAD-LEN * dir-2d.at(1), + ) + content(lbl-pos, + text(fill: arrow-colour, size: 10pt, style: "italic", lbl), + anchor: lbl-anchor) + } + triad-arrow(AXIS-X-2D, 1.30, $x$, "north-west") + triad-arrow(AXIS-Y-2D, 1.30, $y$, "north-east") + triad-arrow(AXIS-Z-2D, 1.22, $z$, "south") + + // 8. Face labels last — always on top; they live outside the cube. + for (name, override) in label-overrides.pairs() { + content(override.pos, + text(fill: black, size: 10pt, name), + anchor: override.anchor) + } +})) diff --git a/docs/advanced/figures/cuboid-3d/generate-cuboid-3d-data.py b/docs/advanced/figures/cuboid-3d/generate-cuboid-3d-data.py new file mode 100644 index 000000000..8f72b21e6 --- /dev/null +++ b/docs/advanced/figures/cuboid-3d/generate-cuboid-3d-data.py @@ -0,0 +1,197 @@ +""" +Data for the 3D cuboid "boundary labels" sketch. + +Isometric projection of a rectangular box with the standard UW3 face +labels (Upper / Lower / Left / Right / Front / Back). Each face gets +an arrow from outside the box toward its centroid, and a text label +at the arrow tail. The cetz figure just renders what this script +emits — no 3D math in Typst. + +Output schema: + + { + "vertices_2d": [[sx, sy], ... 8 entries], + "faces": { + "": { + "vertex_indices": [i, j, k, l], # CCW when looking at face + "visible": bool, # w.r.t. isometric viewer + "arrow_from": [sx, sy], # tail, outside the box + "arrow_to": [sx, sy], # tip, at face centroid + "label_pos": [sx, sy], # anchor for label text + "label_anchor": "west"|"east"|"north"|"south"|..., + }, ... + }, + "faces_back_to_front": [, ...], # painter's-algorithm order + "edges": [ + {"vertices": [i, j], "visible": bool}, ... + ] + } +""" +import json +import math +from pathlib import Path + +# Cuboid half-extents — deliberately non-cubic so the axes read differently. +X_HALF = 1.0 +Y_HALF = 0.75 +Z_HALF = 0.5 + +# Isometric projection. +# Axes: x → right-down, y → left-down, z → up +# Point (x, y, z) → 2D (sx, sy): +# sx = (x - y) * cos(30°) +# sy = z - (x + y) * sin(30°) +COS30 = math.cos(math.radians(30.0)) +SIN30 = 0.5 + + +def project(p): + x, y, z = p + return ((x - y) * COS30, z - (x + y) * SIN30) + + +def project_direction(nx, ny, nz): + """Project a 3D direction vector onto the screen plane.""" + return ((nx - ny) * COS30, nz - (nx + ny) * SIN30) + + +# ── 8 vertices, indexed by (xs, ys, zs) with xs, ys, zs ∈ {−1, +1} ─── +def vertex(xs, ys, zs): + return (xs * X_HALF, ys * Y_HALF, zs * Z_HALF) + + +V = [ + vertex(-1, -1, -1), # 0 + vertex(+1, -1, -1), # 1 + vertex(+1, +1, -1), # 2 + vertex(-1, +1, -1), # 3 + vertex(-1, -1, +1), # 4 + vertex(+1, -1, +1), # 5 + vertex(+1, +1, +1), # 6 + vertex(-1, +1, +1), # 7 +] + +# ── Faces: vertex indices, outward normals, and UW3 label names ────── +# In this convention +x → Right, -x → Left, +y → Back, -y → Front, +# +z → Upper, -z → Lower. +FACES = { + "Upper": {"vertex_indices": [4, 5, 6, 7], "normal": (0, 0, +1)}, + "Lower": {"vertex_indices": [0, 1, 2, 3], "normal": (0, 0, -1)}, + "Front": {"vertex_indices": [0, 1, 5, 4], "normal": (0, -1, 0)}, + "Back": {"vertex_indices": [2, 3, 7, 6], "normal": (0, +1, 0)}, + "Left": {"vertex_indices": [0, 3, 7, 4], "normal": (-1, 0, 0)}, + "Right": {"vertex_indices": [1, 2, 6, 5], "normal": (+1, 0, 0)}, +} + +# ── Edges and which two faces each one borders ──────────────────────── +EDGES = [ + # bottom square + ([0, 1], ("Lower", "Front")), + ([1, 2], ("Lower", "Right")), + ([2, 3], ("Lower", "Back")), + ([3, 0], ("Lower", "Left")), + # top square + ([4, 5], ("Upper", "Front")), + ([5, 6], ("Upper", "Right")), + ([6, 7], ("Upper", "Back")), + ([7, 4], ("Upper", "Left")), + # verticals + ([0, 4], ("Front", "Left")), + ([1, 5], ("Front", "Right")), + ([2, 6], ("Back", "Right")), + ([3, 7], ("Back", "Left")), +] + +# ── Visibility ──────────────────────────────────────────────────────── +# With the projection above (+x → right-down, +y → left-down, +z → up), +# the viewer sits at the (+1, +1, +1) corner direction — upper-back-right. +# A face is visible iff its outward normal has a positive component along +# that viewer direction, i.e. iff nx + ny + nz > 0. +# ───────────────────────────────────────────────────────────────────── +def face_centroid_3d(name): + idxs = FACES[name]["vertex_indices"] + return tuple(sum(V[i][k] for i in idxs) / 4 for k in range(3)) + + +def depth_from_viewer(p3d): + """Larger = closer to the viewer (at +x+y+z direction).""" + return p3d[0] + p3d[1] + p3d[2] + + +for name in FACES: + c3d = face_centroid_3d(name) + FACES[name]["centroid_3d"] = c3d + nx, ny, nz = FACES[name]["normal"] + FACES[name]["visible"] = (nx + ny + nz) > 0 + +# ── 2D projections ──────────────────────────────────────────────────── +vertices_2d = [project(v) for v in V] + +for name, face in FACES.items(): + c2d = project(face["centroid_3d"]) + face["centroid_2d"] = c2d + # Outward-normal direction in 2D, for placing arrow + label outside box. + nx, ny, nz = face["normal"] + dir_2d = project_direction(nx, ny, nz) + dlen = math.hypot(dir_2d[0], dir_2d[1]) + if dlen > 1e-9: + dir_2d = (dir_2d[0] / dlen, dir_2d[1] / dlen) + face["dir_2d"] = dir_2d + +# ── Arrow tail, tip, and label position for each face ──────────────── +# Arrow goes FROM outside (at distance TAIL_DIST along face's 2D outward +# normal) TO the face centroid. Label sits just beyond the arrow tail. +TAIL_DIST = 0.80 +LABEL_DIST = 1.15 + +for name, face in FACES.items(): + dx, dy = face["dir_2d"] + cx, cy = face["centroid_2d"] + face["arrow_from"] = [cx + TAIL_DIST * dx, cy + TAIL_DIST * dy] + face["arrow_to"] = [cx, cy] + face["label_pos"] = [cx + LABEL_DIST * dx, cy + LABEL_DIST * dy] + # Pick a text anchor so the label sits past the tail, not on top of it. + face["label_anchor"] = ( + "south" if dy > 0.5 else + "north" if dy < -0.5 else + "west" if dx > 0.0 else + "east" + ) + +# ── Edge visibility: an edge is hidden if *both* its faces are hidden ─ +edges_out = [] +for verts, (face_a, face_b) in EDGES: + visible = FACES[face_a]["visible"] or FACES[face_b]["visible"] + edges_out.append({"vertices": verts, "visible": visible}) + +# ── Painter's-algorithm order for fills: farthest first ────────────── +# Farthest from viewer ↔ smallest depth_from_viewer ↔ smallest x+y+z. +faces_back_to_front = sorted( + FACES.keys(), key=lambda n: depth_from_viewer(FACES[n]["centroid_3d"]) +) + +# ── Assemble JSON ───────────────────────────────────────────────────── +data = { + "vertices_2d": [[round(x, 4), round(y, 4)] for x, y in vertices_2d], + "faces": { + name: { + "vertex_indices": face["vertex_indices"], + "visible": face["visible"], + "arrow_from": [round(c, 4) for c in face["arrow_from"]], + "arrow_to": [round(c, 4) for c in face["arrow_to"]], + "label_pos": [round(c, 4) for c in face["label_pos"]], + "label_anchor": face["label_anchor"], + } + for name, face in FACES.items() + }, + "faces_back_to_front": faces_back_to_front, + "edges": edges_out, +} + +out = Path(__file__).with_name("cuboid-3d-data.json") +out.write_text(json.dumps(data, indent=2)) +print(f"wrote {out.name}: " + f"{len(data['vertices_2d'])} vertices, " + f"{len(data['faces'])} faces " + f"({sum(1 for f in data['faces'].values() if f['visible'])} visible), " + f"{len(data['edges'])} edges") diff --git 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─────────────────────────────────────────────────────────── +#let arc-colour = rgb("#b0b0b0") // true smooth curve +#let facet-colour = rgb("#1f3a6b") // navy — mesh facets +#let gamma-colour = rgb("#c2410c") // rust — PETSc facet normal +#let true-colour = rgb("#059669") // emerald — true surface normal +#let centre-colour = black + +// ── Geometry access ─────────────────────────────────────────────────── +#let centre = (data.centre.at(0), data.centre.at(1)) +#let radius-end = (data.radius_end.at(0), data.radius_end.at(1)) + +// ── Figure ──────────────────────────────────────────────────────────── +#align(center + horizon, cetz.canvas(length: 3cm, { + import cetz.draw: * + + // 1. True smooth arc — thin dashed grey polyline. + let arc-stroke = (paint: arc-colour, thickness: 0.6pt, dash: "dashed") + for i in range(data.arc_points.len() - 1) { + let p0 = data.arc_points.at(i) + let p1 = data.arc_points.at(i + 1) + line((p0.at(0), p0.at(1)), (p1.at(0), p1.at(1)), stroke: arc-stroke) + } + + // 2. Radius-of-curvature indicator from centre to the arc midpoint. + line(centre, radius-end, + stroke: (paint: arc-colour, thickness: 0.5pt, dash: "dotted")) + // Label the radius midway along it, offset perpendicular. + let r-label-pos = ( + 0.5 * (centre.at(0) + radius-end.at(0)) + 0.07, + 0.5 * (centre.at(1) + radius-end.at(1)), + ) + content(r-label-pos, text(fill: arc-colour, size: 10pt, $R$), + anchor: "west") + + // 3. Facet polyline — thin black. The control points (vertex dots, + // Gauss-point dots) carry the visual weight; the segments between + // them are just the domain boundary. + for i in range(data.facet_vertices.len() - 1) { + let p0 = data.facet_vertices.at(i) + let p1 = data.facet_vertices.at(i + 1) + line((p0.at(0), p0.at(1)), (p1.at(0), p1.at(1)), + stroke: 0.6pt + black) + } + // Facet vertex markers + for v in data.facet_vertices { + circle((v.at(0), v.at(1)), radius: 0.038, + fill: facet-colour, stroke: none) + } + + // 4. Quadrature points with their two normals. + // - true normal (emerald, dashed) ← what free-slip wants + // - facet normal (rust, solid) ← what mesh.Gamma gives + let arrow-len = 0.28 + let true-stroke = (paint: true-colour, thickness: 0.9pt, dash: "dashed") + let gamma-stroke = 1.3pt + gamma-colour + for q in data.quadrature { + let pos = (q.pos.at(0), q.pos.at(1)) + let tn = q.true_normal + let fn = q.facet_normal + + // Facet normal arrow drawn FIRST, so the dashed true normal + // layers on top. Where the two coincide (facet midpoints), the + // green dashes interleave with the rust underneath and both + // colours stay visible — it reads as "they overlap here". + let tip-f = (pos.at(0) + arrow-len * fn.at(0), + pos.at(1) + arrow-len * fn.at(1)) + line(pos, tip-f, stroke: gamma-stroke, + mark: (end: ">", fill: gamma-colour)) + + // True normal arrow on top + let tip-t = (pos.at(0) + arrow-len * tn.at(0), + pos.at(1) + arrow-len * tn.at(1)) + line(pos, tip-t, stroke: true-stroke, + mark: (end: ">", fill: true-colour)) + + // Small quadrature dot + circle(pos, radius: 0.024, fill: black, stroke: none) + } + + // 5. Centre dot + label + circle(centre, radius: 0.038, fill: centre-colour, stroke: none) + content((centre.at(0) + 0.06, centre.at(1) - 0.06), + $O$, anchor: "north-west") + + // 6. Legend in the empty space below the arc. Short sample strokes + // next to each label, so the figure is self-explaining without + // leader lines or per-arrow annotations. + let lx = 0.25 // legend x start (inside the open area) + let ly = 0.55 // top row y + let row = 0.22 // row spacing + let sample-len = 0.28 + + // Row 1: facet normal sample + line((lx, ly), (lx + sample-len, ly), + stroke: gamma-stroke, + mark: (end: ">", fill: gamma-colour)) + content((lx + sample-len + 0.08, ly), + text(fill: gamma-colour, size: 9.5pt, + $hat(n)_Gamma$ + [ (facet, `mesh.Gamma`)]), + anchor: "west") + + // Row 2: true normal sample + line((lx, ly - row), (lx + sample-len, ly - row), + stroke: true-stroke, + mark: (end: ">", fill: true-colour)) + content((lx + sample-len + 0.08, ly - row), + text(fill: true-colour, size: 9.5pt, + $hat(n)_"true"$ + [ (smooth surface)]), + anchor: "west") +})) diff --git a/docs/advanced/figures/curved-bc/generate-curved-bc-data.py b/docs/advanced/figures/curved-bc/generate-curved-bc-data.py new file mode 100644 index 000000000..5af372f8b --- /dev/null +++ b/docs/advanced/figures/curved-bc/generate-curved-bc-data.py @@ -0,0 +1,127 @@ +""" +Data for the "facet normals vs. true normals" figure in +`docs/advanced/curved-boundary-conditions.md`. + +The figure illustrates why `mesh.Gamma` (PETSc facet normals) diverges +from the true smooth-surface normal on a curved boundary: + + - Three straight facets approximate a circular arc. + - At each Gauss quadrature point (2 per facet), the facet normal + is constant across the facet while the true (radial) normal + rotates with position. + +Output schema: + + { + "centre": [cx, cy], + "radius": R, + "arc_points": [[x, y], ...], # densely sampled true arc + "facet_vertices": [[x, y], ...], # points on the circle + "quadrature": [ + {"pos": [x, y], + "facet_normal": [nx, ny], + "true_normal": [nx, ny], + "facet_idx": int}, + ... + ], + "radius_end": [x, y] # arc point at mid-angle + # (end of the radius indicator) + } +""" +import json +import math +from pathlib import Path + +CENTRE = (0.0, 0.0) +RADIUS = 1.5 +ANGLE_START = 30.0 # degrees — chosen so the error angle at +ANGLE_END = 150.0 # quadrature points is visually obvious (~12°) +N_FACETS = 3 +ARC_SAMPLES = 120 + + +def point_at_angle(deg, r=RADIUS): + rad = math.radians(deg) + return (CENTRE[0] + r * math.cos(rad), + CENTRE[1] + r * math.sin(rad)) + + +# 1. Dense sampling of the true arc (for a dashed polyline in Typst) +arc_points = [ + list(point_at_angle( + ANGLE_START + (i / ARC_SAMPLES) * (ANGLE_END - ANGLE_START) + )) + for i in range(ARC_SAMPLES + 1) +] + +# 2. Facet vertices — N_FACETS + 1 points evenly spaced on the arc +facet_vertices = [ + list(point_at_angle( + ANGLE_START + (i / N_FACETS) * (ANGLE_END - ANGLE_START) + )) + for i in range(N_FACETS + 1) +] + +# 3. Three-point Gauss–Legendre quadrature on [-1, 1]: 0, ±sqrt(3/5). +# Mapped to t ∈ [0, 1]: 0.5 ± sqrt(3/5)/2 and 0.5. +# The middle node lies exactly at the chord midpoint, where the +# facet normal and the radial true normal coincide — that's the +# "error vanishes at facet midpoint" case the figure needs to show. +_HALF = 0.5 * math.sqrt(0.6) +GAUSS_T = ( + 0.5 - _HALF, + 0.5, + 0.5 + _HALF, +) + +quadrature = [] +for facet_idx in range(N_FACETS): + p0 = facet_vertices[facet_idx] + p1 = facet_vertices[facet_idx + 1] + dx, dy = p1[0] - p0[0], p1[1] - p0[1] + length = math.hypot(dx, dy) + + # Outward perpendicular to the chord: pick the rotation of (dx, dy) + # whose dot-product with (midpoint - centre) is positive. + mid = ((p0[0] + p1[0]) / 2, (p0[1] + p1[1]) / 2) + cand = (-dy / length, dx / length) + if (cand[0] * (mid[0] - CENTRE[0]) + + cand[1] * (mid[1] - CENTRE[1])) < 0: + cand = (dy / length, -dx / length) + facet_normal = cand + + for t in GAUSS_T: + pos = (p0[0] + t * dx, p0[1] + t * dy) + # True normal: unit radial vector from circle centre through pos. + rx, ry = pos[0] - CENTRE[0], pos[1] - CENTRE[1] + rlen = math.hypot(rx, ry) + true_normal = (rx / rlen, ry / rlen) + quadrature.append({ + "pos": [pos[0], pos[1]], + "facet_normal": [facet_normal[0], facet_normal[1]], + "true_normal": [true_normal[0], true_normal[1]], + "facet_idx": facet_idx, + }) + +# 4. Radius indicator: from centre to arc midpoint +radius_end = list(point_at_angle((ANGLE_START + ANGLE_END) / 2)) + +data = { + "centre": list(CENTRE), + "radius": RADIUS, + "arc_points": [[round(x, 4), round(y, 4)] for x, y in arc_points], + "facet_vertices": [[round(x, 4), round(y, 4)] for x, y in facet_vertices], + "quadrature": [ + {k: ([round(v[0], 4), round(v[1], 4)] if isinstance(v, list) else v) + for k, v in q.items()} + for q in quadrature + ], + "radius_end": [round(radius_end[0], 4), round(radius_end[1], 4)], +} + +out = Path(__file__).with_name("curved-bc-data.json") +out.write_text(json.dumps(data, indent=2)) +print(f"wrote {out.name}: " + f"{len(arc_points)} arc samples, " + f"{len(facet_vertices)} facet vertices, " + f"{len(quadrature)} quadrature points") diff --git a/petsc-custom/bug-reports/README.md b/petsc-custom/bug-reports/README.md new file mode 100644 index 000000000..435dd22da --- /dev/null +++ b/petsc-custom/bug-reports/README.md @@ -0,0 +1,70 @@ +# PETSc Bug Reports + +## DMSetCoordinateDisc breaks DMPlexComputeBdIntegral (2026-04-14) + +**PETSc GitLab**: (link to filed issue) + +**PETSc version**: 3.24.2 (release branch) + +### Summary + +`DMSetCoordinateDisc(dm, userFE, FALSE, FALSE)` on a distributed gmsh-loaded +DM causes `DMPlexComputeBdIntegral` to crash. The coordinate FE created by +`DMSetCoordinateDisc` has broken dual space point subspaces — +`PetscDualSpaceGetPointSubspace` returns NULL for boundary face points, +causing a null pointer dereference in `PetscSpaceCreateSubspace`. + +- `--with-debugging=1`: clean error "Null Pointer: Parameter #2" +- `--with-debugging=0`: SIGSEGV or MPI deadlock + +**Workaround**: Use `DMPlexCreateCoordinateSpace(dm, 1, FALSE, FALSE)` instead +of `DMSetCoordinateDisc`. It creates the FE internally with correct subspace +initialisation. + +### Files + +- `petsc_issue_dmsetcoordinatedisc.c` — self-contained C reproducer +- `box.msh` — gmsh mesh file (or generate with the command in the .c file) + +### Build and run + +```bash +# Generate mesh (if box.msh is not available) +gmsh -2 -clmax 0.125 -o box.msh -parse_string ' + SetFactory("OpenCASCADE"); + Rectangle(1) = {0,0,0,1,1}; + Physical Surface(99) = {1}; + Physical Curve(11) = {1}; + Physical Curve(12) = {3}; +' + +# Compile +mpicc -o repro petsc_issue_dmsetcoordinatedisc.c \ + -I$PETSC_DIR/include -I$PETSC_DIR/$PETSC_ARCH/include \ + -L$PETSC_DIR/$PETSC_ARCH/lib -lpetsc \ + -Wl,-rpath,$PETSC_DIR/$PETSC_ARCH/lib + +# Run (crashes with np >= 1) +mpirun -np 2 ./repro box.msh +``` + +### Call chain + +``` +DMPlexComputeBdIntegral + → DMPlexComputeBdIntegral_Internal + → DMGetCoordinateField (field cache is NULL — cleared by DMSetCoordinateDisc) + → DMCreateCoordinateField_Plex + → DMFieldCreateDS → DMFieldDSGetHeightDisc + → PetscFECreateHeightTrace → PetscFECreatePointTrace + → PetscDualSpaceGetPointSubspace → returns NULL + → PetscSpaceCreateSubspace(bsp, NULL, ...) → CRASH +``` + +### Related: Underworld3 issue #96 + +This bug was discovered during investigation of +[underworldcode/underworld3#96](https://github.com/underworldcode/underworld3/issues/96). +The UW3 workaround (`UW_DMForceCoordinateField`) forces coordinate field creation +and strips inherited boundary labels from the coordinate DM after +`DMPlexCreateCoordinateSpace`. diff --git a/petsc-custom/bug-reports/petsc_issue_dmsetcoordinatedisc.c b/petsc-custom/bug-reports/petsc_issue_dmsetcoordinatedisc.c new file mode 100644 index 000000000..ac8afbfbc --- /dev/null +++ b/petsc-custom/bug-reports/petsc_issue_dmsetcoordinatedisc.c @@ -0,0 +1,135 @@ +static char help[] = + "Reproducer: DMSetCoordinateDisc breaks DMPlexComputeBdIntegral on distributed meshes.\n\n" + "After calling DMSetCoordinateDisc on a distributed gmsh-loaded DM,\n" + "DMPlexComputeBdIntegral segfaults (--with-debugging=0) or reports\n" + "'Null Pointer: Parameter #2' in PetscSpaceCreateSubspace (--with-debugging=1).\n" + "The null pointer comes from PetscDualSpaceGetPointSubspace returning NULL\n" + "for boundary face points on the coordinate FE created by DMSetCoordinateDisc.\n\n" + "Without DMSetCoordinateDisc (using the coordinate space from the gmsh load),\n" + "everything works. DMPlexCreateCoordinateSpace also works as a replacement.\n\n" + "Requires a gmsh .msh file as first argument.\n" + "Generate one with: gmsh -2 -clmax 0.125 -o box.msh <(echo '\n" + " SetFactory(\"OpenCASCADE\");\n" + " Rectangle(1) = {0,0,0,1,1};\n" + " Physical Surface(99) = {1};\n" + " Physical Curve(11) = {1}; // Bottom\n" + " Physical Curve(12) = {3}; // Top\n" + "')\n\n" + "Run: mpirun -np 2 ./reproducer box.msh\n" + " --with-debugging=1: 'Null Pointer: Parameter #2' in PetscSpaceCreateSubspace\n" + " --with-debugging=0: SIGSEGV or MPI deadlock\n"; + +#include +#include + +/* Trivial boundary integrand: constant 1 */ +static void bd_f0(PetscInt dim, PetscInt Nf, PetscInt NfAux, + const PetscInt uOff[], const PetscInt uOff_x[], + const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], + const PetscInt aOff[], const PetscInt aOff_x[], + const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], + PetscReal t, const PetscReal x[], const PetscReal n[], + PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[]) +{ + f0[0] = 1.0; +} + +int main(int argc, char **argv) +{ + DM dm; + const char *meshfile; + + PetscFunctionBeginUser; + PetscCall(PetscInitialize(&argc, &argv, NULL, help)); + + /* Get mesh filename from command line */ + PetscCheck(argc > 1, PETSC_COMM_WORLD, PETSC_ERR_USER, "Usage: %s ", argv[0]); + meshfile = argv[1]; + + /* Load gmsh mesh and distribute */ + PetscCall(DMPlexCreateGmshFromFile(PETSC_COMM_WORLD, meshfile, PETSC_TRUE, &dm)); + { + DM distDM = NULL; + PetscCall(DMPlexDistribute(dm, 0, NULL, &distDM)); + if (distDM) { PetscCall(DMDestroy(&dm)); dm = distDM; } + } + { + PetscInt pStart, pEnd; + PetscCall(DMPlexGetChart(dm, &pStart, &pEnd)); + PetscCall(PetscSynchronizedPrintf(PETSC_COMM_WORLD, " chart = (%d, %d)\n", pStart, pEnd)); + PetscCall(PetscSynchronizedFlush(PETSC_COMM_WORLD, PETSC_STDOUT)); + } + + /* ── THIS TRIGGERS THE BUG ── + * Call DMSetCoordinateDisc with a user-created PetscFE. + * This clears the cached coordinate field (DMSetCoordinateField(dm, NULL)). + * When DMPlexComputeBdIntegral later calls DMGetCoordinateField, PETSc + * lazily recreates it via DMCreateCoordinateField_Plex. The new coordinate + * field's FE (set by DMSetCoordinateDisc) has broken dual space point + * subspaces — PetscDualSpaceGetPointSubspace returns NULL for boundary + * face points, causing PetscFECreatePointTrace to segfault. + * + * WORKAROUND: use DMPlexCreateCoordinateSpace(dm, 1, FALSE, FALSE) instead. + * It creates the FE internally with correct subspace initialisation. + */ + { + PetscFE coordFE; + PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, 2, 2, PETSC_TRUE, "coord_", 3, &coordFE)); + PetscCall(DMSetCoordinateDisc(dm, coordFE, PETSC_FALSE, PETSC_FALSE)); + PetscCall(PetscFEDestroy(&coordFE)); + } + PetscCall(PetscPrintf(PETSC_COMM_WORLD, "DMSetCoordinateDisc done\n")); + + /* Add a field and create DS */ + { + PetscFE fe; + PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, 2, 1, PETSC_TRUE, "field_", -1, &fe)); + PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe)); + PetscCall(PetscFEDestroy(&fe)); + PetscCall(DMCreateDS(dm)); + } + + /* DMPlexComputeBdIntegral — crashes here */ + PetscCall(PetscPrintf(PETSC_COMM_WORLD, "DMPlexComputeBdIntegral...\n")); + { + Vec gvec; + DMLabel label; + PetscInt Nf; + PetscSection sec; + + PetscCall(DMGetLocalSection(dm, &sec)); + PetscCall(PetscSectionGetNumFields(sec, &Nf)); + PetscCall(DMCreateGlobalVector(dm, &gvec)); + PetscCall(VecSet(gvec, 1.0)); + PetscCall(DMGetLabel(dm, "Face Sets", &label)); + if (label) { + void (**funcs)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], + const PetscScalar[], const PetscScalar[], const PetscScalar[], + const PetscInt[], const PetscInt[], + const PetscScalar[], const PetscScalar[], const PetscScalar[], + PetscReal, const PetscReal[], const PetscReal[], + PetscInt, const PetscScalar[], PetscScalar[]); + PetscScalar *integral, global_val; + PetscInt val = 11; /* physical group tag for bottom boundary */ + + PetscCall(PetscCalloc1(Nf, &funcs)); + funcs[0] = (typeof(funcs[0]))bd_f0; + PetscCall(PetscCalloc1(Nf, &integral)); + PetscCall(DMPlexComputeBdIntegral(dm, gvec, label, 1, &val, funcs, integral, NULL)); + + PetscCallMPI(MPIU_Allreduce(&integral[0], &global_val, 1, MPIU_SCALAR, MPIU_SUM, + PetscObjectComm((PetscObject)dm))); + PetscCall(PetscPrintf(PETSC_COMM_WORLD, " integral = %g\n", (double)global_val)); + PetscCall(PetscFree(funcs)); + PetscCall(PetscFree(integral)); + } else { + PetscCall(PetscPrintf(PETSC_COMM_WORLD, " no 'Face Sets' label found\n")); + } + PetscCall(VecDestroy(&gvec)); + } + + PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Done.\n")); + PetscCall(DMDestroy(&dm)); + PetscCall(PetscFinalize()); + return 0; +} diff --git a/publications/blog-posts/constitutive-models.md b/publications/blog-posts/constitutive-models.md new file mode 100644 index 000000000..82ff20de5 --- /dev/null +++ b/publications/blog-posts/constitutive-models.md @@ -0,0 +1,240 @@ +--- +title: "Constitutive Models in Symbolic Form" +status: published +published: 2026-04-13 +url: https://www.underworldcode.org/constitutive-models-in-symbolic-form/ +feeds_into: [paper-1] +target: underworldcode.org (Ghost) +tags: [underworld, constitutive-models, rheology, geodynamics, SymPy] +--- + +# Constitutive Models in Symbolic Form + +In Underworld2, adding a new rheology was a matter of writing C code inside the StGermain framework, compiling it, and registering it with the component system. The barrier was high enough that most users never tried. The available rheologies were the ones the developers had implemented, and combining them required understanding the C internals. + +In Underworld3, a constitutive model is a Python class where the relationship between fluxes and gradients is encoded as a SymPy expression. You can build a viscous model, add plasticity, add elasticity, make it anisotropic. At every stage the mathematics is visible, inspectable, and differentiable. The framework handles Jacobians, C code generation, and PETSc integration. You handle the physics. + +```python +stokes = uw.systems.Stokes(mesh) +stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = viscosity_fn +``` + +This post explains how constitutive models work in UW3, from simple viscous flow through to viscoelastic-plastic rheologies with stress history. + +## The Constitutive Relationship + +A constitutive model in Underworld3 defines the relationship between a flux (e.g. stress - a momentum flux) and gradients of the unknowns (e.g. strain rate - gradients of velocity). For a Stokes flow problem, the solver needs a flux term $\mathbf{F _ 1}$ that expresses the deviatoric stress: + +$$ +\sigma _ {ij} = C _ {ijkl} \, \dot\varepsilon _ {kl} +$$ + +where $C _ {ijkl}$ is the constitutive tensor (viscosity in this case) and $\dot\varepsilon$ is the symmetric strain rate tensor derived from the velocity gradient. For isotropic viscous flow, $C _ {ijkl}$ reduces to $2\eta \, I _ {ijkl}$ where $\eta$ is the viscosity and $I$ is the symmetric identity tensor. For more complex rheologies, the constitutive tensor can depend on the strain rate itself, on pressure, temperature, stress history, or material orientation. + +The constitutive model's job is to build this tensor symbolically. The solver reads the model's `.flux` property, which returns the stress as a SymPy matrix expression. From there, the JIT pipeline described in our [SymPy-to-C post](/how-underworld3-turns-sympy-into-c/) takes over: automatically deriving Jacobians, unwrapping nested expressions, C code generation, PETSc integration. + +## Viscous Flow: The Starting Point + +The simplest constitutive model is `ViscousFlowModel`. It has one parameter: shear viscosity. + +```python +stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = uw.expression( + r"\eta", uw.quantity(1e21, "Pa*s") +) +``` + +The viscosity can be a constant, a UWexpression with units, a SymPy expression involving temperature and pressure, or a mesh variable. The model does not care. It builds the stress tensor symbolically: + +$$ +\sigma = 2\eta \, \dot\varepsilon +$$ + +You can inspect this at any time: + +```python +stokes.constitutive_model.flux +# Returns: 2 * η * ε̇(u) — as a SymPy Matrix +``` + +In a Jupyter notebook, this renders as mathematics. You can see exactly what the solver will compute. If the viscosity expression is wrong, you see it here before running the solver. + +## Parameters as Guarded Descriptors + +A common source of bugs in scientific code is mis-spelling a parameter name. You write `stokes.constitutive_model.Parameters.viscosty = 1e21` and nothing complains. The parameter you intended to set keeps its default value. The solver runs. The answer is wrong. + +UW3's parameter system prevents this. Every constitutive model defines a `_Parameters` class whose attributes are descriptors. If you try to set an attribute that does not match a declared parameter, you get an immediate `AttributeError` listing the valid names: + +```python +stokes.constitutive_model.Parameters.viscosty = 1e21 +# AttributeError: Cannot set 'viscosty' on ViscousFlowModel Parameters. +# Valid parameters: shear_viscosity_0 +# (Did you mean 'shear_viscosity_0'? Use .viscosity as a shorthand.) +``` + +The descriptor names are the API. `shear_viscosity_0` is both the internal name and the user-facing setter. For convenience, viscous models also provide a `.viscosity` alias that maps to `shear_viscosity_0`. + +Each parameter descriptor carries a LaTeX symbol, a default value factory, a description, and optional units. The defaults are created lazily through the owning model's symbol factory, ensuring that every parameter gets a unique SymPy symbol even when multiple models coexist. + +## Anisotropy and Tensor Representations + +The scalar viscosity in `ViscousFlowModel` produces an isotropic constitutive tensor. But many geodynamics problems involve directional weakness: fault zones, shear bands, crystallographic fabric. `TransverseIsotropicFlowModel` handles this by introducing a director vector $\mathbf{n}$ and a second viscosity: + +```python +stokes.constitutive_model = uw.constitutive_models.TransverseIsotropicFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = eta_matrix # matrix viscosity +stokes.constitutive_model.Parameters.shear_viscosity_1 = eta_fault # fault-plane viscosity +stokes.constitutive_model.Parameters.director = n_vector # orientation +``` + +The constitutive tensor becomes: + +$$ +C _ {ijkl} = 2\eta _ 0 \, I _ {ijkl} + 2(\eta _ 0 - \eta _ 1) \, A _ {ijkl}(\mathbf{n}) +$$ + +where $A _ {ijkl}$ is the anisotropic correction involving products of the director components. When $\eta _ 0 = \eta _ 1$, the correction vanishes and you recover isotropic flow. When $\eta _ 1 < \eta _ 0$, the material is weak along planes perpendicular to the director. + +Building this tensor correctly requires care with index symmetries. The rank-4 constitutive tensor $C _ {ijkl}$ has 81 components in 3D (16 in 2D), but the symmetries of stress and strain rate reduce the independent entries. The standard approach in finite element work is to flatten the symmetric tensors into vectors and the constitutive tensor into a matrix. There are two common ways to do this, and the difference matters. + +### Voigt Notation + +In Voigt notation, the stress and strain rate tensors are written as vectors by listing the independent components: + +$$ +\tau _ I = (\tau _ {11}, \tau _ {22}, \tau _ {12}), \quad \dot\varepsilon _ I = (\dot\varepsilon _ {11}, \dot\varepsilon _ {22}, 2\dot\varepsilon _ {12}) +$$ + +Note the factor of 2 on the off-diagonal strain rate. The constitutive matrix $C _ {IJ}$ is then the rearrangement of the rank-4 tensor without scaling. For isotropic viscosity in 2D: + +$$ +\left[\begin{matrix} \tau _ {11} \\\\ \tau _ {22} \\\\ \tau _ {12} \end{matrix}\right] = +\left[\begin{matrix} \eta & 0 & 0 \\\\ 0 & \eta & 0 \\\\ 0 & 0 & \eta/2 \end{matrix}\right] +\left[\begin{matrix} \dot\varepsilon _ {11} \\\\ \dot\varepsilon _ {22} \\\\ 2\dot\varepsilon _ {12} \end{matrix}\right] +$$ + +This is what you will find in most finite element textbooks. It works for computing stress from strain rate, but it has a problem: $\tau _ I \dot\varepsilon _ I \neq \tau _ {ij}\dot\varepsilon _ {ij}$. The vector inner product does not reproduce the tensor inner product. And $C _ {IJ}$ does not transform correctly under rotations. + +### Mandel Notation + +Mandel notation fixes both problems by applying a scaling matrix $\mathbf{P}$ that puts a factor of $\sqrt{2}$ on the off-diagonal components: + +$$ +\tau^{ * } _ I = P _ {IJ}\,\tau _ J, \quad \dot\varepsilon^{ * } _ I = P _ {IJ}\,\dot\varepsilon _ J, \quad C^{ * } _ {IJ} = P _ {IK}\,C _ {KL}\,P _ {LJ} +$$ + +where $\mathbf{P} = \text{diag}(1, 1, \sqrt{2})$ in 2D, or $\text{diag}(1,1,1,\sqrt{2},\sqrt{2},\sqrt{2})$ in 3D. In Mandel form, the isotropic constitutive matrix becomes: + +$$ +C^{ * } _ {IJ} = \eta \, \delta _ {IJ} +$$ + +This is just $\eta$ times the identity. The fourth-order symmetric identity tensor, which has an awkward $1/2$ factor in its off-diagonal rank-4 components, becomes the matrix identity in Mandel form. + +The advantage of this approach is that rotations work naturally. If $\mathbf{R}$ is a rotation matrix, then the rotated Mandel constitutive matrix is: + +$$ +C'^{ * } _ {IJ} = R^{ * } _ {IK}\, C^{ * } _ {KL}\, R^{ * T} _ {LJ} +$$ + +where $R^{ * }$ is the Mandel-form rotation matrix derived from $\mathbf{R}$. This is why UW3 builds the transverse isotropic constitutive tensor in Mandel form. The anisotropic correction is defined in the material frame, rotated to the global frame using the director, and converted back to the rank-4 tensor. In Voigt notation, the same rotation would require tracking which components get the factor of 2 and which do not. + +### How UW3 Uses These Representations + +The internal representation is the full rank-4 tensor $C _ {ijkl}$. The Mandel form is available to the user through the `.C` property (capital C) for inspection and for supplying custom anisotropic tensors. The raw rank-4 tensor is available through `.c` (lowercase). If you provide a scalar viscosity, the model builds the rank-4 tensor directly. If you provide a Mandel matrix, the model converts it. Stress is passed to PETSc in Voigt form via `.flux_1d` to match its symmetric tensor storage conventions. The conversions between these representations are handled by utility functions in `maths/tensors.py`, and the index book keeping is automatic and dimension-independent. + +## Adding Plasticity + +`ViscoPlasticFlowModel` extends `ViscousFlowModel` with a yield stress. When the deviatoric stress exceeds the yield stress, the effective viscosity drops to keep the stress at the yield surface: + +```python +stokes.constitutive_model = uw.constitutive_models.ViscoPlasticFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = eta +stokes.constitutive_model.Parameters.yield_stress = uw.expression( + r"\tau_y", uw.quantity(100, "MPa") +) +``` + +The plastic viscosity is computed from the yield stress and the second invariant of the strain rate: + +$$ +\eta _ \textrm{pl} = \frac{\tau _ y}{2 \, \dot\varepsilon _ {II}} +$$ + +The effective viscosity is the lesser of the viscous and plastic values. +$$ +\eta _ \textrm{eff} = \min(\eta _ \textrm{v}, \eta _ \textrm{pl}) +$$ +The model provides several other ways to combine them, because the choice affects Newton solver convergence. The default ("smooth") form uses a corrected harmonic blend: +$$ +\eta _ \textrm{eff} = \eta _ v \cdot \frac{1 + f}{1 + f + f^2}, \quad f = \frac{\eta _ \textrm{v}}{\eta _ \textrm{pl}} +$$ + +This function is smooth everywhere, approaches $\eta _ v$ when $f \to 0$ (below yield), and approaches $\eta _ {pl}$ exactly when $f \to \infty$ (fully yielded). Other modes include harmonic averaging, a soft-min approximation, and a sharp min. The smooth default works well with Newton iteration because the Jacobian is continuous. + +None of this blending logic requires special solver code. The effective viscosity is a SymPy expression. The solver differentiates it symbolically for the Jacobian. If you switch from smooth to sharp yielding, the Jacobian updates automatically. + +## Adding Elasticity: Stress Has Memory + +Viscous and plastic models are instantaneous. The stress depends only on the current strain rate. Elastic behaviour introduces memory: the stress depends on the deformation history. + +`ViscoElasticPlasticFlowModel` handles this. The Maxwell viscoelastic rheology combines viscous and elastic responses: + +$$ +\dot\varepsilon = \frac{\sigma}{2\eta} + \frac{\dot\sigma}{2\mu} +$$ + +Rearranging and discretising in time, the stress at the current step depends on the stress at previous steps. This stress history is a transported term, advected (and rotated) with the flow. + +```python +stokes = uw.systems.VE_Stokes(mesh, order=2) +stokes.constitutive_model = uw.constitutive_models.ViscoElasticPlasticFlowModel +stokes.constitutive_model.Parameters.shear_viscosity_0 = eta +stokes.constitutive_model.Parameters.shear_modulus = uw.expression( + r"\mu", uw.quantity(1e10, "Pa") +) +``` + +The time discretisation uses backward differentiation formulas (BDF) with coefficients that adapt to variable timestep sizes. At order 1, this is the implicit Euler method. At order 2, BDF-2 gives second-order accuracy in time. When the timestep changes abruptly, the model falls back to BDF-1 automatically to avoid instabilities from extrapolating stress history over a large time gap. + +The stress history lives on particles via the solver's `DFDt` (flux time derivative) infrastructure. When you assign a constitutive model that requires stress history, the solver creates the necessary particle storage and sets up advection automatically. The same BDF/Adams-Moulton framework that handles temperature advection handles stress advection. The constitutive model declares `requires_stress_history = True`, and the solver takes care of the rest. + +If you don't want to use particles for + +For VEP problems, the viscoelastic effective strain rate includes contributions from the stress history, and the plastic yield criterion is evaluated against this total deformation rate. The `bdf_blend` parameter controls blending between BDF-1 and BDF-2 near the yield surface, where pure BDF-2 can produce oscillations. The model auto-detects the appropriate blend: pure VE problems get full BDF-2 accuracy, while VEP problems get a stable near-optimal blend. + +Recent work has extended the anisotropic model to `TransverseIsotropicVEPFlowModel`, combining directional weakness with viscoelastic stress memory and plastic yielding. The yield criterion is evaluated on the resolved shear stress on the fault plane, computed from the full stress tensor and the director orientation. In UW3, this is a class that inherits from the VEP model and overrides the stress computation with additional director terms. The Jacobian follows automatically. In UW2, it would have been extremely difficult to implement. + +## The Solver's View + +From the solver's perspective, a constitutive model is just an object with a `.flux` property that returns a SymPy Matrix. The same object pattern is used for constitutive models for stokes flow, heat diffusion, Darcy flow ... The solver does not know whether the flux comes from a constant viscosity, a temperature-dependent Frank-Kamenetskii law, a viscoelastic model with stress history, or an anisotropic fabric model. It differentiates the flux to get the Jacobian, compiles both to C, and registers them with PETSc. + +The assignment pattern reflects this: + +```python +# Assign a class — solver instantiates with its own Unknowns +stokes.constitutive_model = uw.constitutive_models.ViscousFlowModel + +# Or assign an instance you've already configured +model = uw.constitutive_models.ViscoElasticPlasticFlowModel(stokes.Unknowns, order=2) +model.Parameters.shear_viscosity_0 = eta +model.Parameters.shear_modulus = mu +stokes.constitutive_model = model +``` + +When you assign a model, the solver shares its `Unknowns` object with the model. This gives the model access to the velocity gradient (for computing strain rate), the DFDt stress history (for viscoelasticity), and the coordinate system (for computing directors in curvilinear geometry, for example). The model and solver are collaborators, not independent objects. + +## The Design Pattern + +The constitutive model system embodies a design choice that runs through all of Underworld3: separate the physics from the numerics. The physics lives in the constitutive model. It knows about viscosity, yield stress, elastic moduli, directors, stress history. It expresses all of this using SymPy objects. + +The numerical part lives in the solver. This knows about weak forms, Jacobians, PETSc assembly, Newton iteration, time stepping. It reads the model's symbolic expressions and compiles them. + +The boundary between the two is a SymPy Matrix. Everything on one side of that boundary is human-readable physics. On the other side is machine-generated numerics. You can change the physics without touching the solver. You can change the solver without touching the physics. And because the boundary is symbolic, both sides are inspectable at every stage. + +In UW2, the physics and numerics were entangled in C. Changing one required understanding both. In UW3, you can write a new rheology in an afternoon, in a notebook, without compiling anything. That is the practical consequence of making constitutive models symbolic objects. + +--- + +*The Underworld project is supported by AuScope and the Australian Government through the National Collaborative Research Infrastructure Strategy (NCRIS). 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a/publications/blog-posts/figures/finding-particles/boundary-demo.typ b/publications/blog-posts/figures/finding-particles/boundary-demo.typ new file mode 100644 index 000000000..f2b61f391 --- /dev/null +++ b/publications/blog-posts/figures/finding-particles/boundary-demo.typ @@ -0,0 +1,229 @@ +#import "@preview/cetz:0.3.4" + +#set page(width: auto, height: auto, margin: 8pt) +#set text(size: 9pt) + +// ── Data ───────────────────────────────────────────────────────────── +#let mesh = json("boundary-demo-data.json") + +#let pt(i) = { + let v = mesh.vertices.at(i) + (v.at(0), v.at(1)) +} + +#let VIEW = mesh.view + +// ── Helpers ────────────────────────────────────────────────────────── +#let tri-centroid(tri) = { + let a = pt(tri.at(0)) + let b = pt(tri.at(1)) + let c = pt(tri.at(2)) + ((a.at(0) + b.at(0) + c.at(0)) / 3, + (a.at(1) + b.at(1) + c.at(1)) / 3) +} + +#let in-view(p) = { + calc.abs(p.at(0)) <= VIEW and calc.abs(p.at(1)) <= VIEW +} + +// ── Colours ────────────────────────────────────────────────────────── +// Domain A perspective +#let a-inside = rgb(40, 80, 160, 70) // strong blue +#let a-boundary = rgb(120, 150, 200, 45) // light blue-grey +#let a-outside = rgb(240, 240, 240, 30) // near white + +// Domain B perspective +#let b-inside = rgb(180, 50, 50, 70) // strong red +#let b-boundary = rgb(200, 140, 140, 45) // light red-grey +#let b-outside = rgb(240, 240, 240, 30) // near white + +#let stroke-mesh = 0.25pt + rgb("#c0c0c0") +#let boundary-stroke = 1.0pt + rgb("#444444") + +// Control point colours +#let cp-inside-colour = black +#let cp-outside-colour = rgb("#b0b0b0") // grey +#let cp-outside-stroke = 0.3pt + rgb("#555555") // thin dark outline + +#let colour-a = rgb("#2563eb") // blue +#let colour-b = rgb("#dc2626") // red +#let colour-xp = rgb("#7c3aed") // violet + +#let xa = (mesh.test_point_a.at(0), mesh.test_point_a.at(1)) +#let xb = (mesh.test_point_b.at(0), mesh.test_point_b.at(1)) + +// ── Dot helper ─────────────────────────────────────────────────────── +#let dot(p, label: none, direction: (0.06, 0.06), align-to: "west", + radius: 0.028, colour: black, label-colour: none) = { + import cetz.draw: * + circle(p, radius: radius, fill: colour, stroke: none) + if label != none { + let lcolour = if label-colour == none { black } else { label-colour } + content( + (p.at(0) + direction.at(0), p.at(1) + direction.at(1)), + text(fill: lcolour, label), + anchor: align-to, + ) + } +} + +// ── Panel drawing function ─────────────────────────────────────────── +#let draw-panel(zones, inside-col, boundary-col, outside-col, + focus-domain, panel-label, panel-colour) = { + import cetz.draw: * + + // 1. Draw triangles with zone colouring + for (idx, tri) in mesh.triangles.enumerate() { + let c = tri-centroid(tri) + if in-view(c) { + let zone = zones.at(str(idx), default: "outside") + let fill-col = if zone == "inside" { inside-col } + else if zone == "boundary" { boundary-col } + else { outside-col } + line( + pt(tri.at(0)), pt(tri.at(1)), pt(tri.at(2)), + close: true, + fill: fill-col, + stroke: stroke-mesh, + ) + } + } + + // 2. Domain boundary edges — heavy if this domain's boundary, thinner otherwise + let secondary-stroke = 0.5pt + rgb("#555555") + for edge in mesh.boundary_edges { + let p0 = pt(edge.at(0)) + let p1 = pt(edge.at(1)) + if in-view(p0) or in-view(p1) { + let d0 = edge.at(2) + let d1 = edge.at(3) + let involves-focus = d0 == focus-domain or d1 == focus-domain + line(p0, p1, stroke: if involves-focus { boundary-stroke } else { secondary-stroke }) + } + } + + // 3. Boundary control point pairs — only on edges involving focus domain + for cp in mesh.boundary_control_points { + if cp.domain_plus != focus-domain and cp.domain_minus != focus-domain { + continue + } + let p-plus = (cp.pos_plus.at(0), cp.pos_plus.at(1)) + let p-minus = (cp.pos_minus.at(0), cp.pos_minus.at(1)) + if in-view(p-plus) or in-view(p-minus) { + let plus-is-inside = cp.domain_plus == focus-domain + let minus-is-inside = cp.domain_minus == focus-domain + + if plus-is-inside { + circle(p-plus, radius: 0.014, fill: cp-inside-colour, stroke: none) + } else { + circle(p-plus, radius: 0.014, fill: cp-outside-colour, stroke: cp-outside-stroke) + } + if minus-is-inside { + circle(p-minus, radius: 0.014, fill: cp-inside-colour, stroke: none) + } else { + circle(p-minus, radius: 0.014, fill: cp-outside-colour, stroke: cp-outside-stroke) + } + } + } + + // 4. Test particles and their nearest control point connections + let test-points = ( + (xa, colour-a, $x _ a$, (-0.10, -0.06), "east"), + (xb, colour-b, $x _ b$, (0.08, 0.06), "west"), + ((mesh.test_point.at(0), mesh.test_point.at(1)), + colour-xp, $x _ p$, (0.08, 0.06), "west"), + ) + + // For each test point, find the nearest control point and draw a connector + for tp in test-points { + let pos = tp.at(0) + let col = tp.at(1) + + // Search boundary control points on THIS domain's boundary + // (only edges where one side belongs to focus-domain) + let best-dist = 1e9 + let best-pt = pos + let best-is-inside = true + for cp in mesh.boundary_control_points { + // Skip edges that don't involve this domain + if cp.domain_plus != focus-domain and cp.domain_minus != focus-domain { + continue + } + + let p-plus = (cp.pos_plus.at(0), cp.pos_plus.at(1)) + let p-minus = (cp.pos_minus.at(0), cp.pos_minus.at(1)) + + let d-plus = calc.sqrt( + calc.pow(pos.at(0) - p-plus.at(0), 2) + + calc.pow(pos.at(1) - p-plus.at(1), 2)) + let d-minus = calc.sqrt( + calc.pow(pos.at(0) - p-minus.at(0), 2) + + calc.pow(pos.at(1) - p-minus.at(1), 2)) + + if d-plus < best-dist { + best-dist = d-plus + best-pt = p-plus + best-is-inside = cp.domain_plus == focus-domain + } + if d-minus < best-dist { + best-dist = d-minus + best-pt = p-minus + best-is-inside = cp.domain_minus == focus-domain + } + } + + // Draw thin dashed connector + let connector-col = if best-is-inside { cp-inside-colour } else { luma(120) } + line(pos, best-pt, + stroke: (paint: connector-col, thickness: 0.5pt, + dash: (array: (0.5pt, 1.5pt), phase: 0pt))) + + // Draw the test point dot on top + dot(pos, label: tp.at(2), direction: tp.at(3), align-to: tp.at(4), + radius: 0.024, colour: col, label-colour: col) + } + + // 5. Panel label — bottom right + content((VIEW - 0.15, -VIEW + 0.15), + text(fill: panel-colour, size: 11pt, weight: "bold", panel-label), + anchor: "south-east") +} + +// ── Two-panel layout ───────────────────────────────────────────────── +#let panel-width = 8cm +#let panel-height = 8cm +#let gap = 0.4cm + +#box( + width: 2 * panel-width + gap, + height: panel-height, + { + // Left panel: Domain A's perspective + box( + clip: true, + width: panel-width, + height: panel-height, + stroke: 0.5pt + luma(50%), + align(center + horizon, cetz.canvas(length: 2cm, { + draw-panel( + mesh.zones_a, a-inside, a-boundary, a-outside, + "A", "Domain A's view", rgb("#2563eb"), + ) + })), + ) + h(gap) + // Right panel: Domain B's perspective + box( + clip: true, + width: panel-width, + height: panel-height, + stroke: 0.5pt + luma(50%), + align(center + horizon, cetz.canvas(length: 2cm, { + draw-panel( + mesh.zones_b, b-inside, b-boundary, b-outside, + "B", "Domain B's view", rgb("#dc2626"), + ) + })), + 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