Tarang.jl

A High-Performance (Pseudo-)Spectral PDE Solver

Solve partial differential equations with spectral accuracy on CPUs, GPUs, and distributed clusters — using natural mathematical syntax.

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Installation

using Pkg

# Basic installation
Pkg.add(url="https://github.com/subhk/Tarang.jl")

# With GPU support
Pkg.add(["CUDA", "KernelAbstractions"])

# With MPI support
Pkg.add(["MPI", "PencilArrays", "PencilFFTs"])

Requires Julia 1.10 or later. GPU support requires an NVIDIA GPU with CUDA. MPI requires OpenMPI or MPICH.

Quick Start

1D Diffusion

using Tarang

domain = PeriodicDomain(64)                     # 64-point periodic domain [0, 2pi]
T = ScalarField(domain, "T")                    # Temperature field

problem = IVP([T])
add_substitution!(problem, "kappa", 0.01)
add_equation!(problem, "dt(T) - kappa*lap(T) = 0")

solver = InitialValueSolver(problem, RK222(); dt=0.01)
run!(solver; stop_time=1.0)

2D Rayleigh-Benard Convection

using Tarang

# Channel domain: periodic in x (Fourier), bounded in z (Chebyshev)
domain = ChannelDomain(256, 64; Lx=4.0, Lz=1.0, dealias=3/2)

p = ScalarField(domain, "p")               # Pressure
b = ScalarField(domain, "b")               # Buoyancy
u = VectorField(domain, "u")               # Velocity

problem = IVP(variables)
add_parameters!(problem, kappa=kappa, nu=nu, Lz=Lz)

add_equation!(problem, "div(u) + tau_p = 0")
add_equation!(problem, "dt(b) - kappa*lap(b) + lift(tau_b1, -1) + lift(tau_b2, -2) = -u dot grad(b)")
add_equation!(problem, "dt(u) - nu*lap(u) + grad(p) + lift(tau_u1, -1) + lift(tau_u2, -2) = -u dot grad(u) + b*ez")

fixed_value!(problem, "b", "z", 0.0, Lz)   # Hot bottom
fixed_value!(problem, "b", "z", Lz, 0.0)   # Cold top
no_slip!(problem, "u", "z", 0.0)            # No-slip bottom
no_slip!(problem, "u", "z", Lz)             # No-slip top

solver = InitialValueSolver(problem, RK222(); dt=0.125)
run!(solver; stop_time=50.0, log_interval=100)

See examples/ for complete runnable scripts including QG turbulence, rotating shallow water, and more.

GPU

using Tarang, CUDA

# Add arch=GPU() -- everything else stays the same
domain = PeriodicDomain(512, 512; arch=GPU(), dtype=Float32)
field = ScalarField(domain, "u")
forward_transform!(field)   # Uses cuFFT automatically

# Single GPU
julia --project=. examples/gpu_example.jl

# Multi-GPU with MPI (4 GPUs)
mpiexec -n 4 julia --project=. examples/gpu_example.jl

MPI

# Run any script in parallel with MPI
mpiexec -n 4 julia --project=. examples/ivp/rayleigh_benard_2d.jl

Spectral Bases

Basis	Domain	Use Case
RealFourier	Periodic	Horizontal directions, real-valued fields
ComplexFourier	Periodic	Complex-valued fields
ChebyshevT	Bounded	Wall-bounded domains, boundary conditions
Legendre	Bounded	Alternative to Chebyshev

Time Integrators

Family	Schemes
IMEX Runge-Kutta	RK111, RK222, RK443, RKSMR
Multistep IMEX	CNAB1, CNAB2, SBDF1--SBDF4
Exponential	ETD_RK222, ETD_CNAB2, ETD_SBDF2
Diagonal IMEX	DiagonalIMEX_RK222, DiagonalIMEX_RK443, DiagonalIMEX_SBDF2

Testing

julia --project=. -e 'using Pkg; Pkg.test()'   # CPU test suite
julia --project=. test/run_mpi_ci.jl 4          # MPI tests across 4 ranks

CPU and MPI tests run on GitHub Actions; GPU tests (CUDA + NCCL) run on JuliaGPU Buildkite (.buildkite/pipeline.yml), since GitHub-hosted runners have no GPU. See the testing guide for running GPU/MPI tests locally and for enabling GPU CI.