Gauss Integration Points
For integrate, we are going to use two geometries: for a triangle(T3 or T6) and for a square(Q4 or Q8). If you don't know about the Base Elements' Geometry, we strongly recommend you to see it before.
 |
 |
 |
|---|---|---|
| 1 Point | 3 points | 4 points |
| Number | Points | Weight |
|---|---|---|
| 1 | (0, 0) | 1/2 |
| (1/6, 1/6) | 1/6 | |
| 3 | (2/3, 1/6) | 1/6 |
| (1/6, 2/3) | 1/6 | |
| (1/5, 1/5) | 25/96 | |
| 4 | (3/5, 1/5) | 25/96 |
| (1/5, 3/5) | 25/96 | |
| (1/3, 1/3) | -9/32 |
 |
 |
 |
|---|---|---|
| 1 Point | 4 points | 9 points |
| Number | Points | Weight |
|---|---|---|
| 1 | (0, 0) | 4 |
| (-a, -a) | 1 | |
| 4 | (a, -a) | 1 |
| (-a, a) | 1 | |
| (a, a) | 1 | |
| (-b, -b) | 25/81 | |
| (0, -b) | 40/81 | |
| (b, -b) | 25/81 | |
| (-b, 0) | 40/81 | |
| 9 | (0, 0) | 64/81 |
| (b, 0) | 40/81 | |
| (-b, b) | 25/81 | |
| (0, b) | 40/81 | |
| (b, b) | 25/81 |
Where a = 1/sqrt(3) and b = sqrt(3/5)