Laplace

Solves the ​Laplace equation u_xx + u_yy = 0 in a rectangular domain, by iteratively applying a stencil function.

The first argument is the number of iterations to use. The second is a BMP file containing boundary conditions.

 repa-laplace 10000 pls-400x400.bmp pls-400x400-out.bmp

Code

The main algorithm is at ​Solver.hs

The wrapper is at ​Main.hs

Test Data

In the input file, greyscale gives the boundary conditions, blue specifies where to determine the solution.

pls-400x400.bmp	pls-400x400-out.bmp
​full size	​full size

Runtime

Compiled with GHC 6.13.20100309. 400x400 image. 10000 iterations.

Running on a Intel i7 iMac. 2.8Ghz, 4 cores x 2 threads/core. 256k L1, 8MB L2, 8GB main memory.

Times stated include IO.

Threads	Time(s)
1	64.67
2	37.29
3	27.45
4	31.96
5	28.08
6	24.39
7	23.83
8	24.67