poisson-solver's Introduction

Poisson Solver

This project solve Poisson's equation on a 2D grid using either:

A parallel openMP/openACC implementation of the Gauss-Seidel method
or LAPACK

The goal was to practice openMP and openACC parallelization. This was a learning exercise and is not intended to serve as a comparison between LAPACK and GS method.

There is a build script scripts/build.sh.

The binary bin/solver outputs the discrete grid u_grid to a fort file fort.10. You can check that both methods produce the same answer.

Hardware Requirements

I have only tested on NVIDIA GPUs
For NVIDIA GPUs and openMP offloading a GPU with Compute Capability >= 7.0 is required

Results

openMP (CPU only)

Intel CPU - ifort compiler

For problem size:

ugrid[200,200]
tol = 1e-11 (GS only)

For this test run I compiled the code with ifort version 2021.7.0 (oneapi) but the code also works with GNU compiler gfortran.

The test was run on CPU Intel(R) Core(TM) i5-6400 CPU @ 2.70GHz with 16 Gb RAM.

Walltime (s)

Procs	LAPACK	Gauss-Seidel
1	823	25
2	434	16
4	265	11

Maximum Memory

LAPACK	Gauss-Seidel
11.6Gb	22Mb

Arm CPU - Gnu compiler

The test was run on arm CPU Neoverse-N1 with 512 Gb RAM.

Problem size u_grid dims = [300,300] number of iterations = 192018

Cores	Time (s)
80	15.4646
64	14.1203
32	15.4587
16	21.6295
8	38.4833
4	70.8669
2	136.7466
1	270.7637

openACC (GPU)

The test was run on nvidia GPU NVIDIA A100 with 40 Gb RAM connected to the arm system above.

Problem size u_grid dims = [300,300] number of iterations = 192018

GPU	Time (s)
na	17.7678

TODO

Continue to profile openACC version. Check for unneccessary memory transfers.

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poisson-solver's Issues

Build errors

I am trying to build this on our cluster. The build fails, and I found this error message:

   17 |   subroutine get_xy_pos(r, c, x, y)
      |
Error: ‘is_recursive.0’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:17:0: Error: ‘is_recursive.0’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:17:0: Error: ‘is_recursive.0’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:17:0: Error: ‘is_recursive.0’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:17:0: Error: ‘is_recursive.0’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:52:0:

   52 |   end subroutine init_grid
      |
Error: ‘is_recursive.14’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:52:0: Error: ‘is_recursive.14’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:52:0: Error: ‘is_recursive.14’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:52:0: Error: ‘is_recursive.14’ requires a ‘declare’ directive for use in a ‘routine’ function
/home/alessio/src/Poisson-Solver/src/grid_mod.f90:52:0: Error: ‘is_recursive.14’ requires a ‘declare’ directive for use in a ‘routine’ function

I am using NVHPC 22.5 and GCC 9.4.0

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