Laplace equation solver

Solve laplace equation using Jacobi/Gauss-Seidel method.

C

The C version contains a sequential and a parallel (using MPI) version.

C
- bin: build directory
- src
    - 2darrays: functions for 2d array handling
    - solvers: implementations of Jacobi and Gauss-Seidel solvers
    - laplace_seq.c: sequential version
    - laplace_mpi.c: parallel version

How to use

0. Requirements: MPI (for the parallel version)

1. Compile using the Makefile

   cd C
   make all

2. Run the sequential version using

   ./bin/laplace_seq METHOD NX NY TOLERANCE

   • METHOD: use Jacobi solver if 0, Gauss-Seidel if 1
   • NX NY: number of points in the grid
   • TOLERANCE: target max difference for convergence

   Example:

   ./bin/laplace_seq 0 128 128 1e-6

3. Run the parallel version using

   mpirun -np NUMPROC ./bin/laplace_mpi METHOD NX NY TOLERANCE

   Command arguments are as above, plus

   • NUMPROC: number of processors

   Example:

   mpirun -np 4 ./bin/laplace_mpi 0 128 128 1e-6

4. The command returns number of iterations and time needed for convergence. The data is in laplace.dat and can be plotted using (requires numpy, matplotlib)

   python ../python/plot.py laplace.dat

Python

The python version contains a sequential and a parallel version (using mpi4py).

How to use

0. Install all requirements (numpy, mpi4py, matplotlib, numba)

   cd python
   pip install -r requirements.txt

1. Run the sequential version using

   python laplace_seq.py METHOD NX NY TOLERANCE

   • METHOD
     • jacobi_seq: sequential version of Jacobi solver
     • jacobi_vec: vectorized version of Jacobi solver using numpy functions
     • gs_seq: sequential version of Gauss-Seidel solver
     • gs_vec: semi-vectorized version of Gauss-Seidel solver
   • NX NY: number of points in the grid
   • TOLERANCE: target max difference for convergence

   Example:

   python laplace_seq.py jacobi_vec 128 128 1e-6

2. Run the parallel version using

   mpirun -np NUMPROC python laplace_mpi.py METHOD NX NY TOLERANCE

   Command arguments are as above, plus

   • NUMPROC: number of processors

   Example:

   mpirun -np 4 python laplace_mpi.py jacobi_vec 128 128 1e-6

3. Run the numba version using

   python laplace_numba.py NX NY TOLERANCE

   Example:

   python laplace_numba.py 128 128 1e-6

4. The command returns number of iterations, time needed for convergence and plots the solution.