Parallel Poisson's equation Solver

Solve the 2D Poisson's equation

$$ \frac{\partial^2}{\partial x^2} f(x, y) + \frac{\partial^2}{\partial y^2} f(x, y) = g(x, y) $$

on a square in parallel using OpenMPI. Successive over-relaxation is used to obtain a solution $f$ from RHS $g$. Solution is parallelized using domain decomposition on the unit square, which allows each CPU to solve a piece of the whole problem. Code written in C, with Python plotting. See doc.pdf for further documentation.

Usage:

./parps <infile> <outfile> <n> <gamma> <crit>

infile = input file for $g$ as an $n \times n$ matrix, edges are boundary conditions for $f$

outfile = solution output file for $f$ as an $n \times n$ matrix

n = system size

gamma = over-relaxation parameter $\gamma \in ]1, 2[$

crit = convergence criterion (sum of all differences between iterations)

Plotting

To plot the example result matrices and compare them:

./plotmat.py serial.dat parallel.dat

To monitor convergence of solutions from log files in real time, a Gnuplot script can be used:

gnuplot residual.gp