nataraj2 / poissonfortran

Solves the cell centered, inhomogeneous Poisson equation in 2D with PetSc

Parallel Poisson solver using PETSc (C++ and Fortran)

This repository containes the code for solving a Poisson equation in parallel in two dimensions in PetSc. It solves the inhomogeneous Poisson equation with Neumann boundary conditions on all boundaries.

Governing equation, domain and boundary conditions

The Poisson equation in two-dimensions is given by
$\cfrac{\partial^2 u}{\partial x^2} + \cfrac{\partial^2 u}{\partial y^2} = f$.
In this example $f = 8\pi^2\cos(2\pi x)\cos(2\pi y)$ and the domain is given by $(0,1)\times(0,1)$. Neumann boundary conditions are imposed on all boundaries $\cfrac{\partial u}{\partial n} = 0$. The exact solution is given by $u(x,y) = \cos(2\pi x)\cos(2\pi y)$.

Installation and compilation

1. git clone https://github.com/nataraj2/petsc.git
2. ./configure --with-cc=mpicc --with-cxx=mpicxx --with-fc=mpif90
3. Then set PETSC_DIR = <path>. The output of step 2 on the screen will tell the exact command. Just copy paste it. Add it to the bashrc file.
4. The Cpp and Fortran directories contain the code for C++ and Fortran respectively. To run, just do sh run_poisson2d_neumann.sh
5. python PoissonSolution.py - plots the contours of the exact and petsc solutions.