Parallel performances of a multigrid poisson solver

Practical implementation of the parallel multigrid method (MG) for solving the Poisson equation on arbitrary 3-dimensional domains using finite difference approximations and Neumann boundary conditions is described and compared to the SOR method. Some details on discretization are given and the resulting system of linear equations is analysed. The implemented program is based on the domain decomposition, uses MPI communication library and was tested on a workstation cluster based on 750 MHz Athlon processors and connected in a mesh with 100 Mb/s communication links. Speed-up is analysed for different numbers of processors and domain sizes. The parallel MG method achieves parallel efficiency greater than 0.6 for domains with more than 105 grid points and is faster than parallel SOR for domain sizes greater than 104 points.