Parallelization of the Multigrid Method on High Perfomance Computers

This article gives an introduction to the multigrid method. It discusses the issues involved and provides suggestions for parallelization of the multigrid method on HPC platforms. As an example problem, we consider cell-centered finite differences for the Poisson problem on a rectangular domain with uniform meshes. We consider two different intergrid transfer operators and investigate the convergence behavior of the multigrid method with these operators. In addition, different solvers are tested as a “lowest level” solver at the dip of the V -cycle of the multigrid algorithm. Furthermore, the scaling property of the multigrid method on massively parallel machines is investigated. We show that the multigrid algorithm has both good weak and strong scaling properties up to thousands of processors.