A robust multigrid solver on parallel computers

In this paper two well-known robust multigrid solvers for anisotropic operators on structured grids are compared: alternating-plane smoothers with full coarsening and plane smoothers combined with semicoarsening. The study takes into account not only numerical properties but also architectural ones, focusing on cache memory exploitation and parallel characteristics. Experimental results for the sequential algorithms have been obtained on two different systems based on the MIPS R10000 processor but with different L2 cache sizes (an SGI O2 workstation and an SGI Origin 2000 system). Two different parallel implementations for the latter robust approach have been considered. The first one has optimal parallel characteristics but due to deterioration of the convergence properties its realistic efficiency is not satisfactory. In the second one, some processors remain idle during a short period of time on every multigrid cycle, however the algorithm is more efficient since it preserves the numerical properties of the sequential version. Parallel experiments have also been taken on a Cray T3E system.