Robust Multigrid Algorithms for 3D Elliptic Equations on Structured Grids

摘要

Two well-known robust multigrid solvers for anisotropic operators on structured grids are compared. The study takes into account not only numerical properties but also architectural ones, focusing on cache memory exploitation and parallel characteristics. Although the alternating-plane approach is the best choice for sequential implementations, it has poorer parallel properties. For the semi-coarsening one two different parallel implementations have been considered. The first one has optimal parallel characteristics but due to deterioration of the convergence properties its global 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.