Residual scaling techniques in multigrid, II: Practical applications

摘要

This paper focuses on the practical applications of the multigrid residual scaling techniques and is the continuation of a companion paper: Residual scaling techniques in multigrid, I: Equivalence proof [Appl. Math. Comput. 86:283–303 (1997)]. We discuss the computational issues of some residual scaling techniques which have been proven mathematically equivalent. A heuristic residual analysis technique, based on the geometry of the grid points and the relaxation pattern, is introduced to estimate the optimal residual scaling factor for a high-order multigrid method. We compare the performance of a typical pre-optimization (pre-acceleration) technique with a typical post-optimization (post-acceleration) technique and show that the pre-optimization is preferable in both convergence and efficiency. Our numerical results support the theoretical conclusions made in the companion paper and demonstrate the full advantage of the pre-optimization technique over the post-optimization technique.