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Residual scaling techniques in multigrid, II: Practical applications

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
90
Identifiers
DOI: 10.1016/s0096-3003(97)00400-1
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract 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.

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