USING SYMMETRIES AND ANTISYMMETRIES TO ANALYZE A PARALLEL MULTIGRID ALGORITHM - THE ELLIPTIC BOUNDARY-VALUE PROBLEM CASE

作     者：DOUGLAS, CC SMITH, BF 

作者机构：NYUCOURANT INST MATH SCIDEPT MATHNEW YORKNY 10012 

出 版 物：《SIAM JOURNAL ON NUMERICAL ANALYSIS》 (工业与应用数学会数值分析杂志)

年 卷 期：1989年第26卷第6期

页      面：1439-1461页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：65W05 65N15 65N10 partial differential equations parallel multigrid robust multigrid solver domain decomposition direct method iterative method convergence rates 

摘      要：Symmetry and antisymmetry properties of a class of elliptic partial differential equations are exploited to prove when a particular parallel multilevel algorithm is a direct method rather than the usual iterative method. No smoothing is required for this result. Examples are presented, including variable coefficient ones. A connection between the algorithm in this article and domain decomposition is established, even though this algorithm is more general and different. The parallel algorithm is also analyzed when it is iterative and it is shown how to increase processor utilization. Hackbusch’s robust multigrid algorithm [“A new approach to robust multi-grid solvers, in ICIAM ’87 : Proceedings of the First International Conference on Industrial and Applied Mathematics, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1988, pp. 111–126] is analyzed for some model problems and it is shown that the parallel algorithm in this article uses much less computer time with at most the same amount of storage.