NDLI: SchurRAS: A Restricted Version of the Overlapping Schur Complement Preconditioner

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Li, Zhongze Saad, Yousef
Copyright Year	2006
Abstract	This paper presents a preconditioner based on solving approximate Schur complement systems with the overlapping restricted additive Schwarz (RAS) methods. The construction of the preconditioner, called SchurRAS, is as simple as in the standard RAS. The communication requirements for each application of the preconditioning operation are also similar to those of the standard RAS approach. In the particular case when the degree of overlap is one, then SchurRAS and RAS involve exactly the same communication volume per step. In addition, SchurRAS has the same degree of parallelism as RAS. In some numerical experiments with a model problem, the convergence rate of the method was found to be similar to that of the multiplicative Schwarz (MS) method. The Schur-based RAS usually outperforms the standard RAS both in terms of iteration count and CPU time. For a few two-dimensional scaled problems, SchurRAS was about twice as fast as the stardard RAS on 64 processors.
Starting Page	1787
Ending Page	1801
Page Count	15
File Format	PDF
ISSN	10648275
DOI	10.1137/040608350
e-ISSN	10957197
Issue Number	5
Volume Number	27
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-26
Access Restriction	Subscribed
Subject Keyword	Schur complement techniques restricted additive Schwarz preconditioner Iterative methods for linear systems domain decomposition additive Schwarz preconditioner Parallel computation distributed sparse linear systems Sparse matrices Multigrid methods; domain decomposition parallel preconditioning
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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