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A weakly overlapping domain decomposition preconditioner for the finite element solution of elliptic partial differential equations

Bank, R.E., Jimack, P.K., Nadeem, S.A. and Nepomnyaschikh, S.V. (2002) A weakly overlapping domain decomposition preconditioner for the finite element solution of elliptic partial differential equations. SIAM Journal on Scientific Computing, 23 (6). pp. 1817-1841. ISSN 1064-8275

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Abstract

We present a new two-level additive Schwarz domain decomposition preconditioner which is appropriate for use in the parallel finite element solution of elliptic partial differential equations (PDEs). As with most parallel domain decomposition methods each processor may be assigned one or more subdomains, and the preconditioner is such that the processors are able to solve their own subproblem(s) concurrently.

The novel feature of the technique proposed here is that it requires just a single layer of overlap in the elements which make up each subdomain at each level of refinement, and it is shown that this amount of overlap is sufficient to yield an optimal preconditioner. Some numerical experiments-posed in both two and three space dimensions-are included to confirm that the condition number when using the new preconditioner is indeed independent of the level of mesh refinement on the test problems considered.

Item Type: Article
Copyright, Publisher and Additional Information: © 2002 Society for Industrial and Applied Mathematics. This is an author produced version of a paper published in 'SIAM Journal on Scientific Computing'
Keywords: domain decomposition, Schwarz methods, sparse linear systems, finite element discretization
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Repository Assistant
Date Deposited: 14 Dec 2006
Last Modified: 05 Jun 2014 05:20
Published Version: http://dx.doi.org/10.1137/S1064827501361425
Status: Published
Publisher: SIAM
Refereed: Yes
Identification Number: 10.1137/S1064827501361425
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1736

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