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A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations

Bank, R.E. and Jimack, P.K. (2001) A new parallel domain decomposition method for the adaptive finite element solution of elliptic partial differential equations. Concurrency and Computation: Practice and Experience, 13 (5). pp. 327-350. ISSN 1532-0626

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Abstract

We present a new domain decomposition algorithm for the parallel finite element solution of elliptic partial differential equations. As with most parallel domain decomposition methods each processor is assigned one or more subdomains and an iteration is devised which allows the processors to solve their own subproblem(s) concurrently. The novel feature of this algorithm however is that each of these subproblems is defined over the entire domain - although the vast majority of the degrees of freedom for each subproblem are associated with a single subdomain (owned by the corresponding processor). This ensures that a global mechanism is contained within each of the subproblems tackled and so no separate coarse grid solve is required in order to achieve rapid convergence of the overall iteration.

Furthermore, by following the paradigm introduced in [15], it is demonstrated that this domain decomposition solver may be coupled easily with a conventional mesh refinement code, thus allowing the accuracy, reliability and efficiency of mesh adaptivity to be utilized in a well load-balanced manner. Finally, numerical evidence is presented which suggests that this technique has significant potential, both in terms of the rapid convergence properties and the efficiency of the parallel implementation.

Item Type: Article
Copyright, Publisher and Additional Information: © 2001 John Wiley & Sons, Ltd. This is an author produced version of a paper published in 'Concurrency and Computation: Practice and Experience'
Keywords: partial differential equations, parallel computing, domain decomposition, mesh adaptivity, finite element method
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: 16 Nov 2006
Last Modified: 09 Jun 2014 07:03
Published Version: http://dx.doi.org/10.1002/cpe.569
Status: Published
Publisher: John Wiley & Sons, Ltd.
Refereed: Yes
Identification Number: 10.1002/cpe.569
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1714

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