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Parallel application of a novel domain decomposition preconditioner for the adaptive finite-element solution of three-dimensional convection-dominated PDEs

Jimack, P.K. and Nadeem, S.A. (2003) Parallel application of a novel domain decomposition preconditioner for the adaptive finite-element solution of three-dimensional convection-dominated PDEs. Concurrency and Computation: Practice and Experience, 15 (10). pp. 939-956. ISSN 1532-0626

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Abstract

We describe and analyse the parallel implementation of a novel domain decomposition preconditioner for the fast iterative solution of linear systems of algebraic equations arising from the discretization of elliptic partial differential equations (PDEs) in three dimensions. In previous theoretical work, this preconditioner has been proved to be optimal for symmetric positive-definite (SPD) linear systems.

In this paper, we provide details of our three-dimensional parallel implementation and demonstrate that the technique may be generalized to the solution of non-symmetric algebraic systems, such as those arising when convection-diffusion problems are discretized using either Galerkin or stabilized finite-element methods (FEMs). Furthermore, we illustrate the potential of the preconditioner for use within an adaptive finite-element framework by successfully solving convection-dominated problems on locally, rather than globally, refined meshes.

Item Type: Article
Copyright, Publisher and Additional Information: © 2003 John Wiley & Sons, Ltd. This is an author produced version of a paper published in 'Concurrency and Computation: Practice and Experience'
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: 21 Nov 2006
Last Modified: 04 Jun 2014 19:44
Published Version: http://dx.doi.org/10.1002/cpe.740
Status: Published
Publisher: John Wiley & Sons, Ltd.
Refereed: Yes
Identification Number: 10.1002/cpe.740
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1737

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