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Parallel application of a novel domain decomposition preconditioner for the adaptive finite‐element solution of three‐dimensional convection‐dominated PDEs
Author(s) -
Jimack P. K.,
Nadeem S. A.
Publication year - 2003
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.740
Subject(s) - preconditioner , domain decomposition methods , discretization , finite element method , multigrid method , partial differential equation , mathematics , galerkin method , discontinuous galerkin method , linear system , polygon mesh , elliptic partial differential equation , mathematical analysis , physics , geometry , thermodynamics
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. Copyright © 2003 John Wiley & Sons, Ltd.