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IMA Journal of Numerical Analysis Advance Access originally published online on May 23, 2008
IMA Journal of Numerical Analysis 2009 29(3):508-538; doi:10.1093/imanum/drn023
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Alternate slice-based substructuring in three dimensions

L. Angela Mihai{dagger}

Department of Chemical Engineering, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK

Alan W. Craig

Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, UK

{dagger} Email: lam40{at}cam.ac.uk

Received on 20 April 2007. Revised on 21 March 2008.


  Abstract

The slice-based substructuring methods introduced in this paper are Schur complement solvers for the decomposition of a three-dimensional domain into multiple disjoint subdomains with interior crosspoints. The subdomains are assembled into nonoverlapping slices such that the edges of each slice lie on the boundary of the given domain and the union of the faces between slices contains all of the interior vertices. For the subproblems corresponding to the various faces, a direct fast Poisson solver is used. Scalability is achieved in two stages where the slices change such that the faces between slices at one stage are orthogonal to the faces between slices at the other. The two stages guarantee a good rate of convergence of the resulting preconditioned iterative procedure, which is optimal with respect to the partitioning parameters.

Key Words: domain decomposition; Schwarz method; Schur complement; iterative substructuring; elliptic equations; finite elements


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