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A domain decomposition method using efficient interface-acting preconditioners


Author: Serge Kräutle
Journal: Math. Comp. 74 (2005), 1231-1256
MSC (2000): Primary 65N55; Secondary 65Y05, 65M70, 35J05
DOI: https://doi.org/10.1090/S0025-5718-04-01706-5
Published electronically: September 17, 2004
MathSciNet review: 2137001
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Abstract: The conjugate gradient boundary iteration (CGBI) is a domain decomposition method for symmetric elliptic problems on domains with large aspect ratio. High efficiency is reached by the construction of preconditioners that are acting only on the subdomain interfaces. The theoretical derivation of the method and some numerical results revealing a convergence rate of 0.04-0.1 per iteration step are given in this article. For the solution of the local subdomain problems, both finite element (FE) and spectral Chebyshev methods are considered.

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Additional Information

Serge Kräutle
Affiliation: Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstrasse 3, 91054 Erlangen, Germany
Email: kraeutle@am.uni-erlangen.de

DOI: https://doi.org/10.1090/S0025-5718-04-01706-5
Keywords: Parallelization, domain decomposition, preconditioning, FETI
Received by editor(s): October 18, 2003
Received by editor(s) in revised form: February 9, 2004
Published electronically: September 17, 2004
Additional Notes: This work was supported by the Deutsche Forschungsgemeinschaft (DFG) and the Centre National de la Recherche Scientifique (CNRS)
Article copyright: © Copyright 2004 American Mathematical Society