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Domain Decomposition Methods

Schwarz Methods

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Book cover Applied Mathematics and Scientific Computing

Abstract

Domain decomposition is a major focus of contemporary research in numerical analysis of partial differential equations. Among the reasons for considering domain decomposition are: parallel computing, modeling of different physical phenomena in different subregions and complicated geometries, and its solid and elegant theoretical foundation. In this text, we provide an introduction to domain decomposition methods. We describe a general variational framework to construct and analyze domain decomposition methods in terms of subspaces and projectionlike operators. This allows a unified analysis of both Schwarz methods (where there is overlap of subregions) and substmcturing methods (where there is no overlap). We also discuss important ingredients commonly used in this research area such as inexact solvers, coarse spaces and nonnested spaces. We provide the basics of the abstract Schwarz theory, giving several proofs, in order to demonstrate the requirements needed for designing good preconditioners.

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Author information

Authors and Affiliations

  1. Mathematical Sciences Department, Worcester Polytechnic Institute, Worcester, MA, 01609, USA

    Marcus Sarkis

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  1. Marcus Sarkis
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Editor information

Editors and Affiliations

  1. University of Zagreb, Zagreb, Croatia

    Zlatko Drmač , Vjeran Hari  & Zvonimir Tutek ,  & 

  2. University of Rijeka, Rijeka, Croatia

    Luka Sopta

  3. University of Hagen, Hagen, Germany

    Krešimir Veselić

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Sarkis, M. (2002). Domain Decomposition Methods. In: Drmač, Z., Hari, V., Sopta, L., Tutek, Z., Veselić, K. (eds) Applied Mathematics and Scientific Computing. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4532-0_1

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  • DOI: https://doi.org/10.1007/978-1-4757-4532-0_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-3390-4

  • Online ISBN: 978-1-4757-4532-0

  • eBook Packages: Springer Book Archive

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