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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: F. Magoulès
Chapter 7

Domain Decomposition for Nonsymmetric and Indefinite Linear Systems

M. Sarkis1,2 and D. Szyld3

1Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
2Department of Mathematical Sciences, Worcester Polytechnic Institute, MA, United States of America
3Department of Mathematics, Temple University, Philadelphia PA, United States of America

Full Bibliographic Reference for this chapter
M. Sarkis, D. Szyld, "Domain Decomposition for Nonsymmetric and Indefinite Linear Systems", in F. Magoulès, (Editor), "Mesh Partitioning Techniques and Domain Decomposition Methods", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 165-188, 2007. doi:10.4203/csets.17.7
Keywords: additive Schwarz preconditioning, Krylov subspace iterative methods, minimal residuals methods, GMRES, indefinite and nonsymmetric elliptic problems, energy norm minimisation.

Many problems in engineering sciences lead to nonsymmetric and indefinite linear systems. Such problems arise for example in fluid dynamics, acoustics and advection-diffusion problems. In this chapter, we discuss preconditioned Krylov subspace methods for such systems. The preconditioners are based on domain decomposition methods. We present the known abstract convergence theory for these preconditioners, and how it is applied to a few problems.

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