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M. Sarkis^1,2 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

doi:10.4203/csets.17.7

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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.

Abstract

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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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Computational Science, Engineering & Technology Series ISSN 1759-3158 CSETS: 17 MESH PARTITIONING TECHNIQUES AND DOMAIN DECOMPOSITION METHODS Edited by: F. Magoulès Chapter 7 Domain Decomposition for Nonsymmetric and Indefinite Linear Systems M. Sarkis^1,2 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 doi:10.4203/csets.17.7 purchase the full-text of this chapter 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. Abstract 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. purchase the full-text of this chapter (price £25) go to the previous chapter go to the next chapter return to the table of contents return to the book description purchase this book (price £95 +P&P)
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