Saxe-Coburg Publications - ISBN 978-1-874672-29-6

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

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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Front Page Publications New Books Edited Books Complete Catalogue Forthcoming Books Our Authors Search Pricelist Ordering Author-zone General Info	MESH PARTITIONING TECHNIQUES AND DOMAIN DECOMPOSITION METHODS Edited by: F. Magoulès Chapter 7 Domain Decomposition for Nonsymmetric and IndefiniteLinear 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 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. Return to the contents page Return to the book description
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