Computational & Technology Resources
an online resource for computational,
engineering & technology publications
Computational Science, Engineering & Technology Series
MESH PARTITIONING TECHNIQUES AND DOMAIN DECOMPOSITION METHODS
Edited by: F. Magoulès
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
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.
purchase the full-text of this chapter (price £25)