2011 | OriginalPaper | Buchkapitel
Optimized Schwarz Methods for Domains with an Arbitrary Interface
verfasst von : Shiu Hong Lui
Erschienen in: Domain Decomposition Methods in Science and Engineering XIX
Verlag: Springer Berlin Heidelberg
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Optimized Schwarz methods form a class of domain decomposition methods for the solution of partial differential equations. Optimized Schwarz methods employ a first or higher order boundary condition along the artificial interface to accelerate its convergence. In the literature, analysis of optimized Schwarz methods rely on Fourier analysis and so the domains are restricted to be regular (rectangle or disk). By expressing the interface operator in terms of Poincare–Steklov operators, we are able to derive upper bounds of the spectral radius of the operator for Poisson-like problems for two essentially arbitrary subdomains. For a first order (Robin) boundary operator