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Convergence Properties of Overlapping Schwarz Domain Decomposition Algorithms - MaRDI portal

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Convergence Properties of Overlapping Schwarz Domain Decomposition Algorithms

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Publication:6224969

arXiv1104.4294MaRDI QIDQ6224969

Author name not available (Why is that?)

Publication date: 21 April 2011

Abstract: In this paper, we partially answer open questions about the convergence of overlapping Schwarz methods. We prove that overlapping Schwarz methods with Dirichlet transmission conditions for semilinear elliptic and parabolic equations always converge. While overlapping Schwarz methods with Robin transmission conditions only converge for semilinear parabolic equations, but not for semilinear elliptic ones. We then provide some conditions so that overlapping Schwarz methods with Robin transmission conditions converge for semilinear elliptic equations. Our new techniques can also be potentially applied to others kinds of partial differential equations.












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