Convergence Properties of Overlapping Schwarz Domain Decomposition Algorithms

Details Convergence Properties of Overlapping Schwarz Domain Decomposition Algorithms Convergence Properties of Overlapping Schwarz Domain Decomposition Algorithms

2011-04-21

arxiv.org/abs/1104.4294v1

Mathematics

Numerical Analysis

Scientific paper

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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