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Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation

Published online by Cambridge University Press:  01 April 2014

Minh-Binh Tran*
Affiliation:
Basque Center for Applied Mathematics, Alameda de Mazarredo, 14 48009 Bilbao, Basque Country, Spain.. tbinh@bcamath.org
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Abstract

We present in this paper a proof of well-posedness and convergence for the parallel Schwarz Waveform Relaxation Algorithm adapted to an N-dimensional semilinear heat equation. Since the equation we study is an evolution one, each subproblem at each step has its own local existence time, we then determine a common existence time for every problem in any subdomain at any step. We also introduce a new technique: Exponential Decay Error Estimates, to prove the convergence of the Schwarz Methods, with multisubdomains, and then apply it to our problem.

Type
Research Article
Copyright
© EDP Sciences, SMAI 2014

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