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Parallel Schwarz Waveform Relaxation Algorithm for anN-dimensional semilinear heat equation∗

Published online by Cambridge University Press:  01 April 2014

Minh-Binh Tran
Minh-Binh Tran*
Affiliation:
Basque Center for Applied Mathematics, Alameda de Mazarredo, 14 48009 Bilbao, Basque Country, Spain.. [email protected]
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Abstract

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

Keywords

Domain decompositionwaveform relaxationSchwarz methodssemilinear heat equation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 3 , May 2014 , pp. 795 - 813
Copyright
© EDP Sciences, SMAI 2014

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