Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation∗
Basque Center for Applied Mathematics, Alameda de Mazarredo, 14 48009 Bilbao,
Basque Country, Spain.
Revised: 12 August 2013
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.
Mathematics Subject Classification: 65M12
Key words: Domain decomposition / waveform relaxation / Schwarz methods / semilinear heat equation
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