Parallel Schwarz Waveform Relaxation Algorithm for an N-Dimensional Semilinear Heat Equation

Details Parallel Schwarz Waveform Relaxation Algorithm for an N-Dimensional Semilinear Heat Equation Parallel Schwarz Waveform Relaxation Algorithm for an N-Dimensional Semilinear Heat Equation

2010-06-07

arxiv.org/abs/1006.1323v2

Mathematics

Analysis of PDEs

Scientific paper

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.

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