| Issue |
ESAIM: M2AN
Volume 48, Number 3, May-June 2014
|
|
|---|---|---|
| Page(s) | 795 - 813 | |
| DOI | https://doi.org/10.1051/m2an/2013121 | |
| Published online | 01 April 2014 | |
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.
tbinh@bcamath.org
Received:
20
September
2012
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
© EDP Sciences, SMAI 2014
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