Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, p. 795-813
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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.

DOI : https://doi.org/10.1051/m2an/2013121
Classification:  65M12
Keywords: domain decomposition, waveform relaxation, Schwarz methods, semilinear heat equation
@article{M2AN_2014__48_3_795_0,
     author = {Tran, Minh-Binh},
     title = {Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     pages = {795-813},
     doi = {10.1051/m2an/2013121},
     mrnumber = {3264335},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_3_795_0}
}
Tran, Minh-Binh. Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 3, pp. 795-813. doi : 10.1051/m2an/2013121. http://www.numdam.org/item/M2AN_2014__48_3_795_0/

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