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.
Mots-clés : 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 }, pages = {795--813}, publisher = {EDP-Sciences}, volume = {48}, number = {3}, year = {2014}, doi = {10.1051/m2an/2013121}, mrnumber = {3264335}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2013121/} }
TY - JOUR AU - Tran, Minh-Binh TI - Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 795 EP - 813 VL - 48 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2013121/ DO - 10.1051/m2an/2013121 LA - en ID - M2AN_2014__48_3_795_0 ER -
%0 Journal Article %A Tran, Minh-Binh %T Parallel Schwarz Waveform Relaxation Algorithm for an N-dimensional semilinear heat equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 795-813 %V 48 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2013121/ %R 10.1051/m2an/2013121 %G en %F 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 , Tome 48 (2014) no. 3, pp. 795-813. doi : 10.1051/m2an/2013121. http://archive.numdam.org/articles/10.1051/m2an/2013121/
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