[Un espace grossier robuste pour les méthodes de Schwarz optimisées : SORAS-GenEO-2]
Les méthodes de Schwarz optimisées sont des méthodes très populaires, qui ont été introduites dans [11] pour des problèmes elliptiques et dans [3] pour des phénomènes de propagation d'ondes. Nous construisons ici un espace grossier pour lequel le taux de convergence de la méthode à deux niveaux peut être prescrit à l'avance sans hypothèse sur la régularité des coefficients. Ceci est rendu possible par l'introduction d'une version symétrisée de la méthode ORAS (Optimized Restricted Additive Schwarz) [17] ainsi que par l'identification des modes problématiques via deux problèmes aux valeurs propres généralisées au lieu d'un seul comme dans [16,15] pour les méthodes ASM (Additive Schwarz method), BDD (Balancing Domain Decomposition [12]) ou FETI (Finite-Element Tearing and Interconnection [6]).
Optimized Schwarz methods (OSM) are very popular methods that were introduced in [11] for elliptic problems and in [3] for propagative wave phenomena. We build here a coarse space for which the convergence rate of the two-level method is guaranteed regardless of the regularity of the coefficients. We do this by introducing a symmetrized variant of the ORAS (Optimized Restricted Additive Schwarz) algorithm [17] and by identifying the problematic modes using two different generalized eigenvalue problems instead of only one as in [16,15] for the ASM (Additive Schwarz method), BDD (Balancing Domain Decomposition [12]) or FETI (Finite-Element Tearing and Interconnection [6]) methods.
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@article{CRMATH_2015__353_10_959_0,
author = {Haferssas, Ryadh and Jolivet, Pierre and Nataf, Fr\'ed\'eric},
title = {A robust coarse space for optimized {Schwarz} methods: {SORAS-GenEO-2}},
journal = {Comptes Rendus. Math\'ematique},
pages = {959--963},
publisher = {Elsevier},
volume = {353},
number = {10},
year = {2015},
doi = {10.1016/j.crma.2015.07.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.07.014/}
}
TY - JOUR AU - Haferssas, Ryadh AU - Jolivet, Pierre AU - Nataf, Frédéric TI - A robust coarse space for optimized Schwarz methods: SORAS-GenEO-2 JO - Comptes Rendus. Mathématique PY - 2015 SP - 959 EP - 963 VL - 353 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.07.014/ DO - 10.1016/j.crma.2015.07.014 LA - en ID - CRMATH_2015__353_10_959_0 ER -
%0 Journal Article %A Haferssas, Ryadh %A Jolivet, Pierre %A Nataf, Frédéric %T A robust coarse space for optimized Schwarz methods: SORAS-GenEO-2 %J Comptes Rendus. Mathématique %D 2015 %P 959-963 %V 353 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.07.014/ %R 10.1016/j.crma.2015.07.014 %G en %F CRMATH_2015__353_10_959_0
Haferssas, Ryadh; Jolivet, Pierre; Nataf, Frédéric. A robust coarse space for optimized Schwarz methods: SORAS-GenEO-2. Comptes Rendus. Mathématique, Tome 353 (2015) no. 10, pp. 959-963. doi : 10.1016/j.crma.2015.07.014. http://www.numdam.org/articles/10.1016/j.crma.2015.07.014/
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