A robust coarse space for optimized Schwarz methods: SORAS-GenEO-2

Ryadh Haferssas; Pierre Jolivet; Frédéric Nataf

doi:10.1016/j.crma.2015.07.014

Numerical analysis

A robust coarse space for optimized Schwarz methods: SORAS-GenEO-2
[Un espace grossier robuste pour les méthodes de Schwarz optimisées : SORAS-GenEO-2]

Présenté par : Olivier Pironneau

Ryadh Haferssas ^1,² ; Pierre Jolivet ^1,² ; Frédéric Nataf ^1,²

¹ Laboratoire Jacques-Louis-Lions, CNRS UMR 7598, Université Pierre-et-Marie-Curie, 75252 Paris cedex 05, France
² INRIA Rocquencourt, Alpines, BP 105, 78153 Le Chesnay cedex, France

Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 959-963.

Résumé
Abstract

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.

Reçu le : 2015-01-05
Accepté le : 2015-07-30
Publié le : 2015-10-01

DOI : 10.1016/j.crma.2015.07.014

Affiliations des auteurs :

Ryadh Haferssas ^{1, 2} ; Pierre Jolivet ^{1, 2} ; Frédéric Nataf ^{1, 2}

¹ Laboratoire Jacques-Louis-Lions, CNRS UMR 7598, Université Pierre-et-Marie-Curie, 75252 Paris cedex 05, France
² INRIA Rocquencourt, Alpines, BP 105, 78153 Le Chesnay cedex, France

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     author = {Ryadh Haferssas and Pierre Jolivet and Fr\'ed\'eric Nataf},
     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},
}

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Ryadh Haferssas; Pierre Jolivet; Frédéric Nataf. A robust coarse space for optimized Schwarz methods: SORAS-GenEO-2. Comptes Rendus. Mathématique, Volume 353 (2015) no. 10, pp. 959-963. doi : 10.1016/j.crma.2015.07.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.07.014/

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