Comptes Rendus
no. 11
Numerical Analysis
Non-overlapping additive Schwarz methods tuned to highly heterogeneous media
[Méthodes de Schwarz additives sans recouvrement pour des milieux très hétérogènes]

Présenté par : Olivier Pironneau

Yvon Maday1, 2 ; Frédéric Magoulès3
1 Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, BP 187, 75252 Paris cedex 05, France
2 Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA
3 Institut Elie-Cartan de Nancy, université Henri-Poincaré, BP 239, 54506 Vandoeuvre-les-Nancy cedex, France
Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 701-705.

Dans cette Note une variante de l'algorithme de Schwarz est introduite pour des milieux très hétérogènes. Cette méthode utilise des conditions d'interfaces optimisées spécialement conçues pour tenir compte de l'hétérogénéité entre les sous-domaines. L'étude mathématique de ces conditions d'interfaces est dans un premier temps présentée. Une analyse asymptotique en fonction de la finesse du maillage et du rapport de l'hétérogénéité est ensuite détaillée.

In this Note an improved version of the Schwarz domain decomposition method is introduced for highly heterogeneous media. This method uses new optimized interface conditions specially designed to take into account the heterogeneity between the subdomains on the interfaces. The mathematical analysis of these interface conditions is first presented. Then the asymptotic analysis upon the mesh size parameter together with the heterogeneity ratio is detailed.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.09.032
Yvon Maday 1, 2 ; Frédéric Magoulès 3

1 Laboratoire Jacques-Louis Lions, université Pierre et Marie Curie, BP 187, 75252 Paris cedex 05, France
2 Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA
3 Institut Elie-Cartan de Nancy, université Henri-Poincaré, BP 239, 54506 Vandoeuvre-les-Nancy cedex, France 
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     language = {en},
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Yvon Maday; Frédéric Magoulès. Non-overlapping additive Schwarz methods tuned to highly heterogeneous media. Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 701-705. doi : 10.1016/j.crma.2005.09.032. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.032/

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[8] L. Gerardo Giorda, F. Nataf, Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients, RR 561, CMAP, 2004

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[10] P.-L. Lions On the Schwarz alternating method. III: A variant for nonoverlapping subdomains (T. Chan; R. Glowinski; J. Périaux; O. Widlund, eds.), Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, held in Houston, TX, March 20–22, 1989, SIAM, Philadelphia, PA, 1990

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