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Comptes Rendus Mathématique
Volume 342, n° 11
pages 883-886 (juin 2006)
Doi : 10.1016/j.crma.2006.03.024
Received : 7 November 2005 ;  accepted : 14 Mars 2006
Improved interface conditions for a non-overlapping domain decomposition of a non-convex polygonal domain
Conditions dʼinterface améliorées pour une décomposition dʼun domaine polygonal non convexe
 

Chokri Chniti a , Frédéric Nataf a , Francis Nier b
a CMAP, École polytechnique, 91128 Palaiseau cedex, France 
b IRMAR, campus de Beaulieu, 35042 Rennes cedex, France 

Abstract

We propose a local improvement of domain decomposition methods which fits with the singularities occurring in the solutions of elliptic equations in polygonal domains. This short presentation focuses on a model elliptic problem with the decomposition of a non-convex polygonal domain into convex polygonal subdomains. After explaining the strategy and the theoretical design of adapted interface conditions at the corner, we present numerical experiments which show that these new interface conditions satisfy some optimality properties. To cite this article: C. Chniti et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).

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Résumé

Dans cette Note nous proposons une amélioration locale des méthodes de décomposition de domaine adaptée aux singularités présentes dans les solutions de problèmes elliptiques dans des domaines polygonaux. Cette courte présentation se limite à un problème elliptique modèle où un domaine polygonal non convexe est décomposé en sous-domaines convexes. Après avoir brièvement présenté la stratégie et la détermination théorique des conditions dʼinterface adaptées au coin, nous présentons des résultats numériques qui montrent que ces nouvelles conditions dʼinterface vérifient des propriétés dʼoptimalité. Pour citer cet article : C. Chniti et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.


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