[Conditions d'interface améliorées pour une décomposition d'un domaine polygonal non convexe]
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 d'interface adaptées au coin, nous présentons des résultats numériques qui montrent que ces nouvelles conditions d'interface vérifient des propriétés d'optimalité.
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.
Accepté le :
Publié le :
Chokri Chniti 1 ; Frédéric Nataf 1 ; Francis Nier 2
@article{CRMATH_2006__342_11_883_0,
author = {Chokri Chniti and Fr\'ed\'eric Nataf and Francis Nier},
title = {Improved interface conditions for a non-overlapping domain decomposition of a non-convex polygonal domain},
journal = {Comptes Rendus. Math\'ematique},
pages = {883--886},
publisher = {Elsevier},
volume = {342},
number = {11},
year = {2006},
doi = {10.1016/j.crma.2006.03.024},
language = {en},
}
TY - JOUR AU - Chokri Chniti AU - Frédéric Nataf AU - Francis Nier TI - Improved interface conditions for a non-overlapping domain decomposition of a non-convex polygonal domain JO - Comptes Rendus. Mathématique PY - 2006 SP - 883 EP - 886 VL - 342 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2006.03.024 LA - en ID - CRMATH_2006__342_11_883_0 ER -
%0 Journal Article %A Chokri Chniti %A Frédéric Nataf %A Francis Nier %T Improved interface conditions for a non-overlapping domain decomposition of a non-convex polygonal domain %J Comptes Rendus. Mathématique %D 2006 %P 883-886 %V 342 %N 11 %I Elsevier %R 10.1016/j.crma.2006.03.024 %G en %F CRMATH_2006__342_11_883_0
Chokri Chniti; Frédéric Nataf; Francis Nier. Improved interface conditions for a non-overlapping domain decomposition of a non-convex polygonal domain. Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 883-886. doi : 10.1016/j.crma.2006.03.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.024/
[1] Improved interface condition for 2D domain decomposition with corner: a theoretical determination http://hal.ccsd.cnrs.fr/ccsd-00018965
[2] The best interface conditions for domain decomposition methods: Absorbing boundary conditions, Absorbing Boundary and Layers, Domain Decomposition Methods, Nova Sci. Publ., 2001, pp. 348-373
[3] Boundary problems for elliptic equations in domains with conical or angular points, Trudy Moskov. Mat. Obshch., Volume 16 (1967), pp. 209-292
[4] F. Nier, Remarques sur les algorithmes de décomposition de domaines, in : Séminaire EDP de l'Ecole Polytechnique (1998–1999), Exposé numéro IX
[5] Domain Decomposition Methods for Partial Differential Equations, Oxford Science Publications, xxx, 1999
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