[Développement asymptotique des valeurs et fonctions propres d'un problème aux limites 2-D relatif à deux cavités reliées par un trou de petite taille.1]
Cette Note présente la dérivation du développement asymptotique au 2nd ordre des valeurs et des fonctions propres de l'opérateur associé à une équation elliptique complétée par une condition aux limites de Dirichlet sur un domaine formé de deux cavités reliées par un trou de petite taille. Le développement asymptotique est effectué relativement à la taille du trou. La principale caractéristique de la méthode est de donner lieu à une procédure numérique permettant de calculer les valeurs propres sans recourir à un maillage raffiné autour du trou.
This Note presents the derivation of the 2nd-order asymptotic expansion of the eigenvalues and the eigenfunctions of the operator associated to an interior elliptic equation supplemented by a Dirichlet boundary condition on a domain consisting of two cavities linked by a hole of small size. The asymptotic expansion is carried out with respect to the size of the hole. The main feature of the method is to yield a robust numerical procedure making it possible to compute the eigenvalues without resorting to a refined mesh around the hole.
Accepté le :
Publié le :
Abderrahmane Bendali 1 ; Alain Huard 1 ; Abdelkader Tizaoui 1 ; Sébastien Tordeux 1 ; Jean-Paul Vila 1
@article{CRMATH_2009__347_19-20_1147_0,
author = {Abderrahmane Bendali and Alain Huard and Abdelkader Tizaoui and S\'ebastien Tordeux and Jean-Paul Vila},
title = {Asymptotic expansions of the eigenvalues of a {2-D} boundary-value problem relative to two cavities linked by a hole of small size},
journal = {Comptes Rendus. Math\'ematique},
pages = {1147--1152},
publisher = {Elsevier},
volume = {347},
number = {19-20},
year = {2009},
doi = {10.1016/j.crma.2009.09.005},
language = {en},
}
TY - JOUR AU - Abderrahmane Bendali AU - Alain Huard AU - Abdelkader Tizaoui AU - Sébastien Tordeux AU - Jean-Paul Vila TI - Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size JO - Comptes Rendus. Mathématique PY - 2009 SP - 1147 EP - 1152 VL - 347 IS - 19-20 PB - Elsevier DO - 10.1016/j.crma.2009.09.005 LA - en ID - CRMATH_2009__347_19-20_1147_0 ER -
%0 Journal Article %A Abderrahmane Bendali %A Alain Huard %A Abdelkader Tizaoui %A Sébastien Tordeux %A Jean-Paul Vila %T Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size %J Comptes Rendus. Mathématique %D 2009 %P 1147-1152 %V 347 %N 19-20 %I Elsevier %R 10.1016/j.crma.2009.09.005 %G en %F CRMATH_2009__347_19-20_1147_0
Abderrahmane Bendali; Alain Huard; Abdelkader Tizaoui; Sébastien Tordeux; Jean-Paul Vila. Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1147-1152. doi : 10.1016/j.crma.2009.09.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.005/
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☆ This work was supported by the French National Research Agency under grant no. ANR-08-SYSC-001.
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