Asymptotic expansions of the eigenvalues of a 2-D boundary-value problem relative to two cavities linked by a hole of small size

Abderrahmane Bendali 1 Alain Huard 1 Abdelkader Tizaoui 1 Sébastien Tordeux 1 Jean-Paul Vila 1
1 IMT - Institut de Mathématiques de Toulouse UMR5219
Abstract : This note presents the derivation of the second-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.
Type de document :
Article dans une revue
C. R. Math. Acad. Sci. Paris, Académie des Sciences / Elsevier Masson SAS, 2009, 347 (19-20), pp.1147--1152. 〈10.1016/j.crma.2009.09.005〉
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Contributeur : Sébastien Tordeux <>
Soumis le : mardi 19 octobre 2010 - 11:55:48
Dernière modification le : vendredi 26 octobre 2018 - 10:45:54

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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. C. R. Math. Acad. Sci. Paris, Académie des Sciences / Elsevier Masson SAS, 2009, 347 (19-20), pp.1147--1152. 〈10.1016/j.crma.2009.09.005〉. 〈inria-00527437〉

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