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; Alain Huard; Abdelkader Tizaoui; Sébastien Tordeux; Jean-Paul Vila

doi:10.1016/j.crma.2009.09.005

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〉

Domaine :

Mathématiques [math] / Analyse numérique [math.NA]

Mathématiques [math] / Equations aux dérivées partielles [math.AP]

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https://hal.inria.fr/inria-00527437
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Soumis le : mardi 19 octobre 2010 - 11:55:48
Dernière modification le : mercredi 23 mai 2018 - 17:58:04

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

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

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