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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Authors: | Abderrahmane Bendali Alain Huard Abdelkader Tizaoui Sébastien Tordeux Jean-Paul Vila |
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Institution: | Toulouse University, INSA, Mathematical Institute of Toulouse (UMR-CNRS 5219), 135, avenue de Rangueil, 31077 Toulouse, France |
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Abstract: | 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. To cite this article: A. Bendali et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). |
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