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Matched Asymptotic Expansions of the Eigenvalues of a 3-D Boundary-Value Problem Relative to Two Cavities Linked by a Hole of Small Size

Published online by Cambridge University Press:  20 August 2015

Abderrahmane Bendali ,
M’Barek Fares ,
Abdelkader Tizaoui  and
Sébastien Tordeux
Abderrahmane Bendali*
Affiliation:
Electromagnetism and Acoustics, CERFACS, 42 Avenue Gaspard Coriolis, F-31100 Toulouse, France Toulouse University, INSA-Toulouse, Mathematical Institute of Toulouse, UMR-CNRS 5219, 135 avenue de Rangueil, F-31077 Toulouse, France
M’Barek Fares*
Affiliation:
Electromagnetism and Acoustics, CERFACS, 42 Avenue Gaspard Coriolis, F-31100 Toulouse, France
Abdelkader Tizaoui*
Affiliation:
Toulouse University, INSA-Toulouse, Mathematical Institute of Toulouse, UMR-CNRS 5219, 135 avenue de Rangueil, F-31077 Toulouse, France
Sébastien Tordeux*
Affiliation:
Laboratoire de Mathématiques et de leurs Applications, UMR-CNRS 5142, Université de Pau et des Pays de l’Adour, F-64013 Pau, France Project Team MAGIQUE-3D, INRIA Bordeaux-Sud-Ouest, F-64013 Pau, France
*
Email address:abendali@insa-toulouse.fr
Email address:fares@cerfacs.fr
Email address:abdelkader.tizaoui@gmail.com
Corresponding author.Email:sebastien.tordeux@univ-pau.fr
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Abstract

In this article, we consider a domain consisting of two cavities linked by a hole of small size. We derive a numerical method to compute an approximation of the eigenvalues of an elliptic operator without refining in the neighborhood of the hole. Several convergence rates are obtained and illustrated by numerical simulations.

Keywords

34E0535J0565M6078M3078M35Elliptic operatormatched asymptotic expansionseigenvalue problemfinite elements
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 456 - 471
Copyright
Copyright © Global Science Press Limited 2012

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References

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