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Approximation by generalized impedance boundary conditions of atransmission problem in acoustic scattering

Published online by Cambridge University Press:  15 September 2005

Xavier Antoine  and
Hélène Barucq
Xavier Antoine
Affiliation:
Université Paul Sabatier, Laboratoire de Mathématiques pour l'Industrie et la Physique (CNRS UMR 5640), UFR MIG, 118, route de Narbonne, 31062 Toulouse Cedex 4, France. [email protected]
Hélène Barucq
Affiliation:
Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques Appliquées (CNRS FRE 2570), IPRA, avenue de l'Université, 64000 Pau, France.
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Abstract

This paper addresses some results on the development of an approximate methodfor computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressiblefluid. The basic idea of the method consists in using on-surface differentialoperators that locally reproduce the interior propagation phenomenon. This approach leads tointegral equation formulations with a reduced computational cost compared to standard integral formulations couplingboth the transmitted and scattered waves. Theoreticalaspects of the problem and numerical experiments are reported to analyze the efficiency ofthe method and precise its validity domain.

Keywords

Helmholtz equationacousticsintegral equationsgeneralized impedance boundary conditionsexistence and uniqueness results.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 5 , September 2005 , pp. 1041 - 1059
Copyright
© EDP Sciences, SMAI, 2005

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