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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. antoine@mip.ups-tlse.fr
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 method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the transmitted and scattered waves. Theoretical aspects of the problem and numerical experiments are reported to analyze the efficiency of the 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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