Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
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@example.com
2 Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques Appliquées (CNRS FRE 2570), IPRA, avenue de l'Université, 64000 Pau, France.
Revised: 7 March 2005
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.
Mathematics Subject Classification: 35J05 / 35J25 / 35S15 / 65N38 / 78A45
Key words: Helmholtz equation / acoustics / integral equations / generalized impedance boundary conditions / existence and uniqueness results.
© EDP Sciences, SMAI, 2005