Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 5, p. 1041-1059

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.

DOI : https://doi.org/10.1051/m2an:2005037
Classification:  35J05,  35J25,  35S15,  65N38,  78A45
Keywords: Helmholtz equation, acoustics, integral equations, generalized impedance boundary conditions, existence and uniqueness results
@article{M2AN_2005__39_5_1041_0,
     author = {Antoine, Xavier and Barucq, H\'el\`ene},
     title = {Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {5},
     year = {2005},
     pages = {1041-1059},
     doi = {10.1051/m2an:2005037},
     zbl = {1074.78004},
     mrnumber = {2178572},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_5_1041_0}
}
Antoine, Xavier; Barucq, Hélène. Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 5, pp. 1041-1059. doi : 10.1051/m2an:2005037. http://www.numdam.org/item/M2AN_2005__39_5_1041_0/

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