Approximation by multipoles of the multiple acoustic scattering by small obstacles and application to the Foldy theory of isotropic scattering.

Abderrahmane Bendali (1, 2) , Pierre-Henri Cocquet (3, 4) , Sébastien Tordeux (5, 6)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CERFACS - Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique
3 ONERA - The French Aerospace Lab [Toulouse]
4 Centre Universitaire d'Informatique
5 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
6 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

The asymptotic analysis, carried out in this paper, for the problem of a multiple scattering of a time-harmonic wave by obstacles whose size is small as compared with the wavelength establishes that the effect of the small bodies can be approximated at any order of accuracy by the field radiated by point sources. Among other issues, this asymptotic expansion of the wave furnishes a mathematical justification with optimal error estimates of Foldy's method that consists in approximating each small obstacle by a point isotropic scatterer. Finally, it is shown how this theory can be further improved by adequately locating the center of phase of the point scatterers and taking into account of self-interactions.

Keywords: acoustics; multiple scattering; small scatterers; Foldy's model; matched asyptotic expansions

Domains: Numerical Analysis [math.NA]; Analysis of PDEs [math.AP]

Abderrahmane Bendali, Pierre-Henri Cocquet, Sébastien Tordeux. Approximation by multipoles of the multiple acoustic scattering by small obstacles and application to the Foldy theory of isotropic scattering.. Archive for Rational Mechanics and Analysis, 2016, 219 (3), pp.1017-1059. ⟨10.1007/s00205-015-0915-5⟩. ⟨hal-01025436⟩