WIAS Preprint No. 1853, (2013)

Direct and inverse acoustic scattering by a collection of extended and point-like scatterers



Authors

  • Hu, Guanghui
  • Mantile, Andrea
  • Sini, Mourad

2010 Mathematics Subject Classification

  • 35R30 78A45 35J05 35J25 35J57 35L05

Keywords

  • Inverse scattering, point interaction, two-scale problem, factorization method

Abstract

We are concerned with the acoustic scattering by an extended obstacle surrounded by point-like obstacles. The extended obstacle is supposed to be rigid while the point-like obstacles are modeled by point perturbations of the exterior Laplacian. In the first part, we consider the forward problem. Following two equivalent approaches (the Foldy formal method and the Krein resolvent method), we show that the scattered field is a sum of two contributions: one is due to the diffusion by the extended obstacle and the other arises from the linear combination of the interactions between the point-like obstacles and the interaction between the point-like obstacles with the extended one. In the second part, we deal with the inverse problem. It consists in reconstructing both the extended and point-like scatterers from the corresponding far-field pattern. To solve this problem, we describe and justify the factorization method of Kirsch. Using this method, we provide several numerical results and discuss the multiple scattering effect concerning both the interactions between the point-like obstacles and between these obstacles and the extended one.

Appeared in

  • Multiscale Model. Simul., 12 (2014) pp. 996--1027.

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