• DOI:10.1137/130932107
• Corpus ID: 17905244

Direct and Inverse Acoustic Scattering by a Collection of Extended and Point-Like Scatterers

@article{Hu2014DirectAI,
  title={Direct and Inverse Acoustic Scattering by a Collection of Extended and Point-Like Scatterers},
  author={Guanghui Hu and Andrea Mantile and Mourad Sini},
  journal={Multiscale Model. Simul.},
  year={2014},
  volume={12},
  pages={996-1027}
}

• G. Hu, A. Mantile, M. Sini
• Published 30 October 2013
• Mathematics
• Multiscale Model. Simul.

This paper concerns 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 ...