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Title: Direct and inverse acoustic scattering by a collection of extended and point-like scatterers
Authors: Hu, GuanghuiMantile, AndreasSini, Mourad
Issue Date: 2013
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1853, ISSN 0946 – 8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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.
Keywords: Inverse scattering; point interaction; two-scale problem; factorization method
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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