FM-BEM and topological derivative applied to inverse acoustic scattering - Archive ouverte HAL
Book Sections Year : 2007

FM-BEM and topological derivative applied to inverse acoustic scattering

Abstract

This study is set in the framework of inverse scattering of scalar (e.g. acoustic) waves. A qualitative probing technique based on the distribution of topological sensitivity of the cost functional associated with the inverse problem with respect to the nucleation of an infinitesimally-small hard obstacle is formulated. The sensitivity distribution is expressed as a bilinear formula involving the free field and an adjoint field associated with the cost function. These fields are computed by means of a boundary element formulation accelerated by the Fast Multipole method. A computationally fast approach for performing a global preliminary search based on the available overspecified boundary data is thus defined. Its usefulness is demonstrated through results of numerical experiments on the qualitative identification of a hard obstacle in a bounded acoustic domain, for configurations featuring O(105) nodal unknowns and O(106) sampling points.
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hal-00121987 , version 1 (22-12-2006)

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Marc Bonnet, Nicolas Nemitz. FM-BEM and topological derivative applied to inverse acoustic scattering. M. Schanz, O. Steinbach. Boundary element analysis: mathematical aspects and applications, Springer, pp.187-212, 2007, ⟨10.1007/978-3-540-47533-0_8⟩. ⟨hal-00121987⟩
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