Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering

N. Nemitz (1) , Marc Bonnet (1)

1 LMS - Laboratoire de mécanique des solides

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 $O(10^{5})$ nodal unknowns and O(10^{6})$ sampling points.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

N. Nemitz, Marc Bonnet. Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering. Engineering Analysis with Boundary Elements, 2008, 32, pp.957-970. ⟨10.1016/j.enganabound.2007.02.006⟩. ⟨hal-00167341⟩