A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems

Frédérique Le Louër (1)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß Newton method and show numerical experiments in the special case of star-shaped obstacles.

Mots clés: Fréchet derivative; penetrable obstacle; boundary integral equation system; Elastic scattering; regularized Newton type method

Domaines: Analyse numérique [math.NA]

Frédérique Le Louër. A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems. Inverse Problems, 2015, 31 (11), ⟨10.1088/0266-5611/31/11/115006⟩. ⟨hal-01152319v2⟩