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

摘要

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 elasto-dynamics. 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 Frechet differentiability of the boundary to far-field operator and give a characterization of the first Frechet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gau beta-Newton method and show numerical experiments in the special case of starshaped obstacles.