Title: A fast reconstruction algorithm for geometric inverse problems using topological sensitivity analysis and Dirichlet-Neumann cost functional approach,
Abstract: This paper is concerned with the detection of objects immersed in anisotropic
media from boundary measurements. We propose an accurate approach based on the
Kohn-Vogelius formulation and the topological sensitivity analysis method. The
inverse problem is formulated as a topology optimization one minimizing an
energy like functional. A topological asymptotic expansion is derived for the
anisotropic Laplace operator. The unknown object is reconstructed using a
level-set curve of the topological gradient. The efficiency and accuracy of the
proposed algorithm are illustrated by some numerical results. MOTS-CLÉS :
Problème inverse géométrique, Laplace anisotrope, formulation de
Kohn-Vogelius, analyse de sensibilité, optimisation topologique.