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arXiv · 1707.03589

A fast reconstruction algorithm for geometric inverse problems using topological sensitivity analysis and Dirichlet-Neumann cost functional approach

Maatoug Hassine·Imen Kallel
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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-CL\'ES : Probl\`eme inverse g\'eom\'etrique, Laplace anisotrope, formulation de Kohn-Vogelius, analyse de sensibilit\'e, optimisation topologique.

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Maatoug Hassine, Imen Kallel. 2017-07-12. A fast reconstruction algorithm for geometric inverse problems using topological sensitivity analysis and Dirichlet-Neumann cost functional approach. https://arxiv.org/abs/1707.03589

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