Second-order topological expansion with respect
to the insertion of small coated inclusion 

 B. Meftahi
Universite de Tunis El Manar, Ecole Nationale d’Ingenieurs de Tunis,
ENIT-LAMSIN, B.P. 37, 1002 Tunis, 

Abstract. In this paper, we consider the inverse problem of recovering coated inclusions from boundary measurements. To solve the inverse problem numerically, we propose a Kohn-Vogelius type functional and we perform its rst as well as its second-order topological gradient.
The rst-order topological gradient usually involves the state and the adjoint solutions and their gradients estimated at the point where the topological perturbation is performed. In the case of second-order topological gradient, non-local terms which have a higher computational cost appear. In this work, we aime at determining the relevance of these non-local terms from the numerical point of view.

Keywords: Inverse problem,Topological optimization, Second-order asymptotic
analysis, Coated inclusion

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