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

Belhassen Meftahi (1)

1 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]

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 first as well as its second-order topological gradient. The first-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 nonlocal terms from the numerical point of view.

Mots clés: Inverse problem; Topological optimization; Second-order asymptotic analysis; Coated inclusion

Domaines: Mathématiques [math]

Belhassen Meftahi. Second-order topological expansion with respect to the insertion of small coated inclusion. Colloque Africain sur la Recherche en Informatique et en Mathématiques Appliquées, Oct 2020, Thiès, Senegal. ⟨hal-02934477⟩