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Conference papers

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

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 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.
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Submitted on : Wednesday, September 9, 2020 - 1:14:52 PM
Last modification on : Wednesday, October 28, 2020 - 12:10:04 PM
Long-term archiving on: : Thursday, December 3, 2020 - 12:47:48 AM

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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⟩

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