Abstract
This paper is concerned with the reconstruction of objects immersed in anisotropic media from boundary measurements. The aim of this paper is to propose an alternative approach based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The idea is to formulate the reconstruction problem as a topology optimization one minimizing an energy-like function. We derive a topological asymptotic expansion for the anisotropic Laplace operator. The unknown object is reconstructed using level-set curve of the topological gradient. We make finally some numerical examples proving the efficiency and accuracy of the proposed algorithm.
Highlights
In this work we will establish a topological sensitivity analysis for the anisotropic Laplace operator
The aim of this paper is to propose an alternative approach based on the KohnVogelius formulation and the topological sensitivity analysis method
The topological sensitivity analysis consists of studying the variation of a given cost functional with respect to the presence of a small domain perturbation, such as the insertion of inclusions, cavities, cracks or source-terms
Summary
In this work we will establish a topological sensitivity analysis for the anisotropic Laplace operator. The first step of our approach is based on the Kohn-Vogelius formulation which rephrase the considered geometrical inverse problem into a topology optimization one. It leads to define for any given permutation. To solve the topological optimization problem (P) and detect the location of the unknown object we will derive a topological sensitivity analysis for the Kohn-Vogelius function J which gives the variation of a criterion with respect to the presence of a small Dirichlet geometric perturbation in the domain.
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