Kohn-Vogelius formulation and topological sensitivity analysis based method for solving geometric inverse problems

In this paper, we propose an alternative approach combining the advantages of the Kohn-Vogelius formulation and the topological sensitivity analysis method for solving geometric inverse problems. The Kohn-Vogelius formulation can rephrase the geometric inverse problem into a shape optimization one minimizing an energy-like function. The sensitivity analysis gives the leading term of the energy-like function variation with respect to the presence of a small geometry perturbation inside the computational domain. The obtained theoretical results lead to build a fast and accurate numerical reconstruction algorithm. The efficiency and accuracy of the proposed algorithm are illustrated by some numerical results.