Abstract
In this work, a class of bilateral free boundary problem is considered. This identification problem is formulated as a shape optimization problem via the definition of a cost functional. The existence of an optimal solution for the optimization problem is proved. An augmented Lagrangian approach is used to facilitate the computation of the shape derivatives. A numerical approach is proposed to solve iteratively the shape optimization problem, also we prove its convergence. Various type of domains are investigated to confirm the validity of the presented approach. For the numerical stability we investigate the shape without and with noisy data.
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