Identification of unknown obstacles using boundary elements and shape differentiation

In this paper, we consider the application of shape differentiation and boundary elements to shape identification problems in infinite acoustic media using gradient minimization methods. An analytical expression of the first derivative of an integral functional with respect to a moving surface (the boundary of the unknown scatterer) is established in the case of a penetrable bounded obstacle illuminated by a know incident pressure wave. This formulation is incorporated in an unconstrained minimization algorithm using gradients, (namely BFGS quasi-Newton) in order to solve numerically the inverse problem. Numerical results are presented for the search of a rigid bounded obstacle embedded in an infinite 3D acoustic medium, where the measurements are taken to b values of the pressure field on a remote measurement surface. They demonstrate the efficiency of the proposed method. Some computational issues (accuracy, CPU time, influence of measurements errors) are discussed.