The use of optimization in the reconstruction of obstacles from acoustic or electromagnetic scattering data

We consider some three dimensional time harmonic acoustic and electromagnetic scattering problems for bounded simply connected obstacles. We consider the following inverse problem: from the knowledge of several far field patterns generated by the obstacle when hit by known incoming waves and from the knowledge of some a-priori information about the obstacle, i.e. boundary impedance, shape symmetry, etc., reconstruct the shape or the shape and the impedance of the obstacle. There are a large number of effective numerical methods to solve the direct problem associated with this inverse problem, but techniques to solve the inverse problem are still in their infancy. We reformulate the inverse problem as two different unconstrained optimization problems. We present a review of results obtained by the authors on the inverse problem and we give some ideas concerning the solution of the direct problem by efficient parallel algorithms.

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