AN OPTIMIZATION METHOD FOR THE INVERSE SCATTERING PROBLEM OF THE BIHARMONIC WAVE

We consider an inverse scattering problem of reconstructing the shape of a cavity in an infinitely thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. We first approximate the out-of-plane displacement of the plate by potentials over an auxiliary circle and then reformulate the inverse problem into an optimization problem. The convergence properties are established to show that when the regularization parameter tends to zero, the minimizer of the optimization problem tends to a solution of the inverse scattering problem. Numerical experiments are designed to verify the performance of the proposed method.