| Abstract: |
| The reconstruction of the shape of scattering objects from the knowledge of the far field pattern of scattered electromagnetic waves is a challenging problem in inverse scattering theory. Several approaches to such severely ill-posed problems are discussed in the past in case of linear scattering models. But for scattering objects given by nonlinear media or nonlinear boundary conditions much less is known. As a recent contribution we discuss the dependence of scattered waves on perturbations of the shape of such scattering object. This leads to a shape derivative, the so called domain derivative, of solutions of the underlying partial differential equations. We show existence and certain characterizations of these derivatives in case of nonlinear boundary value problems. Additionally, based on the given characterization of the domain derivative an all-at-once Newton-type regularization method is suggested for solving the inverse reconstruction problem in case of far field data from just one incident field. The numerical performance of such a scheme is illustrated by some numerical examples. |
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