“The Domain Derivative for Time Harmonic Electromagnetic Scattering Problems”
Wednesday February 3rd 2021 at 17:00 - Zoom - Frank Hettlich (Karlsruhe Institute of Technology, Germany)
The dependence of time harmonic electromagnetic waves on the shape of scattering object is a challenging problem in inverse scattering theory as well as for shape optimization. We introduce the domain derivative for time harmonic electromagntic fields. By a variational approach existence and representations of such domain derivatives can be shown in case of different boundary conditions in appropriate Sobolev spaces. Furthermore, the appraoch is extended in showing a second derivative with respect to perturbations of the object. The characterizations of the domain derivatives can be applied to inverse scattering problems. As an illustration we consider the reconstruction of the shape of a perfectly conducting scatterer from the far field pattern of one scattered wave. It is shown that characterizations of the domain derivatives can be used succefully in iterative regularization schemes for such an severly ill-posed problem. Furthermore, also an application of the derivative for a shape optimization problem is discussed.