Abstract
In this paper an inverse obstacle scattering problem for the Helmholtz equation with nonlinear impedance boundary condition is considered. For a certain class of nonlinearities, well-posedness of the direct scattering problem is proven. Furthermore, differentiability of solutions with respect to the boundary is shown by the variational method. A characterization of the derivative allows for iterative regularization schemes in solving the inverse problem, which consists in reconstructing the scattering obstacle from the far field pattern of a scattered wave. An all-at-once Newton-type regularization method is developed to illustrate the use of the domain derivative by some numerical examples.
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