The domain derivative in inverse obstacle scattering with nonlinear impedance boundary condition

Abstract

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.