Inverse Scattering for a Locally Perturbed Half-Plane
R. Kress and T. Tran
Abstract:
We consider the inverse problem to determine the shape
of a local perturbation of a perfectly conducting plate from a
knowledge of the far field pattern of the scattering of TM
polarized time-harmonic electromagnetic waves by reformulating it
as inverse scattering problem for a planar domain with corners.
For its approximate solution we propose a regularized Newton
iteration scheme. For a foundation of Newton type methods we
establish the Fréchet differentiability of the solution to the
scattering problem with respect to the boundary and investigate
the injectivity of the linearized mapping. Some numerical examples
for the feasibility of the method are presented. For the sake of
completeness, the first part of the paper outlines the solution of
the direct scattering problem via an integral equation of the
first kind including the numerical solution.
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