INVERSE SCATTERING FROM AN OPEN ARC

A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a sound-soft or perfectly conducting are from a knowledge of the far-field pattern for the scattering of time-harmonic plane waves. Frechet differentiability with respect to the boundary is shown for the far-field operator, which for a fixed incident wave maps the boundary are onto the far-field pattern of the scattered wave. For the sake of completeness, the first part of the paper gives a short outline on the corresponding direct problem via an integral equation method including the numerical solution.