A Newton method is presented for the approximate solution of the inverse problem to determine the shape of a two-dimensional crack from a knowledge of the far field pattern for the scattering of time-harmonic elastic plane waves. Fréchet differentiability with respect to the boundary is shown for the far field operator, which for a fixed incident wave maps the crack onto the far field pattern of the scattered wave. Some numerical reconstructions illustrate the feasibility of the method.
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Rainer Kreß (1996) studied this question.
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