The author recalls the notion of the domain derivative of a functional. The existence and a characterization of the domain derivative of the far-field pattern for a scattering problem with Dirichlet boundary condition is proved. The second part uses this characterization for an efficient implementation of a Gauss-Newton method for solving the inverse obstacle scattering problem. The author deals with the sensitivity of the linearized obstacle problem.
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Andreas Kirsch (1993) studied this question.
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