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Inverse scattering from an open arc. (English) Zbl 0824.35030
The first part of this paper studies the questions of uniqueness and existence of the direct scattering problem for an open arc with Dirichlet boundary conditions. Then the far field pattern is introduced and a reciprocity principle proved. In Section 4 the author investigates a special Nyström method based on the integral equation approach. Then the inverse problem is studied which is to determine the shape of the arc from the knowledge of the far field pattern. In Section 5 a uniqueness result is shown. Then the author suggests a Newton method for the numerical solution of the inverse scattering problem. He proves that the far field operator is differentiable and gives a characterization of the Fréchet derivative.
MSC:
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35P25Scattering theory (PDE)
35R30Inverse problems for PDE
65Z05Applications of numerical analysis to physics