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Zbl 0824.35030
Kress, Rainer
Inverse scattering from an open arc. (English)
[J] Math. Methods Appl. Sci. 18, No.4, 267-293 (1995). ISSN 0170-4214; ISSN 1099-1476/e

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.
[A.Kirsch (Erlangen)]

MSC 2000:: *35J05 Laplace equation, etc.
35P25 Scattering theory (PDE)
35R30 Inverse problems for PDE
65Z05 Applications to physics

Keywords: Nyström method; Newton method; Fréchet derivative

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