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Zbl 0894.35079
Mönch, Lars
On the inverse acoustic scattering problem by an open arc: The sound-hard case.
(English)
[J] Inverse Probl. 13, No.5, 1379-1392 (1997). ISSN 0266-5611

The author studies the inverse problem to determine the shape of an open arc from the knowledge of the far field patterns of scattered acoustic waves. A Neumann boundary condition is imposed on the arc. The author proves uniqueness of the inverse problem and Fréchet differentiability of the operator $F$ which maps the parametrization $\gamma$ of the arc into the far field pattern $u_\infty$. He applies a Newton-type method to the equation $F(\gamma)= u_\infty$ for solving the inverse scattering problem. Numerical examples illustrate the practicability of the method.
[A.Kirsch (Karlsruhe)]
MSC 2000:
*35P25 Scattering theory (PDE)
35R30 Inverse problems for PDE
35J05 Laplace equation, etc.

Keywords: numerical examples; uniqueness; Fréchet differentiability; Newton-type method

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