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The Landweber iteration applied to inverse conductive scattering problems. (English) Zbl 0917.35160

The author studies the direct and inverse scattering problem for conductive boundary conditions. In the electromagnetic case, these conditions model thin layers of high conductivities. The variational approaches for both, the E- and H-mode, are discussed. In the first part, the Fréchet derivative of the mapping \(\partial D\mapsto u_\infty\) is studied where \(\partial D\) denotes the boundary of the scatterer and \(u_\infty\) the corresponding far field pattern (fixed frequency and angle of incidence). The author derives characterization of the Fréchet derivatives in terms of more complicated boundary value problems.
In the second part of the paper, this characterization is used for an efficient implementation of the Landweber method for solving the inverse scattering problem, i.e. the determination of \(\partial D\) from the knowledge of \(u_\infty\). Some numerical examples conclude this paper.

MSC:

35R30 Inverse problems for PDEs
90C52 Methods of reduced gradient type
35P25 Scattering theory for PDEs
78A45 Diffraction, scattering
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