Frechet Differentiability of a Field Operator for Scattering from an Open Screen
KARPENKO PHYSICO-MECHANICAL INST LVIV (UKRAINE)
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The inverse problem which we consider is to determine the shape of two-dimensional open screen from the knowledge of the field on a curve for the electromagnetic plane waves scattering. Prof. R. Kress in his papers has proposed to reconstruct the scatterers shape from the knowledge of the far field pattern 1-2. We extend this approach to the inverse problem of determining the shape of a two-dimensional open scatterer from the knowledge of the scattered field on a curve. In particular, we investigate the Frechet differentiability of a field operator for scattering from an open screen with the boundary as prerequisite for the theoretical foundation of the gradient methods or Newton type methods for the approximate solution of this nonlinear and improperly posed problem. The aim of this paper is to provide a proof for Frechet differentiability with respect to the boundary of an operator, which maps the boundary of an open screen onto the scattered field and to obtain expression of this derivatives.
- Radiofrequency Wave Propagation
- Numerical Mathematics