Abstract
The inverse problem under consideration is to reconstruct the shape of a homogeneous dielectric infinite cylinder from the far-field pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We propose an inverse algorithm that extends the approach suggested by Johansson and Sleeman [T. Johansson and B. Sleeman, Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern, IMA J. Appl. Math. 72 (2007), pp. 96–112] for the case of the inverse problem for a perfectly conducting scatterer. It is based on a system of nonlinear boundary integral equations associated with a single-layer potential approach to solve the forward scattering problem. We present the mathematical foundations of the method and exhibit its feasibility by numerical examples.
Acknowledgement
The research of A.A. was supported by the German Research Foundation DFG through the Graduiertenkolleg Identification in Mathematical Models.