A second degree Newton method for an inverse scattering problem for a dielectric cylinder

The inverse obstacle scattering problem we are interested is to reconstruct the image of an infinitely long homogeneous dielectric cylinder from the far field pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We extend the approach suggested by Kress and Lee [18] that combines the ideas of Hettlich and Rundell [10] and Johansson and Sleeman [14] for the case of the inverse problem for a perfectly conducting scatterer to the case of penetrable scatterer. The inverse problem is depended on a system of non-linear boundary integral equations associated with a single layer approach to solve the direct scattering problem. We show the mathematical foundations of the method and illustrate its feasibility by numerical examples

Keywords:

Helmholtz Equation, Inverse Scattering, Transmission Boundary Condition, Non-Linear Integral Equations, Gauss-Newton Iteration Methods Single-Layer Approach.,

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