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

Abstract

fulfilling the transmission conditions I nverse scattering theory is concerned with methods for retrieving information on the geometry and the physical properties of obstacles from scattering of acoustic and electromagnetic wave. In the direct scattering problem the object is given and it is required to find the scattered wave. In the inverse scattering problem we want to receive information on geometry of the shape or physical parameters of the scattering object. The inverse obstacle scattering problem that we currently deal with is considered for time-harmonic waves. The scattering object is assumed to be a homogeneous scatterer and the inverse problem is to reconstruct an image of the scatterer. In this manuscript we are interested in dielectric obstacles and restrict ourselves to the sufficiently long cylinders. This