Generalized impedance boundary conditions for dielectric coatings and its application in non-destructive testing

The aim of this thesis is to derive the Generalized Impedance Boundary Conditions(GIBC) that model thin dielectric coatings with variable width located on a perfect electric or magnetic conducting object. By being treated the 2-D electromagnetic scattering problem for both TM and TE polarizations related to these coated objects, the expressions of the GIBCs are obtained up to the third order with respect to the coating width. In order to derive these expressions including material and geometrical (such as curvature and thickness) properties of the coating, so-called scaled asymptotic expansions are adapted to the problem dealed here. In the second stage of the thesis, in order to show the validation of the GIBC expressions, the direct scattering problem is solved through the finite element method by arranging suitable variational formulas. Additionally, particular attention is given to the cases where the inner boundary has corner singularities and the variational formulas are rearranged. The numerical simulations illustrate that the method developed for the coatings having not only smooth boundaries but also innerboundaries with corner singularities is very effective for the coatings having thicknesses less than one tenth of the wavelength of incident wave when the third order approximation is used, for both Dirichlet and Neumann type object cases.xixIn the last stage of the thesis, we deal an inverse scattering problem whose aim is to determine the thickness variation of a dielectric thin coating located on a perfect electric (magnetic) conducting structure of unknown shape. In order to determine the thickness function in the expression of the GIBCs, it is first required to calculate total field and its normal and tangential derivatives appearing in the GIBCs. These required fields appearing in the GIBCs are obtained by the analytical continuation of the measured data to the coating surface through the single layer potential representation. Then, the resulting system of non-linear differential equations for the unknown coating thickness is solved iteratively via the Newton-Raphson method byexpanding the thickness function in a series of exponentials. The validation and accuracy of the approach presented here are illustrated through several numerical examples.Keywords: Scattering problems, generalized impedance boundary conditions, thin coatings, Newton-Raphson method, electromagnetic waves