Basic Study Of Electromagnetic Scattering From Dielectric And Coated Structures--Integral Equation Method And Its Fast Solver

The rigorous modeling and high efficient calculation of electromagnetic scattering from arbitrary shaped three-dimensional dielectric or conducting bodies with dielectric coating is studied in this dissertation. It is discussed from three points. First, formulating for solving the electromagnetic characteristics; secondly, the details of effectively solving the integral equations by moment of method (MoM) and fast numerical methods; thirdly, analyzing the iterative convergence characteristics, the ability for overcoming the interior resonance and the applicability of different integral equations and comparing them.Firstly, the three kinds of numerical methods, which are the integral equation method, the differential equation method and the hybrid method, to calculate the electromagnetic scattering from the dielectric and the coated bodies are presented. In the following, the two sections are submitted to analyze and research the dielectric and coated conducting bodies by using the volume integral equation and surface integral equation separately.In the first section, the volume integral equation for the dielectric bodies is presented. First, the weak form of Green function is recited to solve the integral singularity. The MoM enhanced by the TFQMR-FFT is employed to solve the equation. Then, the method is extended in a straightforward manner to the finite periodic dielectric structures and the dielectric tapered rod antennas. It is a very effective solution that succeeds in realizing the rigorous electromagnetic modeling.In the second section, the surface integral equation is presented to calculate the electromagnetic scattering characteristics from the coated and partially coated conducting bodies. In order to investigate them, the two kinds of surface integral equations for the dielectric bodies are shown. These formulations are free of the interior resonant problem. The key points in the calculation are introduced such as the selection of the basis function and testing function, the way to solve the integral singularity of Green function and so on.Then, a new combined field integral equation is proposed to solve the scattering from the coated and partially coated conducting bodies. The other two equations compare with this new equation from iterative characteristics, the ability of dealingwith the interior resonance and the applicability. It is an important work that can provide the reference for correctly using the surface integral equation to solve those problems.Finally, the fast multipole method (FMM) combined with the CG iterative solution is employed to significantly accelerate the matrix-vector multiplication with the requirement of calculating the large electric size. This method uses the uniform group division and the integral equation is divided by the aggregative, translative and disaggregative part by the addition theory of the scalar Green's function. Employing the transform invariability of the translative part, the memory requirement is reduced.As a basic research work for electromagnetic scattering characteristics of the 3-D dielectric and coated conducting bodies, it provides the powerful way in rigorous modeling and effective solution.