Acer Function Integral Equation Methods In Electromagnetic Scattering Analysis

As the immense advantage has been taken in expanding capabilities of computers over the past half century, the numerical electromagnetics has been quickly developed by effective numerical techniques applicable to a wide variety of practical electromagnetic radiation and scattering problems. The integral equation formulation in conjunction with the method of moments (MoM) is widely used for the problems in this field. However, the conventional approaches of MoM consume a considerable portion of the total memory and solution time when it comes to the problems which are large in terms of the wavelength, and this, in turn, can place an inordinately heavy burden on the CPU, and cost enormous computational memory and time.Several other techniques have been proposed in the past to reduce the computational time and memory cost of the MoM. One type of them is to accelerate the matrix-vector multiplication. Another type is based on the methods for reducing the matrix size. Examples of the former are the adaptive integral method (AIM), fast multipole method (FMM) and its multilevel extension. The latter includes high order basis function and macro basis function method, with the examples of CBFM and SED basis function method which will be introduced and studied in this thesis.In Chapter One, the historical background of the electromagnetic research is summarized.In Chapter Two, the MoM, FMM and MLFMM are generally introduced, then the advantages and disadvantages of them are discussed.In Chapter Three, the characteristic function (CF) method is studied and extended. The CF method can save the fill-matrix time by circumventing the Gauss integrations for approximating an infinitely small dipole with an equivalent moment. However, the conventional approach is based on EFIE only, which would make the impedance matrix ill-conditioned. In this chapter, the CF method is consummated by CFIE to decrease the condition number of the impedance matrix. As a result, the iteration time is greatly reduced.In Chapter Four, the characteristic basis function method (CBFM) based on the thought of macro-domain is briefly introduced. With this method the matrix size is effectively reduced. Then, with the combination of the physical optics (PO) method and CBFM, existing algorithms are modified in this chapter, the generation of CBFs in CBFM is simplified. In Chapter Five, the sub-entire-domain (SED) basis function method is introduced and applied in the frequency selective surface (FSS) EM scattering problems. Formerly, the SED basis function method is used to analyze periodic PEC structures in free space, while in this chapter, the SED is used to solve the EM scattering problem of FSS with medium layers.In Chapter Six, the study in this thesis is summarized, and the modifications together with the potential applications of the methods discussed are forecasted.