Improvement Researches On The Finite-Difference Frequency-Domain Method

The finite-difference frequency-domain (FDFD) method based on Maxwell's equations is relatively simple and intuitionistic in both the principle and the form. It can be applied to almost all kinds of electromagnetic problems theoretically, and the final matrix equation is very sparse. But in the classical FDFD method, the whole computational domain needs to be discretized, and a difference equation needs to be set up on each node of cells. Thus, the size of the final matrix equation increases rapidly as the size of the computational domain increases. This brings large burden of both computation and storage, and restricts the applications of the FDFD method. In this dissertation, some techniques are given and combined with the FDFD method to improve this demerit. The contents of the chapters are as follows.In Chapter One, the background of this dissertation is given, and the development of the finite difference method is described briefly. Then, the main work and its significance of this dissertation is presented.The content of Chapter Two is the improvement research of the FDFD method in open space problems and has three parts. In the first part, the principle of the FDFD method is given briefly. In the second part, the domain decomposition scheme based on unknown reordering is applied to the FDFD method in the three-dimensional case. In the third part, an iteration-free multiregion technique (IFMR) is given for problems of multiple objects in open space. Objects are included in corresponding sub-domains repectively which are discretized with cells. The mutual coupling effect among sub-domains is introduced by combining the total-field/scattered-field formulation and the near field to far field transformation based on the eigenfunction series of scattered field. Thus, a lot of cells among subdomains are avoided.The content of Chapter Three is the improvement research of the FDFD method in waveguide problems and has three parts. In the first part, the FDFD method and the mode-matching (MM) method is combined to analyze the problems of guided-wave structures with multiple discontinuousnesses. Only the sub-domains including discontinuousnesses are discretized, and the fields in other sub-domains are expanded with modes; thus, the number of cells are reduced and the efficiency is improved. In the second part, a high order compact two-dimensional (2D) FDFD method is proposed for the dispersion analysis of waveguides. And a corresponding surface impedance boundary condition is also given for modeling lossy metal. In the third part, an improved mode extraction technique is given for waveguides.In Chapter Four, the finite-difference frequency-domain and boundary intergral equation (FDFD-BIE) hybrid method is described. Some efficient techniques for the method of moment, such as the sub-entire domain (SED) basis function technique, the adaptive basis functions/diagonal moment matrix (ABF/DMM) technique, and the wavelets sparselizing technique, are modified and applied to the FDFD-BIE hybrid method.In Chapter Five, the dissertation is summarized, and some future works are proposed.