Research On Sub-Entire Domain Basis Function Method And Its Application

In this dissertation, principle and applications of the sub-entire domain (SED) basis function method that has been recently proposed are introduced and studied.In conventional method of moments (MoM), memory and CPU time are proportional to N~2 and N~3, respectively, where N is the number of unknowns. Therefore, it is only suitable to analyzing electrically small and/or moderate electromagnetic problems. The sub-entire domain basis function method can dramatically reduce the number of unknowns because the physical properties of periodic structures are considered. And it has been used to analyze electromagnetic performance of large-scale periodic structures.In Chapter One, some numerical methods, such as the finite-difference time-domain method, finite element method, the MoM, that are popular in analyzing periodic structures are introduced. Advantages and disadvantages of these methods are also given. Then, main work and meaning of this dissertation are given.In Chapter Two, the SED basis function method is introduced and some improved techniques are proposed. Firstly, the basic principle and related problems of the MoM are introduced. Secondly, the SED basis function method is applied to analyze one-dimensional periodic structures. The accuracy of the SED basis function is validated. Thirdly, two extended SED basis function methods are proposed. They are extended accurate method and simplified SED basis function methods. Finally, dimension-reduction-based SED basis function method is presented. Its accuracy is also validated by several numerical examples. The number of unknowns can be further reduced by using the improved methods.In Chapter Three, several filling techniques of impedance matrix are presented. The characteristic function technique is introduced to computation of impedance matrix. Its advantage is that it can avoid the double surface integration, which is very time consuming. Then, fast fill-technique is proposed in the one-dimensional periodic structures. Finally, fast generation technique of moment matrices in the simplified SED basis function method for two-dimensional probelms is proposed.In Chapter Four, the SED basis function method is extended to analyze the hybrid periodic structures (1-D cases), planar plates, and periodic antenna arrays. Results obtained by using the SED basis function method and the conventional MoM are in good agreement.In Chapter Five, the dissertation is summarized. In addition, improvability and potential applications of the SED basis function method are forecasted.