Space-Domain Finite-Difference And Time-Domain Moment Method And Its Applications

The dissertation introduces the basic theory of space-domain finite-difference and time-domain moment (SDFD-TDM) method, a new numerical method in computational electromagnetics, and its applications.SDFD-TDM method is a time-domain method, in which some computation formulations cannot be restricted by the time stability constraint. Compared with traditional time-domain methods, such as finite-difference time-domain (FDTD) method, the SDFD-TDM method has advantage in efficiency for wide-band and multi-scale electromagnetic problems.When solving time-domain Maxwell differential equations, SDFD-TDM method uses Yee's lattice and central difference technique to discrete space domain, and applies moment method procedure to dealing with time variables. Thus, different choices of basis and testing functions will result in different formulations, and some can be free of stability constraint. It is proved that the FDTD formulation can be derived from the SDFD-TDM method by choosing the triangle basis functions and point-matching testing functions.This dissertation mainly focuses on the following two algorithms and their applications: an order-marching method based on weighted Laguerre polynomials and Galerkin procedure, and an unconditionally stable method based on triangle basis functions and Galerkin procedure. They do not relate to time-marching process and are free of stability constraint. However, they involve the inversion of matrix in the computation.For the order-marching method, this dissertation derives the three-dimensional (3-D) formulation based on the TE₂ case and obtains the second-order absorbing boundary condition (ABC); Combined with two-dimensional (2-D) compact technique in real variables, the uniform transmission lines are analyzed; Combined with 2-D compact technique in complex variables, the exact attenuation constants are extracted; Combined with discrete Fourier transform (DFT), electromagnetic eigenvalue problems are analyzed. For the unconditionally stable method, this dissertation derives 2-D TE_Z mode formulation and first-order ABC, analyzes the numerical dispersion, and calculate the results of the examples with two parallel-plate transmission lines; Finally, the onedimensional (1-D) format of the unconditionally stable method is presented. For each numerical example, the corresponding program is written to validate the accuracy and efficiency of the method.