Advanced FDTD methods with the applications to resonant, propagation and scattering problems

In the past decade, many advanced Finite Difference Time Domain (FDTD) methods were developed. Some focus on the dispersion improvement using higher order spatial discretizations, while others concentrate on the overcome of Courant-Friedrich-Levy (CFL) stability condition by introducing implicit operations. How to obtain the radar cross section (RCS) responses of large scatters under small perturbations by the combination and hybrid of the methods is hot spot in computational electromagnetics. In this dissertation, a novel subgridding method is developed to solve this kind of problem efficiently. The following efforts are made in this dissertation in order to realize this objective: the hybrid and combination of all kinds of advanced FDTD method in two dimensional (2-D) domain and its natural extension to three dimensional (3-D) case; a universally applicable Uniaxial Perfectly Matched Layer (UPML)formulation truncating computational domains in 2-D domain and its natural extension to 3-D case; perfect plane-wave injection formulations for both 2-D and 3-D domains; and novel subgridding techniques to accelerate computations for both 2-D and 3-D electromagnetic problems. With the aid of these novel techniques, the RCS problem can be solved 5 to 10 times faster than the traditional methods without the loss of accuracy. Two numerical examples for 2-D and 3-D cases are presented in this dissertation, which demonstrate that the method developed in this dissertation can achieve perfect balance between computational speed and accuracy.