| Recently, techniques for time domain electromagnetic (EM) simulation have been receiving increasing attention. This thesis focuses on time domain integral equation methods, also known as time domain method of moments (TD-MOM), for analyzing scattering and radiation problems. TD-MOM schemes are applied to problems involving four different environments: three-dimensional (3D) free space, two-dimensional (2D) free space, two-half-spaces, and microstrip. There has been a lot of research on TD-MOM schemes in 3D and 2D free space. At the same time, TD-MOM schemes for layered media structures (such as microstrip) have been little explored. In this thesis, some efforts are presented to improve the stability, enhance the accuracy, and reduce the computational complexity of TD-MOM schemes in 3D and 2D free space. Then, TD-MOM is applied to two specific layered media structures: two-half-spaces and microstrip. By using the “causality trick,” the Green's functions for two-half-spaces and microstrip are greatly simplified, without introducing any theoretical approximation. As a result, the techniques developed in the TD-MOM for 3D and 2D free space can be directly taken advantage of. Microstrip is the most complicated structure concerned in this thesis. A time domain electric field integral equation (EFIE) is established using a rigorously derived microstrip Green's function. A marching-on-in-time (MOT) scheme is constructed to solve this transient EFIE. Finally, a fast algorithm, the plane wave time domain (PWTD) algorithm, is coupled with the MOT solver to accelerate its solution. Numerous numerical examples are shown to validate the TD-MOM in all four environments. |
