Analysis of time-domain integral equation for transient response from 3-D dielectric objects

Abstract

In this dissertation we develope an accurate and stable method for the solution of the transient electromagnetic scattering from 3-dimensional (3-D) dielectric objects using a time domain integral equation. In chapter II, we investigate various methods for solving a time-domain electric field integral equation (TD-EFIE) and a time-domain magnetic field integral equation (TD-MFIE) for analyzing the transient electromagnetic response from three-dimensional dielectric bodies. The solution method in this chapter is based on the method of moments (MoM) that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthogonal basis functions that is derived from the Laguerre functions. These basis functions are also used as the temporal testing. Numerical results involving equivalent currents and far fields computed by the proposed TD-EFIE and TD-MFIE formulations are presented and compared. In chapter III, we present a time domain combined field integral equation (TD-CFIE) formulation to analyze the transient electromagnetic response from three-dimensional dielectric objects. The solution method in this chapter is based on the method of moments (MoM) that involves separate spatial and temporal testing procedures. A set of the RWG (Rao, Wilton, Glisson) functions is used for spatial expansion of the equivalent electric and magnetic current densities and a combination of RWG and its orthogonal component is used as spatial testing. We also investigate spatial testing procedures for the TD-CFIE to select the proper testing function set. We found that two kinds of testing techniques work in TD-CFIE. The time domain unknowns are approximated by a set of orthonormal basis functions that are derived from the Laguerre p...