|Ph.D Thesis||Department of Electrical Engineering|
|Supervisor:||Prof. Leviatan Yehuda|
Numerical time-domain solutions for scattering of electromagnetic waves are essential for wide-band scattering problems such as high-resolution radar and EMP-proof systems, where frequency-domain analysis is as expected inefficient. Common solutions of the time-domain integral equation (TDIE) for such problems employ marching-on in time (MOT) techniques and an explicit sampling of the spatio-temporal domain, which yields simple equations but introduces inherent numerical instability.
In the new approach suggested here, the stable implicit scheme of the method of moments (MoM) is first applied to cast the TDIE into a single matrix equation at all spatial locations and all time instances of interest. For this purpose, we use spatio-temporal wavelet basis functions which are characterized by both spatial and temporal multiresolution. These functions are adequate for two- and three-dimensional problems, enable decoupled temporal and spatial multiresolution, and possess efficient transformation algorithm. Consequently, the resultant matrix equation is usually very large, yet it is not solved directly. Instead, we employ an iterative solution technique which finds a relatively small set of expansion functions for representing the solution. This set is gradually constructed up until a solution at the desired level of accuracy is achieved, at late as well as at early time steps. In this way, the method can efficiently improve the resolution of the solution wherever required, without increasing the overall number of unknowns in the equation.
The new method was successfully applied to the solution of various scattering problems, including scattering by a dielectric layer, a conducting layer, an air-gap in a dielectric medium, one-dimensional photonic crystal, and a wire-antenna. It produced accurate and numerically stable solutions at high levels of compression, and has yielded stable solutions where other methods failed.