Studies On Time Domain Boundary Integral Equation And Its Fast Algorithms And Their Applications

Time domain integral equation (TDIE), providing an appealing avenue for analyzing transient and broadband electromagnetics problems, has been of considerable interest in the computational electromagnetic (CEM) community. Unfortunately, marching-on-in-time (MOT)-based TDIE solvers have been suffered from numerically late-time oscillation and high computational complexities and large memory requirements. The purpose of this thesis is to develop a stable and fast TDIE solver for their applications to practical, real-world problems.Derivations of MOT matrix equations for time domain EFIE, MFIE and CFIE to obtain the transient responses from arbitrarily shaped wire and surface conducting objects are presented firstly in this thesis. The stability and precision of this three TDIEs are studied, when applied to transient analysis from general EM problems. The validity of TDCFIE to eliminate the late-time oscillation for the frequency components corresponding to the internal resonance of the structure is identified, and the effective parameter of linear combination is confirmed by numerical examples. A half-numerical and half-analytical method is proposed for the accurate computation of resistance matrix elements, when the differential form of TDEFIE is applied to transient analysis of wire structure. And the exact modeling and simulation for the wire structure with stepped-radius, wire junction and log-period structure are presented in this thesis. A more accurate equivalent solid angle value in TDMFIE is introduced to correcte the general assumption of solid angle, which allows the accurate analysis of electrically small sharp-edged objects as TDEFIE does.Significant efforts have been expended on the development of fast algorithms of MOT-based TDIE solvers for reducing the high computation complexities and large memory requirements in classical MOT. Firstly, a novel current-based hybrid method of PO coupled TDIE is proposed for analysis of large bodies with significant features that are not electrically large. Dividing the structure into PO region and IE region, the proposed method employs the accuracy of TDIE and the efficiency of PO completely, that dramatically reduces the high computation complexities and memory requirements in classical MOT. Secondly, an approximate technique is implemented to cut down the computational complexity of MOT, according to the distribution of transient current generated during the object is elluminated by a short pulse. As a fast TDIE solver with high accuracy and efficiency, plane wave time domain (PWTD) algorithm is studied deeply in this thesis. The implementations of two-level and multilevel PWTD-enhanced MOT schemes are described and the numerical efficiency is presented. Furthermore, a PWTD-enhanced PO-TDIE hybrid scheme is proposed, which can improve the computational efficiency of aforementioned hybrid method.Compressed storage technique for large sparse matrix is applied in fast TDIE solver for the purpose of further decreasing memory requirements. The precision and efficiency of iterative method, along with preconditioner, are explored in solving the large sparse matrix linear equation which is an indispensable part of the TDIE solver.