Two novel fast algorithms for analysis of low-frequency transient electromagnetic phenomena

Recently, transient electromagnetic scattering associated with electrically small structures raised intense interest among researchers due to rapid increase of frequency and decrease of size in high-speed electronic circuits. In many cases of practical interest, the signal characteristic wavelength is comparable to the dimension of the structures. In such cases, many traditional models such as transmission line does not work well any more and full-wave analysis is required. The fast time domain integral equation (TDIE)-based solvers are good tools for full-wave analysis of high-frequency (RF/microwave) integrated circuits, but these fast TDIE solvers cannot be applied to analysis of electrically small objects (low-frequency problem) directly. Consequently, the development of TDIE solvers for low-frequency problems becomes necessary.;This dissertation first presented two novel fast algorithms that can be employed to accelerate the classic low-frequency TDIE solvers. The first one is referred to as multilevel Cartesian nonuniform grid time domain (ML_CNGTD) algorithm. The NGTD algorithm is based on the observation that at an observer, the delay- and amplitude-compensated field produced by temporally band-limited source constellations can be interpolated by their samples at a set of sparse points surrounding the observer. Previously, a two-level NGTD algorithm was developed. By introducing the multilevel Cartesian computational scheme, ML_CNGTD has lower computational complexity than its two-level counterpart. The second one is called low-frequency time domain fast multipole method (LF-TD-FMM). The LF-TD-FMM algorithm is time domain extension of frequency domain low-frequency FMM and employs a novel subsignal construction technique.;Finally, this dissertation introduced a novel fast low-frequency TDIE solver that is augmented by the LF-TD-FMM algorithm and uses loop-patch basis functions and integral/differential form of TDIE to improve its efficiency and stability. This fast solver can be used for full-wave analysis of high-speed electronic circuits.