The transmission line matrix (TLM) method and its boundary treatments. - Chen, Zhizhang. (University of Ottawa (Canada), 1992)
The Transmission Line Matrix (TLM) numerical algorithm, based on the discrete Huygens' principle, has been extensively used to solve electromagnetic structure problems. The major advantage of this method is its simplicity and flexibility as the vectorial Maxwell's Equations are transformed into a simple numerical model of digital signal processing system. In this thesis, new and efficient numerical modeling concepts and procedures have been developed for the analysis of electromagnetic structures with the TLM method: (1) With the introduction of the equivalent field quantities defined between nodes, the TLM Method has been shown to be exactly equivalent to a finite-difference timedomain (FD-TD) formulation. Therefore, the numerical foundation of the TLM approach has been fully demonstrated and the basis for mathematically understanding the TLM method has been provided. As a result, the conventional TLM boundary conditions has been verified theoretically, and hence a systematic way for constructing the TLM boundary conditions has been developed. In addition, a new boundary description for the TLM method has been proposed, which renders TLM method more flexibility in its boundary treatments. (2) Based on the equivalence between the TLM method and the FD-TD method, an absorbing and a connecting boundary formulations have been developed for TLM simulations. With these formulations, the TLM method can be applied for solving more realistic scattering and radiation problems with open structures. The computation examples given in this thesis are with the structures of waveguides, two-dimensional and three-dimensional obstacles illuminated by plane waves. The numerical results show good agreement with those obtained with the Method of Moment, and thus validate the boundary conditions developed. (3) By using the discrete Fourier Transform, a new algorithm has been developed for interfacing the TLM method with the frequency-domain solutions. The technique employ the prior knowledge of frequency-domain solutions at boundaries and combine them with TLM simulations, leading to considerable decrease in memory and CPU time. It also allows the TLM method to be used with highly conductive materials for solving shielding problems. The good results were obtained with significant reduction of the computation expenditure.
Keywords: Engineering, Electronics and Electrical.