Generalized TLM algorithms with controlled stability margin and their equivalence with finite-difference formulations for modified grids

Generalized TLM formulation based on modified grids of 2-D shunt nodes or 3-D expanded modes are proposed. Generalization consists of permitting flexible control of the numerical stability margin (and thus a time-step for a particular discretization), and of introducing enhanced models for curved boundaries. Formal equivalence between generalized TLM and FDTD algorithms based on the same grid is proved. Simple rules for transforming circuit models (from TLM to FDTD and vice versa) and for their equivalent excitation are given. It is demonstrated that the application of the generalized algorithm reduces computer resources required for the TLM analysis of a circular waveguide by an order of magnitude.>