New transmission-line matrix node for two-dimensional electromagnetic field problems

In this paper a new transmission-line matrix (TLM) node for solving two-dimensional electromagnetic field problems is presented. The node is based on a hexagonal rather than rectangular lattice. The scattering matrix and dispersion relation of the new node are provided. The hexagonal TLM method is equivalent to an explicitly time-stepped finite difference algorithm that uses second-order accurate central difference approximations to spatial and temporal derivatives. Comparisons of the propagation characteristics are made with the original rectangular two-dimensional node. The propagation characteristics of the new node are a weak function of the direction of propagation. Therefore in general problems, the amount of velocity error at a given frequency can be obtained from the dispersion relation. A simple method for correcting the velocity error can be utilized to achieve accurate frequency-domain results for coarse discretizations.