A comparison of the dispersion characteristics associated with the TLM and FD‐TD methods

This paper presents the dispersion characteristics of the FD‐TD algorithm by showing the numerical phase and group velocities of the TEM, TE or TM modal solutions. For the TEM wave propagation, there exist three fundamental directions to which phase and group velocities can be expressed by only a single variable (wave number k or frequency ω). Those special directions were chosen to show the dispersive nature of the FD‐TD algorithm of which the group and phase velocities depend explicitly on frequencies. In view of similarities between the TLM and FD‐TD algorithms, a comparison of phase velocity characteristics of both methods was made. Under the special condition where the stability factor s is larger than 1/2, the FD‐TD algorithm is found less dispersive than that of the original TLM. However, newly developed symmetrical TLM method appears less dispersive than the FD‐TD algorithm. In the numerical simulation of waveguide modal solutions, it was found that there exists an optimum frequency which provide least numerical error in the FD‐TD application. A procedure, which determines the stability factor s and the maximum allowed frequency F max for the best numerical results, is proposed in this paper.