The ADI-FDTD Method for Transverse-Magnetic Waves in Conductive Materials

A numerical dispersion analysis of the alternating-direction implicit finite-difference time-domain method is introduced for transverse-magnetic waves in lossy materials. To provide a general study, the conduction terms are discretized by using a weighted average in time. It is found that the numerical dispersion relation is different to that of the transverse-electric (TE
z
) case. Moreover, contrary to what happens in the TE
z
case, no set of weighted-average parameters makes the accuracy of the formulation independent of how well the time step resolves the material relaxation-time constant. To overcome this problem, a split-field version of Maxwell's equations is considered as the governing equations. Then, by synchronizing in time the lossy terms with the spatial derivatives, the resulting formulation has the same numerical dispersion relation as in the TE
z
case. Moreover, its accuracy becomes independent of the quality of the resolution of the relaxation-time constant by the time step.