Analysis of Two Alternative ADI-FDTD Formulations for Transverse-Electric Waves in Lossy Materials

A numerical dispersion analysis of the alternating-direction implicit finite-difference time-domain method for transverse-electric waves in lossy materials is presented. Two different finite-difference approximations for the conduction terms are considered: the
double-average
and the
synchronized
schemes. The numerical dispersion relation is derived in a closed form and validated through numerical simulations. This study shows that, despite its popularity, the accuracy of the
double-average
scheme is sensitive to how well the relaxation-time constant of the material is resolved by the time step. Poor resolutions lead to unacceptably large numerical errors. On the other hand, for good conductors, the
synchronized
scheme allows stability factors as large as 100 to be used without deteriorating the accuracy significantly.