Some fundamental characteristics of the one-dimensional alternate-direction-implicit finite-difference time-domain method

Some fundamental characteristics are investigated for the alternate-direction-implicit finite-difference time-domain (ADI-FDTD) method in the one-dimensional case, such as growth and dissipation, numerical dispersion, and a time-step size limit. It is shown that this two sub-step method alternates dissipation and growth that exactly compensate and, thus, is unconditionally stable. The numerical dispersion error is larger than for Yee\´s method and there is an "intrinsic temporal numerical dispersion" accuracy limit at zero mesh size, which is the highest accuracy one can obtain with a meaningful time-step size. Also, it is shown that, for some combinations of time step and mesh size, the ADI-FDTD method does not propagate a wave. There is a minimum numerical velocity limited by the mesh density, and the wave attenuates for time-step sizes larger than an "ADI limit." Thus, the time-step size does have an upper bound, which is smaller than the Nyquist limit. The results of numerical experiments are shown to agree well with the theoretical prediction.