Analysis and numerical experiments on the numerical dispersion of two-dimensional ADI-FDTD

The numerical dispersion relations in the literature are inconsistent for the alternate-direction-implicit finite-difference time-domain (ADI-FDTD) method. By analysis of the amplification factors, the numerical dispersion relation is rederived and verified with numerical experiments, with good agreement. The inconsistency of the numerical dispersion relation is resolved. It is shown that ADI-FDTD has some fundamental limits. For a given time step size, there is a velocity error even for zero spatial mesh. For a given spatial mesh size, the mesh does not support a numerical wave at certain time step sizes. As the Nyquist sampling limit is approached, the velocity of the wave approaches zero. At about twice the Nyquist limit, the wave does not propagate. Hence, the Nyquist criterion should be respected in choosing the time step size.