On the dispersion relation of ADI-FDTD

In this letter, we analyze the alternating direction implicit finite-difference time-domain (ADI-FDTD) dispersion relation and find the numerical plane-wave relationship between the magnetic and electric fields, showing that the scheme is not divergence-free. We also show that negative-group-velocity modes with positive phase velocities may appear for high Courant numbers. A parallel comparison is made with the behavior of the classical Yee FDTD and the Crank-Nicolson schemes.