A New Form of the Numerical Dispersion Relation of ADI-FDTD for the 3D Maxwell´s Equations

In this paper, a new form of the numerical dispersion relation of the alternating direction implicit finite difference time domain (ADI-FDTD) method for the 3D Maxwell equations is derived from the equivalent form of ADI-FDTD. It is shown that this new form is simpler than the original one and easy to be used to make further analysis. By comparison with the numerical dispersion relations of the Crank-Nicolson (CN) FDTD scheme and the FDTD scheme it is shown that the numerical dispersion relation of ADI-FDTD is much more closer to that of CN-FDTD than to that of FDTD. The relation between the new form and the original form of the numerical dispersion relation of ADI-FDTD is also given that they are equivalent to each other.