AN ACCURATE AND LOGICALLY CORRECT WAY TO VERIFY THE NUMERICAL DISPERSION RELATIONS OF FDTD AND ADI-FDTD METHODS

摘要

It is well known that the numerical dispersion relations of all kinds of finite-difference time-domain (FDTD) methods, including the conventional FDTD and alternating-direction implicit (ADI) FDTD methods, are derived from the assumption of plane wave. In the past, however, disregarding the above fact, a point source that creates a cylindrical wave was used to numerically validate the numerical dispersion relations of the FDTD-related methods. Strictly speaking, using the point source for the validation is illogical and also incorrect. This is due to the fact that the numerical dispersion relation of the cylindrical wave differs from that of the plane wave. It is demonstrated in this paper that the phase velocity calculated from the point source strongly depends on the positions of the observation points, and that the calculated phase velocity never exactly matches the theoretical prediction, even though the phase velocity of the cylindrical wave gets closer to that of the plane wave when the observation points are located far away from the point source (that is, when the cylindrical wave can be approximately treated as the plane wave). On the contrary, numerical tests indicate that, no matter where the observation points are located, the phase velocity obtained using plane-wave excitation agrees extremely well with the theoretical values. We can therefore conclude that to more accurately and logically verify the numerical dispersion relations of any kinds of FDTD-related algorithms, plane-wave excitation has to be employed.