Low numerical dispersion two-dimensional (2,4) ADI-FDTD method

The numerical dispersion of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method can be improved by approximating the spatial derivatives using the four-point centered finite-difference formula. However, the improvement is not significant when the time step size increases. In this paper, we develop a low numerical dispersion 2-D (2,4) ADI-FDTD method, by which the finite-difference operators are determined by minimizing the error terms in the numerical dispersion relation. The numerical dispersion error is shown to be significantly reduced for any time-step size. In addition, there is an alternative method that results in zero numerical dispersion errors at a specified propagation angle. The numerical dispersion relation of the proposed method is investigated theoretically and compared with the standard ADI-FDTD method as well as with the conventional FDTD method