A Three-Dimensional Fourth-Order ADI-FDTD Method and Its Application in Cavity Problems

Attention was focused on the three-dimensional fourth-order alternating-direction implicit finite-difference time-domain (3D 4^th-order ADI-FDTD) method using the 4^th-order spatial difference and the 2^nd-order temporal difference. Firstly, the numerical formulation of the 4^th-order ADI-FDTD method is presented. Secondly, the numerical dispersion relation is derived analytically. Moreover, the numerical dispersion is investigated as a function of mesh resolution and time step. Finally, several numerical examples for cavity problems are simulated. And it is found that the proposed method is more accurate than the 2^nd-order ADI-FDTD method.