Numerical dispersion analysis for 3-D ADI-FDTD method using higher-order spatial difference

Attention was focused on the numerical dispersion property of 3-D ADI-FDTD (alternating-direction implicit finite-difference time-domain) method using the higher-order spatial difference. First, the iterative formulas of the numerical dispersion relation for the higher-order spatial difference were derived. And secondly, the numerical dispersion values were computed and compared for the second-order, fourth-order, sixth-order and tenth-order spatial difference along the maximum phase-velocity direction and the minimum phase-velocity direction, respectively. And consequently the numerical dispersion was investigated as a function of higher-order spatial difference. Finally it is found that the fourth-order spatial difference is better than others for the uniform cell case.