Numerical reflection analysis of PML absorbing boundary in 3-D GA-A³DI-FDTD method

Attention was focused on a new method to reduce the numerical dispersion of the 3-D ADI-FDTD (three-dimensional alternating-direction implicit finite-difference time-domain) method through artificial anisotropy. First, the numerical formulations of the 3-D ADI-FDTD method were modified. Second, the new numerical dispersion relation was derived. And consequently the relative permittivity tensor of artificial anisotropy could be obtained by the AGA (adaptive genetic algorithm). In order to demonstrate the accuracy and efficiency of the 3-D GA-A³DI-FDTD (genetic algorithm artificial anisotropy ADI-FDTD) method, a hollow waveguide was simulated as an example. Both the relative phase velocity and the numerical reflection of PML (perfectly matched layers) absorbing boundary were investigated for different objective functions of the AGA. And the numerical results of the proposed method were compared with those of the conventional 3-D ADI-FDTD method. It is found that this new method is more accurate and efficient.