Reduction of numerical dispersion of 3-D higher order alternating- direction-implicit finite-difference time-domain method with artificial anisotropy

This paper introduces a new method aimed at reducing the numerical dispersion of the 3-D higher order alternating- direction-implicit finite-difference time-domain (ADI-FDTD) method. First, we modify the numerical formulations of the 3-D higher order ADI-FDTD method with the artificial anisotropy dielectric material and derive the new numerical dispersion relation analytically. In addition, theoretical proof of the unconditional stability is given. Second, the relative permittivity tensor of the artificial anisotropy can be obtained by a simple correction scheme. Furthermore, the numerical dispersion characteristics of the higher order artificial anisotropy ADI-FDTD method are investigated and compared with that of other ADI-FDTD methods, including the second-order ADI-FDTD method, the fourth-order ADI-FDTD method, and the second-order artificial anisotropy ADI-FDTD method. To demonstrate the accuracy and efficiency of the proposed method, three examples are simulated, and the numerical results and the computational requirements of this new method are compared with those of other ADI-FDTD methods and the analytic data.