3D Isotropic Dispersion (ID)-FDTD Algorithm: Update Equation and Characteristics Analysis

Three 3D isotropic dispersion-finite-difference time-domain (ID-FDTD) algorithms are formulated based on two new spatial difference equations. The difference equations approximate the spatial derivatives in Maxwell´s equation using more spatial sampling points distributed in an isotropic manner. The final spatial difference equation is a weighted summation of the two new difference and the conventional central difference equations. Therefore, based on the proposed spatial difference equation and choices of the weighting factors, seven different FDTD schemes can be formulated, which include the Yee scheme. Among the seven schemes, three methods can show isotropy of the dispersion superior to that of the Yee scheme. The weighting factors for the three schemes are numerically determined to minimize the anisotropy of the dispersion by using an optimization technique. In this paper, the dispersion & stability characteristics and the numerical complexity of the three ID-FDTD schemes are addressed. Also, the upper bound of the Courant number of the three ID-FDTD schemes is heuristically proposed and numerically verified. One scattering problem is considered to show the improved accuracy of the proposed ID-FDTD scheme.