Low Numerical Dispersion 3-D HIE-FDTD Methods With Weaker Stability Condition

Abstract

In order to analyze electromagnetic targets with fine structure in one direction more effectively and accurately, optimized 3-D hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) algorithms are formulated based on isotropic dispersion (ID) finite difference (FD) schemes, which are weighted summation of new FD schemes and conventional second-order central FD scheme. Weighting factors for the proposed optimized HIE-FDTD methods can be analytically determined to minimize the anisotropy of the dispersion. The methods also adopt scaling factors for material properties, such as the permittivity and permeability, which can generate nearly the exact phase velocity for a single frequency. Compared with previous several HIE-FDTD methods, the numerical dispersion error of the new methods is significantly reduced, and the Courant-Friedrichs-Lewy stability conditions of the proposed HIE-FDTD methods are weaker, which means that the proposed methods are more flexible in choosing time step size and satisfy the requirement of accuracy and efficiency simultaneously. Numerical simulation demonstrates the effectiveness of the methods.