Stability and Numerical Dispersion Analysis of a 3D Hybrid Implicit-Explicit FDTD Method

Abstract

A three-dimensional hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method is recently proposed for the solution of three-dimensional Maxwell's equations. In this communication, its stability and numerical dispersion relation are derived and analyzed in detail. In order to evaluate its performance, the comparison between it and other two FDTD methods is made, i.e., the Yee-FDTD method and the alternation-direction implicit (ADI)-FDTD method. The final results show that the stability condition of the HIE-FDTD method is relatively relaxed in comparison with that of the Yee-FDTD method. However, the performance of the numerical dispersion of the HIE-FDTD method will unfortunately deteriorate in some special directions, which could be worse than those of the Yee-FDTD method and the ADI-FDTD method.