A Novel 3-D HIE-FDTD Method With One-Step Leapfrog Scheme

Abstract

This paper presents a novel 3-D leapfrog hybrid implicit–explicit finite-difference time-domain (HIE-FDTD) method. By first adopting the Peaceman–Rachford scheme and then the one-step leapfrog scheme, the proposed HIE-FDTD algorithm is implemented in the same manner as the traditional finite-difference time-domain method in which the implicit scheme was applied only in the direction where a fine grid was applied and the explicit scheme was applied in two other directions where a larger grid was used. Further, by introducing auxiliary field variables denoted by $e$ and $h$ , the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Numerical analysis demonstrated that the Courant–Friedrichs–Lewy stability condition of the proposed HIE-FDTD method is determined only by one grid cell size, which is more relaxed than those of the existing HIE-FDTD methods, and the numerical dispersion error is less than that of the alternating-direction implicit method.