An Artificial Anisotropy Four-Step HIE-FDTD Method With Lower Numerical Dispersion Error

Yong-Dan Kong,Qing-Xin Chu,Hong-Yu Zhang,Chu-Bin Zhang

doi:10.1109/access.2020.3034696

Abstract

In this article, by introducing artificial anisotropic (AA) parameters in the four-step hybrid implicit-explicit finite-difference time domain (HIE-FDTD) method, an AA four-step HIE-FDTD method is proposed, which can reduce the numerical dispersion error and improve the computational accuracy. Firstly, the Maxwell's matrix equation is decomposed into four sub-matrix equations by using the split-step scheme, and artificial anisotropy parameters are introduced, then the proposed AA four-step HIE-FDTD is obtained. Furthermore, the stability analysis of the AA four-step HIE-FDTD method shows that the stability condition of the proposed method is closed to the original four-step HIE-FDTD method. Next, the numerical dispersion characteristics of the proposed method are analyzed and compared with other HIE-FDTD methods. The results show that the numerical dispersion error of the proposed method is significantly reduced compared with the four-step HIE-FDTD method. Finally, the performance of the proposed method is further verified by the numerical simulation. Numerical results show that the proposed method has lower numerical dispersion error and higher computational accuracy than that of the four-step HIE-FDTD method.

Highlights

The finite-difference time-domain (FDTD) method [1] is one of the most widely used electromagnetic numerical calculation methods, but the Courant-Friedrichs-Lewy (CFL) stability condition [2] limits the computational efficiency of the method in the miniaturized and complicated electromagnetic field problems.In order to remove the limitation of the CFL stability condition, the alternating-direction implicit (ADI) FDTD method [3], [4] has been proposed
The ADI-FDTD method uses the implicit method to solve iteratively, so that the time step value of the method is no longer controlled by the spatial grid size, larger time steps can be used to improve the computational efficiency
We presented a four-step hybrid implicit-explicit (HIE)-FDTD method with weaker CFL stability condition ( t 2 x / c and t 2 z / c ) in [19]

Summary

INTRODUCTION

The finite-difference time-domain (FDTD) method [1] is one of the most widely used electromagnetic numerical calculation methods, but the Courant-Friedrichs-Lewy (CFL) stability condition [2] limits the computational efficiency of the method in the miniaturized and complicated electromagnetic field problems. Wang et al proposed a new 3D one-step leapfrog HIE-FDTD method in [17] with a CFL stability condition of ∆t < ∆x/c & ∆t < ∆z/c (suppose the fine grid only in the y-direction), and it’s the time step value can be increased compared with the original. This optimization method has been applied to the ADI-FDTD method [21], [22], the WCSFDTD method [23] and the HIE-FDTD methods [24]−[26].

FOMULATION

NUMERICAL DISPERSION ANALYSIS

Methods

NUMERICAL RESULT

Findings

CONCLUSION