A remark on the stability of the HIE-FDTD implementation of graphene dispersion based on the flux density D-E and the current density J-E constitutive relations

Abstract

Recently, the stability of the hybrid implicit-explicit finite difference time domain (HIE-FDTD) implementation of graphene dispersion, based on the current density J-E constitutive relation, has been studied by N. Xu, J. Chen, and J. Wang (Int J Numer Model. 2018; e2536). It has been shown that the introduced J-E implementation retains the standard HIE-FDTD stability constraint. In their study, it is also reported that the stability stringent of the flux density D-E HIE-FDTD implementation, which was found in a previous study, is due the derivations of the field's updating equations. In this communication, it is shown that by using the bilinear Z-transformation technique, the stability of the D-E HIE-FDTD implementation can also lead to the standard HIE-FDTD stability constraint. Therefore, the stability limitation of the HIE-FDTD implementation of the graphene dispersion does not based on the constitutive relation being used but on the employed discretization methodology. Finally, a three-dimensional (3-D) numerical test that investigates the graphene layer transmission coefficient is included to validate the accuracy of the given implementation.