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. (31st July 2019) - Ramadan, Omar
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.