Premium
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
Author(s) -
Ramadan Omar
Publication year - 2019
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2657
Subject(s) - finite difference time domain method , stability (learning theory) , bilinear transform , discretization , bilinear interpolation , dispersion relation , mathematics , graphene , dispersion (optics) , constraint (computer aided design) , mathematical analysis , physics , computer science , condensed matter physics , quantum mechanics , telecommunications , geometry , statistics , bandwidth (computing) , digital filter , machine learning
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.