On the Stability of the RK-FDTD Method for Graphene Modeling

The Runge-Kutta finite-difference time-domain (RK-FDTD) method is an extension of the conventional FDTD technique to include graphene sheets. According to this method, the relationship between the current density and the electric field for graphene is discretized by applying an explicit second-order...

Full description

Saved in:
Bibliographic Details
Published inIEEE transactions on antennas and propagation p. 1
Main Authors Pereda, Jose A., Grande, Ana
Format Journal Article
LanguageEnglish
Published IEEE 2025
Subjects
Antennas and propagation
Current density
Electric fields
Finite difference methods
Finite-difference time-domain (FD-TD) method
Graphene
Mathematical models
Numerical stability
Polynomials
second-order Runge-Kutta (RK) scheme
stability
Stability criteria
Time-domain analysis
Online AccessGet full text

Cover

More Information
Summary:The Runge-Kutta finite-difference time-domain (RK-FDTD) method is an extension of the conventional FDTD technique to include graphene sheets. According to this method, the relationship between the current density and the electric field for graphene is discretized by applying an explicit second-order RK scheme. It has recently been concluded that the RK-FDTD method is subject to the same Courant-Friedrichs-Lewy (CFL) stability limit as the conventional FDTD method. This communication revisits the stability analysis of the RK-FDTD method. To this end, the von Neumann method is combined with the Routh-Hurwitz criterion. As a result, closed-form stability conditions are obtained. It is shown that in addition to the CFL stability limit, the RK-FDTD method must also satisfy new conditions involving graphene parameters. Unfortunately, the RK-FDTD method becomes unstable for commonly used values of these parameters. The theoretical results are confirmed with numerical examples.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2025.3581386