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 finite-difference time-domain (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 a...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/38364 |
| Acceso en línea: | https://hdl.handle.net/10902/38364 |
| Access Level: | acceso abierto |
| Palabra clave: | Finite-difference time-domain (FD-TD) method Graphene Second-order Runge–Kutta (RK) scheme Stability |
| Sumario: | The Runge Kutta finite-difference time-domain (RK-FDTD) method is an extension of the conventional finite-difference time-domain (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 Runge-Kutta (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 (RH) 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. |
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