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...

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Detalles Bibliográficos
Autores: Pereda Fernández, José Antonio|||0000-0002-6347-9237, Grande Sáez, Ana María
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
Descripción
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.