A conservative fourth-order real space method for the (2+1)D Dirac equation

Analysis of Electronic Waveguide Bends in Graphene Subject to Dirac Point Fluctuations

“…To model the (2+1)D Dirac equation, an in-house developed higher-order method [14] was employed. Besides being accurate and efficient in terms of computation time and memory consumption, this method also conserves total energy and mass.…”

Analysis of Electrostatically Induced Interconnect Structures in Single-Layer Graphene via a Conservative First-Principles Modeling Technique

“…In this contribution, a fourth-order method is employed. Note that ( 2) is a Poisson system, and thus it can be shown that the advocated PRK time stepping method conserves the energy and the particle probability density, this in contrast to methods based on standard explicit RK time stepping [3]. These conservation properties allow for long-time needed for accurate interconnect analysis.…”

“…To obtain reliable, accurate simulations, we resort to a novel, first-principles quantum mechanical modeling technique, based on higher-order partitioned Runge-Kutta (PRK) time stepping for the (2+1)D Dirac equation. It was theoretically shown in [3], [4] that this method exhibits excellent conservation properties, mitigating spurious dissipation, and thus allowing for long-time simulations. The method is extended and adapted in this work to analyze the aforementioned interconnect structures.…”