Advanced Numerical Methods for Graphene Simulation with Equivalent Boundary Conditions: A Review

Since the discovery of graphene, due to its excellent optical, thermal, mechanical and electrical properties, it has a broad application prospect in energy, materials, biomedicine, electromagnetism and other fields. A great quantity of researches on the physical mechanism of graphene has been applied to engineering in electromagnetism and optics. To study the properties of graphene, different kinds of numerical methods such as the mixed finite element method (Mixed FEM), the mixed spectral element method (Mixed SEM), Method of Auxiliary Sources (MAS), discontinuous Galerkin time-domain method (DGTD) and interior penalty discontinuous Galerkin time domain (IPDG) have been developed for simulating the electromagnetic field effects of graphene and equivalent boundary conditions such as impedance transmission boundary condition (ITBC), surface current boundary condition (SCBC), impedance matrix boundary condition (IMBC) and surface impedance boundary condition (SIBC) have been employed to replace graphene in the computational domain. In this work, the numerical methods with equivalent boundary conditions are reviewed, and some examples are provided to illustrate their applicability.