Auxiliary differential equation (ADE) method based complying-divergence implicit FDTD method for simulating the general dispersive anisotropic material

Abstract

The preceding works introduced the leapfrog complying divergence implicit finite-difference time-domain (CDI-FDTD) method, which exhibits high accuracy and unconditional stability. In this study, the method is reformulated to simulate general electrically anisotropic and dispersive media. The auxiliary differential equation (ADE) method is employed to solve the equivalent polarization currents, which are then integrated into the CDI-FDTD method. The iterative formulae are presented, and the calculation method is similar to that of the traditional CDI-FDTD method. Additionally, the Von Neumann method is utilized to analyze the unconditional stability of the proposed method. To evaluate the performance of the proposed method, three numerical cases are conducted. These include calculating the transmission and reflection coefficients of a monolayer graphene sheet and a monolayer magnetized plasma, as well as the scattering properties of a cubic block plasma. The numerical results obtained by the proposed method demonstrate its accuracy and efficiency in simulating general anisotropic dispersive media, compared to both the analytical method and the traditional FDTD method.