基于Drude模型的二维左手材料CNAD-FDTD算法研究

Research on CNAD-FDTD Algorithm for Two-Dimensional Left-Handed Materials Based on Drude Model

为了解决时域有限差分方法的计算域截断问题,本文在完全匹配层方法的基础上,将克兰克尼科尔森(crank-nicolson,CN)半隐式差分方式和近似去耦(approximately-decoupling,AD)法相结合,对基于Drude模型的二维左手材料CNAD-FDTD算法进行研究。为验证该方法在二维频率色散左手材料区域的有效性,对色散媒质的Drude模型进行数值仿真。仿真结果表明,本文所提出的方法,不仅打破了常规FDTD的Courant稳定条件(courant-friedrich-levy,CFL)对时间步长的限制,且受色散材料的影响很少,具有良好的吸收效果;随着CN的增大,运行时间逐渐减少,说明本文所提出的算法可以提高运算效率。该研究为左手材料的进一步发展提供了理论依据。

In order to solve the computational domain truncation problem of the finite difference time domain method,this paper combines the Crank-Nicolson(CN)semi-implicit difference method and the approximate decoupling(AD)method based on the perfect matching layer method.This paper mainly studies the two-dimensional left-hand material CNAD-FDTD algorithm based on the Drude model.In order to verify the effectiveness of the method in the two-dimensional frequency dispersion left-hand material region,the Drude model of the dispersive medium is numerically simulated.The simulation results show that the proposed method not only breaks the limitation of the time step of the conventional FDTD courant-friedrich-levy stability condition,but also has little effect on the dispersion material and has a good absorption effect.As the CN increases,the running time decreases gradually,indicating that the algorithm proposed in this paper can improve the computational efficiency.This study provides a theoretical basis for the further development of left-handed materials.