3维交替方向隐式时域有限差分算法及其应用

3-D alternating direction implicit finite difference time domain algorithm and its application

为了克服在传统时域有限差分算法中时间步长受网格尺寸大小的限制,提出一种用于精确模拟波在色散金属结构传播的3维交替方向隐式时域有限差分算法.首先,利用广义关键点色散模型描述金属材料在光学频率下的电磁特性;然后,采用2个1阶微分方程代替2阶广义辅助微分方程的方法,避免时间步长引起的不稳定,降低算法的复杂度和应用难度;最后,用交替方向隐式时域有限差分算法研究1维等离子体模型和3维金属谐振腔结构,将交替方向隐式时域有限差分算法的结果与传统时域有限差分算法进行对比.结果表明二者吻合较好,但交替方向隐式时域有限差分算法的效率更高.

In order to overcome the time step size that was limited by the size of the grid in traditional finite difference time domain algorithm,a unified three-dimensional alternating direction implicit finite difference time domain algorithm was presented for accurately simulating the propagation of waves in a dispersion metal structure.First,the generalized critical points dispersion model was used to describe the electromagnetic properties of metallic materials at optical frequencies.Then,two first-order differential equations were used instead of the second-order generalized auxiliary differential equations,which avoided the instability caused by the time step component,and reduced the complexity and application difficulty of the algorithm.Finally,the alternating direction implicit finite difference time domain algorithm was used to study the one-dimensional plasma model and the three-dimensional metal resonator structure.The results of the alternate direction implicit finite difference time domain algorithm were compared with the traditional finite difference time domain algorithm.The results showed that the two agreed well,and the implicit finite difference time domain algorithm with alternating directions had higher efficiency.