强激光与粒子束, 2012, 24 (11): 2687, 网络出版: 2012-10-12
三维周期结构弱无条件稳定时域有限差分算法
Weakly conditionally stable 3-D FDTD method for periodic structures
周期结构 弱无条件稳定 时域有限差分 交替方向隐式 periodic structure weakly conditionally stable finite-difference time-domain alternating-direction-implicit
摘要
从麦克斯韦方程出发, 导出了适用于周期结构的三维弱无条件稳定时域有限差分(FDTD)算法的迭代式, 在理论上证明了其稳定性条件, 其稳定性条件比普通FDTD的稳定性条件要宽松, 并将周期边界条件应用到迭代式中, 得到了可直接编程迭代的方程, 给出了对其特有的一类非三对角阵的解决办法。最后通过算例将计算结果与常规FDTD及ADI-FDTD计算结果比较, 验证了算法的精确性和有效性。
Abstract
Based on Maxwell’s equations, a weakly conditionally stable finite-difference time-domain(FDTD) method for periodic structures is proposed. The stability condition is verified theoretically. Which is looser than that of the conventional FDTD method. And the Sherman-Morrison formula has been used to solve the non-tridiagonal linear system. The new algorithm has better accuracy and efficiency than the ADI-FDTD, especially for large time step size. A numerical example is presented to demonstrate the efficiency and accuracy of the proposed algorithm. Results show the CPU time for this method can be reduced to about 33% of the ADI-FDTD method.
刘宗信, 陈亦望, 徐鑫, 刘亚文, 孙学刚, 张书迪. 三维周期结构弱无条件稳定时域有限差分算法[J]. 强激光与粒子束, 2012, 24(11): 2687. Liu Zongxin, Chen Yiwang, Xu Xin, Liu Yawen, Sun Xuegang, Zhang Shudi. Weakly conditionally stable 3-D FDTD method for periodic structures[J]. High Power Laser and Particle Beams, 2012, 24(11): 2687.
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