Efficient unconditionally stable one-step leapfrog ADI-FDTD method with low numerical dispersion
Efficient unconditionally stable one-step leapfrog ADI-FDTD method with low numerical dispersion
复制标题
低数值色散的高效无条件稳定一步蛙跳ADI-FDTD方法
DOI：
10.1049/iet-map.2013.0269
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发表时间：
2014-04
期刊：
影响因子：
--
通讯作者：
Rong-Lin Li
中科院分区：
文献类型：
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作者：
Yong-Dan Kong;Qing-Xin Chu;Rong-Lin Li
提出了一种基于控制参数的高效、无条件稳定的一步跳跃交替方向隐式有限差分方法。首先在麦克斯韦方程的矩阵中引入三个控制参数以减小数值色散误差，然后推导出一种有效的一步跳跃ADI-FDTD方法。其次，分析表明，该方法是无条件稳定的。此外，还对该方法的数值色散关系进行了解析推导。第三，给出了控制参数的确定过程。此外，还研究了传播角度、网格大小、时间步长和频率对该方法色散特性的影响。结果表明，该方法的归一化数值相速度误差(NNPVE)和最大NNPVE显著降低。最后，通过两个数值算例验证了该方法的准确性和有效性。
An efficient unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method based on the controlling parameters is presented. First, three controlling parameters are introduced to the matrices of the Maxwell's equations to decrease the numerical dispersion error, and then the formulation of an efficient one-step leapfrog ADI-FDTD method is derived. Second, the analysis shows that the proposed method is unconditionally stable. Moreover, the numerical dispersion relation of the proposed method is derived analytically. Third, the process of determination of the controlling parameters is shown. Furthermore, the effects of the propagation angle, mesh size, time step and frequency on the dispersion characteristics of the proposed method are also investigated. The result shows that the normalised numerical phase velocity error (NNPVE) and maximum NNPVE of the proposed method are decreased significantly. Finally, two numerical examples are simulated to demonstrate the accuracy and efficiency of the proposed method.
DOI：
10.1109/cemtd.2007.4373546
发表时间：
2007-10
期刊：
2007 Workshop on Computational Electromagnetics in Time-Domain
影响因子：
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作者：
S. Cooke;M. Botton;T. Antonsen;B. Levush
通讯作者：
S. Cooke;M. Botton;T. Antonsen;B. Levush