Two Efficient Unconditionally-Stable Four-Stages Split-Step FDTD Methods with Low Numerical Dispersion
Two Efficient Unconditionally-Stable Four-Stages Split-Step FDTD Methods with Low Numerical Dispersion
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DOI：
10.2528/pierb12103011
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发表时间：
2013
影响因子：
--
通讯作者：
Yong-Dan Kong;Q. Chu;Ronglin Li
中科院分区：
文献类型：
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作者：
Yong-Dan Kong;Q. Chu;Ronglin Li
提出了两种基于控制参数的无条件稳定的四步分裂阶时域有限差分（FDTD）方法，该方法具有较低的数值色散。首先，在第一种方法中，麦克斯韦矩阵被分成四个子矩阵。同时引入两个控制参数来减小数值色散误差。因此，时间步被分成四个子步。第二种方法是通过调整第一种方法中推导出的子矩阵的顺序而得到的。其次，对所提出的方法的无条件稳定性和色散关系给出了理论证明。此外，获得所提出的方法的控制参数的过程中示出。再次，研究了所提方法的频散特性，发现所提方法的数值频散误差可以显着减小。最后，为了验证所提出方法的有效性，给出了数值实验。
Two e-cient unconditionally-stable four-stages split- step (SS) flnite-difierence time-domain (FDTD) methods based on controlling parameters are presented, which provide low numerical dispersion. Firstly, in the flrst proposed method, the Maxwell's matrix is split into four sub-matrices. Simultaneously, two controlling parameters are introduced to decrease the numerical dispersion error. Accordingly, the time step is divided into four sub-steps. The second proposed method is obtained by adjusting the sequence of the sub- matrices deduced in the flrst method. Secondly, the theoretical proofs of the unconditional stability and dispersion relations of the proposed methods are given. Furthermore, the processes of obtaining the controlling parameters for the proposed methods are shown. Thirdly, the dispersion characteristics of the proposed methods are also investigated, and numerical dispersion errors of the proposed methods can be decreased signiflcantly. Finally, to substantiate the e-ciency of the proposed methods, numerical experiments are presented.