论文标题
通过FDTD方法的时间步骤对数值分散的研究：避免结论错误
Investigation of Numerical Dispersion with Time Step of The FDTD Methods: Avoiding Erroneous Conclusions
论文作者
论文摘要
人们普遍认为，在有限差分时间域（FDTD）模拟中导致小数字错误。在本文中，我们研究了时间步骤如何影响两种FDTD方法的数值分散，包括FDTD（2,2）方法和FDTD（2,4）方法。通过严格的分析和数值分析，发现FDTD方法的小时间步骤并不总是具有较小的数值错误。我们的发现表明，这两种FDTD方法相对于时间步骤呈现不同的行为：（1）对于FDTD（2,2）方法，较小的时间步骤受到Courant-Friedrichs-Lewy（CFL）条件的限制，会增加数值分散并导致较大的仿真错误； （2）对于FDTD（2,4）方法，随着时间步长的增加，数值分散误差首先减少然后增加。我们的发现还通过几个数值示例，包括波传播，空腔的谐振频率和实用的电磁兼容性（EMC）问题，从一维情况进行了全面验证。
It is widely thought that small time steps lead to small numerical errors in the finite-difference time-domain (FDTD) simulations. In this paper, we investigated how time steps impact on numerical dispersion of two FDTD methods including the FDTD(2,2) method and the FDTD(2,4) method. Through rigorously analytical and numerical analysis, it is found that small time steps of the FDTD methods do not always have small numerical errors. Our findings reveal that these two FDTD methods present different behaviors with respect to time steps: (1) for the FDTD(2,2) method, smaller time steps limited by the Courant-Friedrichs-Lewy (CFL) condition increase numerical dispersion and lead to larger simulation errors; (2) for the FDTD(2,4) method, as time step increases, numerical dispersion errors first decrease and then increase. Our findings are also comprehensively validated from one- to three-dimensional cases through several numerical examples including wave propagation, resonant frequencies of cavities and a practical electromagnetic compatibility (EMC) problem.
