Relaxation of the Courant Condition in the Explicit Finite-Difference Time-Domain Method With Higher-Degree Differential Terms
Relaxation of the Courant Condition in the Explicit Finite-Difference Time-Domain Method With Higher-Degree Differential Terms
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DOI：
10.1109/tap.2023.3234097
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发表时间：
2023-02
影响因子：
5.7
通讯作者：
Harune Sekido;T. Umeda
中科院分区：
文献类型：
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作者：
Harune Sekido;T. Umeda
提出了一种新的显式无耗散的二维和三维时域有限差分（FDTD）方法，用于放松Courant条件。具有二阶和四阶精度的三阶空间差分项与系数一起添加到FDTD的时间发展方程中（2，4）。通过对色散关系的强力搜索得到最优系数，减小了相速度误差，同时满足数值稳定性。新方法在大Courant数时是稳定的，而传统的FDTD方法是不稳定的。新方法也有较小的数值误差相速度比传统的FDTD方法与小的Courant数。
A new explicit and nondissipative finite-difference time-domain (FDTD) method in two and three dimensions is proposed for the relaxation of the Courant condition. The third-degree spatial difference terms with second- and fourth-order accuracies are added with coefficients to the time-development equations of FDTD(2,4). Optimal coefficients are obtained by a brute-force search of the dispersion relations, which reduces phase velocity errors but satisfies the numerical stabilities as well. The new method is stable with large Courant numbers, whereas the conventional FDTD methods are unstable. The new method also has smaller numerical errors in the phase velocity than conventional FDTD methods with small Courant numbers.