A Low-Dispersion Realization of Precise Integration Time-Domain Method Using a Fourth-Order Accurate Finite Difference Scheme
A Low-Dispersion Realization of Precise Integration Time-Domain Method Using a Fourth-Order Accurate Finite Difference Scheme
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DOI：
10.1109/tap.2011.2109673
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发表时间：
2011-04-01
影响因子：
5.7
通讯作者：
Sun, Gang
中科院分区：
文献类型：
--
作者：
Bai, Zhong-Ming;Ma, Xi-Kui;Sun, Gang
为了减轻最近提出的 PITD 方法的数值色散误差，提出了一种改进的精确积分时域 (PITD) 方法，称为 PITD(4) 算法。 PITD(4)方法基于四阶精确有限差分格式和精确积分技术。解析推导了PITD(4)方法的稳定性条件和数值色散关系，并详细研究了空间和时间步长对数值色散的影响。结果发现，采用精密积分技术，PITD(4)方法的稳定性条件远大于传统时域有限差分的Courant-Friedrich-levy（CFL）稳定性条件；由于采用四阶精确有限差分格式，PITD(4)方法的数值色散误差远小于PITD方法。数值算例验证了PITD(4)方法的准确性和有效性，验证了我们对PITD(4)方法数值色散特性的分析。
A modified precise integration time-domain (PITD) method, called PITD(4) algorithm, is presented in order to mitigate the numerical dispersion errors of a recently proposed PITD method. The PITD(4) method is based on both the fourth-order accurate finite-difference scheme and the precise integration technique. Both the stability condition and the numerical dispersion relations of the PITD(4) method are derived analytically and the effects of spatial and time steps on the numerical dispersion are investigated in detail. It is found that with the precise integration technique, the stability condition of the PITD(4) method is much larger than the Courant-Friedrich-levy (CFL) stability condition of the conventional finite difference time domain; with the fourth-order accurate finite-difference scheme, the numerical dispersion errors of the PITD(4) method are much less than that of the PITD methods. Numerical examples are presented to validate the accuracy and the effectiveness of the PITD(4) method, and to verify our analysis of the numerical dispersion characteristics of the PITD(4) method.