An Efficient 2-D Compact Precise-Integration Time-Domain Method for Longitudinally Invariant Waveguiding Structures
An Efficient 2-D Compact Precise-Integration Time-Domain Method for Longitudinally Invariant Waveguiding Structures
复制标题
DOI：
10.1109/tmtt.2013.2261539
复制
发表时间：
2013-07-01
影响因子：
4.3
通讯作者：
Xu Zhuansun
中科院分区：
文献类型：
--
作者：
Kang, Zhen;Ma, Xikui;Xu Zhuansun
基于紧致技术和精细积分（PI）技术，提出了一种二维紧致精细积分时域方法（CPITD），以减小最近提出的紧致时域有限差分（FDTD）算法在模拟纵向不变的电大尺寸波导结构时快速增长的数值色散误差。推导了新算法的稳定性条件和色散方程。所提供的增强FDTD，紧凑的FDTD，和传统的PITD方法表现出通过理论检查的色散性能，随后，通过数值实验验证。结果表明，采用PI技术后，新算法的稳定性判据所允许的最大时间步长比紧凑FDTD方法的Courant-Friedrich-Levy极限大得多，尤其是数值色散误差几乎与时间步长无关，即，在模拟中的任何时间步长都可以实现数值色散误差的明显减小。典型波导结构的数值实验验证和验证了非常有前途的理论结果。这种CPITD算法将是非常有用的电大尺寸和纵向不变的波导结构，因为在2-D域中的网格点的数量减少，大大降低了内存的要求，也减少了总的计算时间，和PI技术几乎消除了时间步长的数值色散的影响，因此，显着减少数值色散误差的任何时间步长。
Based on both the compact technique and the precise-integration (PI) technique, a 2-D compact precise-integration time-domain method (CPITD) is developed in order to mitigate the rapidly growing numerical dispersion errors of a recently proposed compact finite-difference time-domain (FDTD) algorithm with increased time-step size when modeling electrically large and longitudinally invariant waveguiding structures. The stability condition and the dispersion equation of the new algorithm are both derived analytically. The provided enhancement over the FDTD, compact FDTD, and the conventional PITD methods is exhibited through theoretical examination of the dispersion performance, and subsequently, validated by means of numerical experimentation. It is found that with the PI technique, the maximum limit of the time step allowable by the new algorithm's stability criterion is much larger than the Courant-Friedrich-Levy limit of the compact-FDTD method, more particularly, numerical dispersion errors can be made nearly independent of time-step size, i.e., an appreciable reduction of numerical dispersion error is achievable at any time-step size in the simulations. Numerical experimentations of typical waveguide structures verify and validate the very promising theoretical results. This CPITD algorithm will be very useful in electrically large and longitudinally invariant waveguiding structures since the decreased number of grid points in the 2-D domain greatly reduces the memory requirements and also the overall computational time, and the PI technique nearly removes the impact of time-step size on the numerical dispersion, and as a consequence, significantly reduces numerical dispersion error for any time-step size.