非均匀网格GA-A3DI-FDTD法分微波电路

研究了一种减小交替方向隐式时域有限差分法(ADI-FDTD,Alternating-Direction Implicit Finite-Difference Time-Domain)数值色散的新方法GA-A3DI-FDTD(Genetic Algorithm Artificial Anisotropy ADI-FDTD)及其在非均匀网格条件下的应用.首先时添加人工各向异性介质后的非均匀网格ADI-FDTD迭代公式进行修正,得到新的数值色散关系,再利用自适应遗传算法(AGA,adaptive genetic algorithm)得到需要添加的人工各向异性介质的相对介电常数.为了验证方法的正确性和有效性,对几种微波电路进行仿真,分别与传统ADI-FDTD相比较,并且比较对非均匀网格的不同处理方法对计算精度的影响.结果表明:通过正确选择目标函数,得到更加合适的人工各向异性介质,可以再减小三维ADI-FDTD数值色散.     

非均匀网格GA-A3DI-FDTD法分析微波电路

研究了一种减小交替方向隐式时域有限差分法（ADI—FDTD,Alternating-Direction Implicit Finite-Difference Time-Domain）数值色散的新方法GA—A3DI—FDTD（Genetic Algorithm Artificial Anisotropy ADI-FDTD）及其在非均匀网格条件下的应用。首先对添加人工各向异性介质后的非均匀网格ADI—FDTD迭代公式进行修正,得到新的数值色散关系,再利用自适应遗传算法（AGA,adaptive genetic algorithm）得到需要添加的人工各向异性介质的相对介电常数。为了验证方法的正确性和有效性,对几种微波电路进行仿真,分别与传统ADI—FDTD相比较,并且比较对非均匀网格的不同处理方法对计算精度的影响。结果表明：通过正确选择目标函数,得到更加合适的人工各向异性介质,可以再减小三维ADI—FDTD数值色散。     

一种有效减少ADI-FDTD数值色散的方法

ADI—FDTD算法的数值色散效应较为明显，本文的研究表明一种通过添加各向异性媒质来修正相速误差，从而减少FDTD数值色散的方法，同样适用于ADI-FDTD，且收效更为显著。数值运算结果证明该方法能够简单有效地去除较宽频带范围内的色散。     

各向异性介质基片平面波导的直线法分析

本文将直线法推广应用于分析各向异性介质基片平面波导的色散特性,并对屏蔽单微带线和单鳍线的色散特性作了具体分析和计算,数值结果与有关文献结果基本一致.     

基于矢量有限元的任意介质加载波导通用软件设计

本文旨在实现波导问题的通用软件设计,文章完善了各向异性介质填充波导问题的矢量有限元理论,并计算了有耗、各向异性介质加载的任意结构波导模式传输系数、色散曲线和模式电场分布。在计算色散曲线时,本文结合了模式场图以消除HFSS在色散计算过程中对传输模式的误判。对于开放结构波导,采用各项异性介质的完全匹配层（PML）理论实现无限的问题截断。通过与商业电磁仿真软件的计算结果作比较,验证了算法的精确性。     

UPML媒质中的包络ADI-FDTD

由于交替方向隐式时域有限差分法(Alternating-Direction Implicit Finite-Difference Time Domain,ADI-FDTD)的数值色散会随着时间步长的增加而增加,文中讨论了单轴各向异性完全匹配层(uniaxial perfectly matched layer,UPML)媒质中包络交替方向隐式时域有限差分法(Envelope ADI-FDTD),推导了二维Envelope ADI-FDTD UPML的迭代公式,并提出一种新的离散方法。与ADI-FDTD UPML相比,改进后的Envelope ADI-FDTD UPML的时间步长可以取得更大,且能有效地修正相速误差,从而减少数值色散,提高计算精度。     

等离子体的交替方向隐式时域有限差分方法

首次把交替方向隐式时域有限差分法(ADI-FDTD)推广到色散介质——无碰撞非磁化等离子体中，计算了非磁化等离子体与电磁波的相互怍用，使用ADI技术给出了无碰撞等离子体介质中的ADI-FDTD迭代公式．并解析地证明了等离子ADI-FDTD算法也是无条件稳定的，数值计算表明，等离子体ADI-FDTD算法与传统的FDTD的计算结果吻合，计算效率更高。     

色散媒质中ADI-FDTD

基于交替方向隐式(ADI)技术的时域有限差分(FDTD)法是一种非条件稳定的计算方法，该方法的时间步长不受Courant稳定条件限制，而由数值色散误差决定。与传统的FDTD相比，ADI-FDTD增大了时间步长，从而缩短了总的计算时间。本文采用递归卷积方法将ADI-FDTD推广应用于色散媒质，推导了二维情况下色散媒质中的ADI-FDTD迭代公式。应用推导公式计算了色散土壤中目标的散射，并与色散媒质FDTD结果对比，在大量减少计算时间的情况下，两者结果符合很好。     

平面结构波导本征值问题的二维时域差分分析

本文提出了一种求解平面结构波导本征值的普适的方法——二维时域差分法。所分析的对象是一种多层介质结构平面波导,其中介质可以是各向异性的,且在介质界面内可以设置导电薄片。与一般的时域差分法相比,这一方法的空间差分只在波导横截面二维腔内进行,从而不仅减少了计算内存,利于在PC机上运行,且避免了一般时域差分法中开放边界条件处理的困难,增加了数值稳定性。本方法具有频域分析的特点,又拥有时域差分的优点。其计算公式普适,通用性强,极易处理各向异性介质,介质分界面存在众多导电片的情况,用这一方法分析微带线其精度和谱域法相当。利用本方法首次得到了各向异性介质基片的主光轴和结构坐标不一致的情况下的微带线色散特性。     

ADI-FDTD+GRT在波导电路分析中的应用

本文研究时域有限差分法(FDTD)的一种新的时空压缩技术,并应用于波导电路的分析.首先分析了软激励条件下的改进的几何重置技术(GRT),研究了合理选择源面与参考面的放置位置,使GRT不仅减小了吸收边界对计算结果的影响,而且节省了计算空间,还可以精确得到全部散射参量.另外阐述了与交替方向隐式时域有限差分法(ADI-FDTD)相结合,使计算空间和时间同时被压缩,达到节省计算资源的目的.为了衡量ADI-FDTD+GRT算法的计算精度和效率,分析了包含不连续结构的波导作为算例,将其数值计算结果分别与传统FDTD和HFSS作比较,并将端面和参考面不同间距的ADI-FDTD+GRT与传统ADI-FDTD在仿真结果和资源占用方面进行对比,结果表明本文算法是精确和高效的.     

GENETIC ALGORITHM IN REDUCTION OF NUMERICAL DISPERSION OF 3-D ADI-FDTD METHOD

A new method to reduce the numerical dispersion of the three-dimensional Alternating Direction Implicit Finite-Difference Time-Domain （3-D ADI-FDTD） method is proposed. Firstly, the numerical formulations of the 3-D ADI-FDTD method are modified with the artificial anisotropy, and the new numerical dispersion relation is derived. Secondly, the relative permittivity tensor of the artificial anisotropy can be obtained by the Adaptive Genetic Algorithm （AGA）. In order to demonstrate the accuracy and efficiency of this new method, a monopole antenna is simulated as an example. And the numerical results and the computational requirements of the proposed method are compared with those of the conventional ADI-FDTD method and the measured data. In addition the reduction of the numerical dispersion is investigated as the objective function of the AGA. It is found that this new method is accurate and efficient by choosing proper objective function.     

Genetic Algorithm in Reduction of Numerical Dispersion of 3-D Alternating-Direction-Implicit Finite-Difference Time-Domain Method

A new method to reduce the numerical dispersion of the 3-D alternating-direction-implicit finite-difference time-domain method is proposed. Firstly, the numerical formulations are modified with the artificial anisotropy, and the new numerical dispersion relation is derived analytically. Moreover, theoretical proof of the unconditional stability is shown. Secondly, the relative permittivity tensor of the artificial anisotropy can be obtained by the adaptive genetic algorithm. In order to demonstrate the accuracy and efficiency of this new method, several examples are simulated. The numerical results and the computational requirements of the proposed method are then compared with those of the conventional method and measured data. In addition, the reduction of the numerical dispersion is investigated as the objective function of the genetic algorithm. It is found that this new method is accurate and efficient by choosing a proper objective function     

Improvement on the numerical dispersion of 2-D ADI-FDTD with artificial anisotropy

In this letter, by introducing artificial anisotropy into computational space, a simple and efficient approach to reduce numerical dispersion of the two-dimensional alternating direction implicit finite-difference time-domain (ADI-FDTD) method is proposed. It is shown that performance of the ADI-FDTD method can be improved significantly for both single frequency simulations and relatively wideband problems. Consequently, the usefulness and effectiveness of the ADI-FDTD method can be notably enhanced.     

An improved ADI-FDTD method and its application to photonicsimulations

When the alternating direction implicit-finite difference time domain method (ADI-FDTD) is applied to simulating photonic devices, full efficiency can not be achieved if reasonable accuracy is to be kept, due to numerical errors such as numerical dispersion. A simple modification to ADI-FDTD is proposed by calculating the envelope rather than the fast-varying field, so that errors are minimized. A factor of two-five in speed can usually be gained while retaining the same level of accuracy compared with conventional FDTD. The efficiency and the accuracy of this improved approach is demonstrated on several problems, from simple waveguide structures to complex photonic crystal structures     

高阶ADI-FDTD算法的数值色散分析

该文给出高阶交替方向隐时域优先差分(ADI-FDTD)算法,即在ADI-FDTD迭代公式的基础上对时间的差分仍然采用二阶中心差分格式,而对空间的差分则采用四阶中心差分格式,并解析地证明了所给出的高阶ADI-FDTD算法仍然满足无条件稳定方程,同时对增长因子相位的分析,得到数值色散关系,最后对其数值色散误差进行了分析,研究表明与普通ADI-FDTD相比,其色散误差较小。     

A study of the numerical dispersion relation for the 2-D ADI-FDTD method

This letter presents a numerical dispersion relation for the two-dimensional (2-D) finite-difference time-domain method based on the alternating-direction implicit time-marching scheme (2-D ADI-FDTD). The proposed analytical relation for 2-D ADI-FDTD is compared with those relations in the previous works. Through numerical tests, the dispersion equation of this work was shown as correct one for 2-D ADI-FDTD.     

An Arbitrary-Order LOD-FDTD Method and its Stability and Numerical Dispersion

An arbitrary-order unconditionally stable three-dimensional (3-D) locally-one- dimensional finite-difference time-method (FDTD) (LOD-FDTD) method is proposed. Theoretical proof and numerical verification of the unconditional stability are shown and numerical dispersion is derived analytically. Effects of discretization parameters on the numerical dispersion errors are studied comprehensively. It is found that the second-order LOD-FDTD has the same level of numerical dispersion error as that of the unconditionally stable alternating direction implicit finite-difference time-domain (ADI-FDTD) method and other LOD-FDTD methods but with higher computational efficiency. To reduce the dispersion errors, either a higher-order LOD-FDTD method or a denser grid can be applied, but the choice has to be carefully made in order to achieve best trade-off between the accuracy and computational efficiency. The work presented in this paper lays the foundations and guidelines for practical uses of the LOD method including the potential mixed-order LOD-FDTD methods.