Stability and Numerical Dispersion Analysis of a Fourth-Order Accurate FDTD Method

In order to obtain high-order accuracy, a fourth-order accurate finite difference time-domain (FDTD) method is presented by Kyu-Pyung Hwang. Unlike conventional FDTD methods, a staggered backward differentiation scheme instead of the leapfrog scheme is used to approximate the temporal partial differential operator. However, the high order of its characteristic equation derived by the Von Neumann method makes the analysis of its numerical dispersion and stability very difficult. In automatic control theory, there are two effective methods for the stability analysis, i.e., the Routh–Hurwitz test and the Jury test. The combination of the Von Neumann method with each of the two can strictly derive the stability condition, which only makes use of the coefficients of its characteristic equation without numerically solving it. The method of analysis in this paper is also applicable in the stability and numerical analysis of other high-order accurate FDTD methods.     

Numerical Stability and Numerical Dispersion of Compact Conformal Mapping 2D-FDTD Method Used for the Dispersion Analysis of Waveguides

In dispersion analysis of waveguides with particular cross-section by compact 2D-FDTD method, using conformal-boundary coordinates can obtain high computational accuracy. The transformation from conformal-boundary coordinates to rectangular coordinates can be done by conformal mapping technique in order to match Yee algorithm. In this paper, numerical stability and numerical dispersion equation of compact conformal mapping 2D-FDTD (CCM-2D-FDTD) method are derived. It is shown that the upper limit of Courant number for CCM-2D-FDTD is always smaller than 1/√2. As an example, the dispersion equation is used to examine the impact of number of cell for circular waveguide.     

A Study on the Stability and Numerical Dispersion of the Lumped-Network FDTD Method

The lumped-network finite-difference time-domain (LN-FDTD) technique is an extension of the conventional FDTD method that enables the incorporation of linear one-port LNs in a single FDTD cell. This paper studies the stability and the numerical dispersion of this technique. To this end, an isotropic medium that is uniformly loaded with LNs in the $x$-direction is considered as a working model. The stability analysis, based on the von Neumann method, is performed for general $M$th-order LNs and closed-form stability conditions are derived for some particular cases. The numerical dispersion relation is obtained for plane-wave propagation in the proposed LN-loaded medium. It is shown that LNs can be interpreted in terms of an effective frequency-dependent permittivity and, as a consequence, the LN-loaded medium can be viewed as a uniaxial medium. The numerical admittance of the LNs is also obtained showing that, as a side-effect of the time discretization, the LN parameters become frequency-dependent, e.g. for the resistor case, the resistance becomes a function of the frequency.      

辛算法的稳定性及数值色散性分析

引入一种新的数值计算方法 —辛算法求解Maxwell方程,即在时间上用不同阶数的辛差分格式离散,空间分别采用二阶及四阶精度的差分格式离散,建立了求解二维Maxwell方程的各阶辛算法,探讨了各阶辛算法的稳定性及数值色散性.通过理论上的分析及数值计算表明,在空间采用相同的二阶精度的中心差分离散格式时,一阶、二阶辛算法(T1S2、T2S2) 的稳定性及数值色散性与时域有限差分(FDTD)法一致,高阶辛算法的稳定性与FDTD法相当;四阶辛算法结合四阶精度的空间差分格式(T4S4) 较FDTD法具有更为优越的数值色散性.对二维TMz波的数值计算结果表明,高阶辛算法较FDTD法有着更大的计算优势.     

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。     

高阶LOD-FDTD方法的数值特性研究

该文分析并证明了高阶局部1维时域有限差分(LOD-FDTD)方法的数值特性,即：稳定性、数值色散及高阶收敛性。文中首次推导出3维各阶LOD-FDTD方法的增长因子和数值色散关系的一致形式,解析证明了这类方法均是无条件稳定的。基于此一致性关系,首次分析了这类方法的数值色散误差随阶数的收敛情况,并给出收敛性条件。在用此类方法计算谐振腔本征模频率的实验中,数值结果显示高阶方法可达到更优的计算精度,同时不显著增加计算时间。     

Stability and Dispersion Analysis for ADI-FDTD Method in Lossy Media

The stability and dispersion analysis for the alternating-direction-implicit finite-difference time-domain (ADI- FDTD) method in lossy media is presented. Although the stability and numerical dispersion have been analyzed for the ADI-FDTD method, most of the analysis is dedicated to the cases of lossless media. Here, the stability and dispersion analysis is performed for the method in lossy media. The stability analysis theoretically proves the unconditional stability of the ADI-FDTD method in lossy media. Meanwhile, the dispersion analysis reveals the numerical loss and dispersion characteristics of this method. This will be meaningful for the evaluation and further development of the ADI-FDTD method in lossy media     

一种优化参数的LOD-FDTD算法及其数值特性

提出一种改进的参数优化局部一维时域有限差分(LOD-FDTD)方法,该方法将时间步长等分成3步,沿坐标方向加上色散控制因子,以降低数值色散误差。本文首先证明改进方法的稳定性,并分析其数值色散误差。结果表明改进方法的数值色散误差小于传统的LOD-FDTD方法。     

一种数值求解慢波结构色散曲线的新方法

运用场匹配法，推导出一种原则上可数值求解任意圆柱轴对称周期结构慢波波导冷腔TMon模色散曲线的方法。采用该方法编制了计算波纹波导和盘荷波导色散曲线的Matlab程序，计算结果与多维全电磁模拟软件结果的相对误差在1％之内。由于采用了数值积分算法，该方法的计算速度比传统的Bessel函数泰勒级数展开法更快。     

Convolutional Perfectly Matched Layer for an Unconditionally Stable LOD-FDTD Method

This letter presents the development and implementation of the convolutional perfectly matched layer (CPML) for the recently proposed locally 1-D finite difference time domain method LOD-FDTD. Two different examples are simulated. Their results are compared with the FDTD-PML method and it is found that the proposed method has 16 dB less reflection error at a Courant Friedrich Levy number of one.     

Numerical Dispersion Analysis With an Improved LOD–FDTD Method

In this letter, a modified locally one-dimensional finite-difference time-domain (LOD-FDTD) method is proposed. The dispersion behavior is investigated and compared with the conventional LOD-FDTD method. It is found that for a Courant-Friedrich-Levy number equal to 5 the modified LOD-FDTD method performs approximately 20% better than the conventional LOD-FDTD method     

Numerical Stability Analysis of the Thompson-FDTD Method

The stability criterion for the numerical solutions of two-dimensional Maxwell's equations obtained by the method of difference-Thompson transformation (DTTR) combined with the finite difference time domain (FDTD) method is obtained for the first time.     

A Frequency-Dependent LOD-FDTD Method and Its Application to the Analyses of Plasmonic Waveguide Devices

Detailed frequency-dependent formulations are presented for several efficient locally one-dimensional finite-difference time-domain methods (LOD-FDTDs) based on the recursive convolution (RC), piecewise linear RC (PLRC), trapezoidal RC (TRC), auxiliary differential equation, and ${mmb Z}$ transform techniques. The performance of each technique is investigated through the analyses of surface plasmon waveguides, the dispersions of which are expressed by the Drude and Drude-Lorentz models. The simple TRC technique requiring a single convolution integral is found to offer the comparable accuracy to the PLRC technique with two convolution integrals. As an application, a plasmonic grating filter is studied using the TRC-LOD-FDTD. The use of an apodized and a chirped grating is found quite effective in reducing sidelobes in the transmission spectrum, maintaining a large bandgap. Furthermore, a plasmonic microcavity is analyzed, in which a defect section is introduced into a grating filter. Varying the air core width is shown to exhibit tunable properties of the resonance wavelength.      

FDTD Schemes With Minimal Numerical Dispersion

A novel formulation of hybrid finite-difference time-domain (FDTD) methods is presented. Significant reduction of numerical dispersion is achieved by the proposed FDTD methods that combine the second-order and higher-order finite-differences. Also, the proposed FDTD methods exhibit significantly higher solution accuracy than the accuracy of standard FDTD schemes as a result of partial mutual cancellation of numerical errors provided by the developed FDTD update procedure. The residual numerical error of the phase velocity remains low even for sampling of a few points per wavelength. Also, the FDTD schemes based on the proposed approach are faster and more accurate than the corresponding purely higher-order FDTD schemes with the same mesh. Test examples are provided for validation purposes.      

Reduction of Numerical Dispersion Error in 3-D ADI-MRTD Method With the Coarse Mesh

In order to reduce the numerical dispersion in three-dimensional alternating-direction implicit multiresolution time-domain scheme, a correction procedure is introduced. The numerical dispersion relation and the anisotropic correction parameters are considered. The reduction of the numerical dispersion is investigated for single frequency problem and wide-band simulation with the coarse mesh.      

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     

用数值方法研究含负折射率材料的一维光子晶体的色散特性

在传统的二元一维光子晶体中,如果有一种材料在某一段频带范围内显示出负折射率特点,此光子晶体的色散特性肯定不同于传统的光子晶体.首先通过建立简单的模型推导出光波在光子晶体中传播的表达式,然后进行数值模拟和分析,并引入负折射率表达式,仿真得到这种光子晶体的色散图形.研究结果表明,该光子晶体在微波频段存在多个小的禁带,可以作为多通道滤波器.在高频带,当构成光子晶体的两种材料的厚度发生改变时,禁带的位置也会变化.     

PML吸收边界的时域有限差分法的数值色散研究

PML吸收边界以其优异的吸收能力与效果而倍受人们的关注。本文针对运用PML吸收边界的时域有限差分法的数值色散问题进行了研究,并得到了较为满意的结果,PML吸收边界在有效减少电磁 波在边界上的反射的情况下,并没有带来对数值色 散的不良影响。     

纳米Ag-Cu-In-Sn合金粉体的分散稳定性研究

通过等离子体蒸发凝聚法制备纳米Ag-Cu—In—Sn合金粉，初步研究了聚乙烯吡略烷酮K-30（PVP）和十六烷基三甲基溴化铵（CTAB）及其分散工艺对合金粉体分散性能的影响。研究结果表明：随着超声时间的增加，吸光率增大，分散性能变好；与CTAB相比PVP的分散效果更好，其最佳分散浓度为1．8g／L。     

一种改进的时间步进稳定性平均方法

介绍了时域积分方程方法（TDIE）的基本原理,提出一种抑制时域电场积分方程（TDIE）时间步进（MOT）后期振荡的新平均算法,提高了MOT算法后期的稳定性。计算了高斯脉冲波照射到金属立方体时目标表面的电流响应,数值结果表明,该方法简单有效地推迟了TDIE后期震荡时间。