二维非正交坐标系下FDTD方法的数值色散特性

本文详细讨论了二维非正交坐标系下FDTD方法的色散特性，导出了其数值色散方程。理论计算结果表明，非正交FDTD方法的空间色散与网络尺寸、网络内角、波传播方向有密切关系。同时指出，在应用非正交FDTD方法解决有关时域电磁问题时，网格的部分应分量选取网格边长相接近，夹角接近90的情况以减少此方法的数值色散。     

保角变换FDTD算法的数值稳定性与数值色散

本文提出了新的保角变换FDTD算法,推导了保角变换FDTD算法的时间稳定性和数值色散方程。此外,本文以圆波导为例计算了不同网格下TE模数值波长的相对误差,分析了不同传播常数和对极点不同半径的半圆电壁近似下数值波长的相对误差。通过适当地选择网格数,可得到高精度。     

用Cassinian变换FDTD方法分析几种特殊截面波导传输特性

本文把保角变换应用于紧凑格式2D/FDTD算法,给出了保角变换FDTD算法差分公式,提出了焦点的处理方法.用Cassinian变换分别计算了椭圆波导、茧形波导的截止波长与色散曲线,以及屏蔽平行双线高阶模的截止波长.     

ADI-MRTD算法的数值色散性分析

针对传统的时域多分辨分析(MRTD)方法的稳定性不足问题,讨论了一种将交替方向隐式技术(ADI)与MRTD算法相结合的交替方向隐式时域多分辨分析算法(ADI-MRTD)。导出了基于Daubechies小波尺度函数的ADI-MRTD算法的差分公式和色散性方程,同时证明了其仍然满足无条件稳定方程。并讨论了空间步长、时间步长和电磁波传播方向等因素对ADI-MRTD算法的数值色散影响。结果表明:ADI-MRTD算法的数值色散特性优于传统的时域有限差分(FDTD)算法。     

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.     

Dispersion characteristics of slot lines

A new numerical method is developed for the analysis of dispersion characteristics of slot lines. Galerkin's method is applied in the Fourier-transform domain to derive a determinantal equation for the propagation constants. It is shown that accurate numerical results can be obtained with even a 2 × 2 matrix.     

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.     

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     

基于Taylor级数展开定理的高阶FDTD的色散分析

时域有限差分法(FDTD)是计算电磁领域中的一类非常重要的研究工具.而Taylor级数展开定理是构造差分格式的一种重要方法,例如Yee格式采用二阶Taylor格式,Fang格式采用四阶Taylor格式.本文借助于采样定理,详细分析了不同阶Taylor中心差分格式的谱特性以及计算误差,并将任意阶Taylor中心差分格式用于数值求解麦克斯韦方程中,严格导出了稳定性条件和数值色散关系的表达式,引入了新的误差定义来衡量算法的好坏.详细地研究了Courant数、网格分辨率CPW和网格长度比率等因素对于数值色散误差的影响,为基于Taylor差分格式的FDTD算法的研究提供了有用的参考.     

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。     

Compact Subthreshold Current Modeling of Short-Channel Nanoscale Double-Gate MOSFET

A physics-based compact subthreshold current model for short-channel nanoscale double-gate MOSFETs is presented. The potential is modeled using conformal mapping techniques in combination with parabolic approximations. For subthreshold conditions, we have assumed that the electrostatics is dominated by capacitive coupling between the body electrodes. Hence, the potential is obtained as an analytical solution of the 2-D Laplace equation. The current modeling is based on drift-diffusion theory. The modeling results are in good agreement with those of numerical simulations without the use of adjustable parameters.     

A Method of Calculating the Characteristic Impedance of a Strip Transmission Line to a Given Degree of Accuracy

The calculation of the characteristic impedance of the strip transmission line TEM-mode can be reduced to the solution of a two-dimensional potential equation with the strip cross section determining the boundary conditions. Usually this potential equation is solved by conformal mapping, but only the most simple shapes permit exact mapping. Approximations may require considerable work and their accuracy is uncertain. This paper describes an alternative numerical method which is particularly suitable for boundaries consisting of any number of straight lines and right angles. It is based on relaxation methods, but by using also variational principles it derives an approximate value for the impedance, and an upper and lower bound with a difference as small as desirable.     

Lamb波频散特性的数值仿真研究

Lamb波频散特性是进行超声波损伤检测的前提,采用窄带脉冲信号作为激励信号产生Lamb波,并在matlab环境下采用二分法对Lamb波的瑞利-兰姆频率方程进行了数值仿真,绘制了Lamb波在复合材料层合板中传播的频散特性曲线并分析了其特点,为超声波无损检测提供了重要的参考依据。     

A Compact 2-D Finite-Difference Frequency-Domain Method for Dispersion Characteristics Analysis of Trapezoidal-Ridge Waveguides

A compact two-dimension (2-D) finite-difference frequency-domain (FDFD) method is used to analyze the dispersion characteristics of single and double trapezoidal-ridge waveguides. The general 2-D FDFD formulation under orthogonal curvilinear coordinate system is derived from the difference form of Maxwell’s equations, and modified difference formulas at the trapezoidal-ridge section are built. After implementing the boundary conditions, the 2-D FDFD formulation is concluded as an eigen equation and then constructed by a highly sparse matrix. By solving the matrix-eigen equation, the dispersion characteristics of the ridged waveguides can be obtained. Computed results are in good agreements with the previously published and simulated ones, which prove the correctness of the method.     

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.      

Dispersion of an open thin helix

The dispersion equation for the fundamental mode of a helical slow-wave system is obtained and numerically solved with the use of the periodic Green??s function represented in cylindrical coordinates and the method of the linear integral equation for the helix axial current in the thin-conductor approximation. A method is proposed for taking into account a helix winded with the use of conductors with finite cross sections.     

计算复杂形状波导截止频率的高效方法

提出一种使用保角变换结合矩量法,计算复杂形状波导截止频率的新方法,该方法采用解析法或数值法,把复杂截面的波导变换为圆形区域,再采用矩量法求解波导的截止频率。实验结果验证了该方法的有效性。     

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。     

光纤传输模型的数值计算研究

光纤传播模型可以用非线性薛定谔方程描述,本文介绍了求解此方程的数值方法(分步傅立叶法).一般情况下,脉冲沿光纤传播时受到色散和非线性效应的共同作用,而分步傅立叶法假设当传播距离很小时二者是相互独立作用的.文章还介绍了数值模拟时脉冲形状、相位、啁啾、频谱的计算方法.     

具有高阶耦合色散系数双芯非线性光纤耦合器开关的数值分析

基于耦合非线性薛定谔方程(NLSE),利用分裂步长傅里叶方法(SSFM),研究了具有高阶耦合色散系数时,双芯非线性光纤耦合器中的传输和开关特性.模型中,一阶耦合色散系数的存在类似于群速度失配,二阶耦合色散系数类似于群速度色散,并且会对另一个纤芯中的信号产生线性互调制.研究表明当一阶耦合色散系数较小时,光脉冲仍能在二纤芯之间周期性耦合传输,并且表现出良好的开关特性,当一阶耦合色散系数增大时,脉冲耦合传输的周期性和陡峭的开关特性遭到破坏,光脉冲在传输中发生分裂;二阶耦合色散系数使耦合器的耦合长度减短,开关阈值功率增加,开关特性也变得更加陡峭.