基于高阶时域有限差分算法的电磁波传播计算

利用FDTD(2,4)高阶时域有限差分(Finite-Difference Time-Domain,FDTD)算法并结合滑动窗口的思想,对电磁波传播特性进行了仿真计算.采用的高阶FDTD算法在空间上达到四阶精度,与二阶精度的传统FDTD算法相比,在相同每波长采样数的条件下,数值色散误差能得到进一步的减少.在源脉冲传播较长距离时,数值色散的减少使得时域下脉冲扩展现象得到改善,滑动子窗口仍然能包含着激励源脉冲的全部信息,从而可更加准确地计算长距离电波传播特性.另外,在相同的数值色散误差容限下,每波长采样数比传统二阶FDTD方法有所减少,从而节省存储空间,加快计算速度.     

一种新型的高阶时域有限差分方法

相比于传统高阶时域有限差分算法(FDTD)而言,该文提出了一种改进的高阶FDTD的优化方法,该算法基于安培环路定律,通过计算机技术寻找到一组最优的系数使得FDTD方法的全局色散误差达到最小,通过不同分辨率下的点源辐射模拟证明了该方法在较低分辨率的情况下仍然具有极低的相位误差,对于解决电大尺寸结构建模中的数值色散等问题提供了有效的解决方案。     

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.     

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。     

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。     

双芯光子晶体光纤的色散特性研究

文中利用FDTD方法模拟了光波在双芯光子晶体光纤中的色散特性。给出了FDTD方法的理论基础和仿真结果，同时分析了色散特性与占空比的关系，在相同的空气孔间距条件下，占空比越大，反常色散峰值越大，峰值色散点往短波区域移动。     

用基于Coifman尺度函数的多分辨时域分析计算电磁散射

本文利用Coifman尺度函数具有消失矩和紧支集的特点,提出了一种新的多分辨时域分析方法,研究了它的数值色散特性,并与通常的FDTD方法进行了比较.通过算例,表明该方法比通常的FDTD方法需要网格数量少、计算时间快.     

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。     

新型分裂步长时域有限差分法

提出一种新型的分裂步长时域有限差分(NSS-FDTD)法,并对其数值色散进行分析。该方法基于Split-Step方案和Crank-Nicolson方案,采用新的矩阵分解形式,与传统的FDTD算法、SS-FDTD算法相比,减少了计算复杂度。新型算法的推导程序简单,且具有良好的数值色散特性,还加入了一阶Mur吸收边界条件,给出一阶Mur吸收边界差分方程。将数值实验的结果和传统FDTD方法及理论值进行比较,数值结果一致性较好。     

三维最优时域有限差分方法

数值色散是时域有限差分方法(FDTD)中最主要的误差来源,导致数值相速成为频率和方向的函数。文中讨论了一种基于最优有限冲激滤波器设计方法的最优差分格式,从频率空间或者波数空间中实现对理想偏微分算子的逼近,构造一种新的具有低数值色散关系的最优时域有限差分方法。文中导出了其数值色散关系和进行了稳定性分析,并通过与常用的基于泰勒级数展开定理的高阶(2,4)时域有限差分法相比较,发现最优时域有限差分法的数值色散得到了极大的改善。最后通过一个数值例子来验证其有效性。     

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     

An efficient method to reduce the numerical dispersion in the ADI-FDTD

A new approach to reduce the numerical dispersion in the finite-difference time-domain (FDTD) method with alternating-direction implicit (ADI) is studied. By adding anisotropic parameters into the ADI-FDTD formulas, the error of the numerical phase velocity can be controlled, causing the numerical dispersion to decrease significantly. The numerical stability and dispersion relation are discussed in this paper. Numerical experiments are given to substantiate the proposed method.     

Alternating-direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method: algorithm and material dispersion implementation

The alternating-direction implicit finite-difference time-domain (ADI-FDTD) technique is an unconditionally stable time-domain numerical scheme, allowing the /spl Delta/t time step to be increased beyond the Courant-Friedrichs-Lewy limit. Execution time of a simulation is inversely proportional to /spl Delta/t, and as such, increasing /spl Delta/t results in a decrease of execution time. The ADI-FDTD technique greatly increases the utility of the FDTD technique for electromagnetic compatibility problems. Once the basics of the ADI-FDTD technique are presented and the differences of the relative accuracy of ADI-FDTD and standard FDTD are discussed, the problems that benefit greatly from ADI-FDTD are described. A discussion is given on the true time savings of applying the ADI-FDTD technique. The feasibility of using higher order spatial and temporal techniques with ADI-FDTD is presented. The incorporation of frequency dependent material properties (material dispersion) into ADI-FDTD is also presented. The material dispersion scheme is implemented into a one-dimensional and three-dimensional problem space. The scheme is shown to be both accurate and unconditionally stable.     

Investigation on the characteristics of the envelope FDTD based on the alternating direction implicit scheme

This letter presents numerical characteristics of recently developed the envelope FDTD based on the alternating direction implicit scheme (envelope ADI-FDTD). Through numerical simulations, it is shown that the envelope ADI-FDTD is unconditionally stable and we can get better dispersion accuracy than the traditional ADI-FDTD by analyzing the envelope of the signal. This fact gives the opportunity to extend the temporal step size to the Nyquist limit in certain cases. Numerical results show that the envelope ADI-FDTD can be used as an efficient electromagnetic analysis tool especially in the single frequency or band limited systems.     

Envelope ADI–FDTD Method and Its Application in Three-Dimensional Nonuniform Meshes

The envelope alternating-direction-implicit finite difference time domain (ADI-FDTD) method in 3-D nonuniform meshes was proposed and studied. The phase velocity error for the envelope ADI-FDTD and ADI-FDTD methods in uniform and nonuniform meshes and different temporal increments were studied. A cavity problem was studied using the envelope ADI-FDTD and ADI-FDTD methods in graded meshes and the conventional FDTD method in a uniform mesh. The simulation results show that the envelope ADI-FDTD performs better than the ADI-FDTD in numerical accuracy     

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     

色散媒质中ADI-FDTD的PML

基于交替方向隐式(ADI)技术的时域有限差分法(FDTD)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,而是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。该文采用递归卷积(RC)方法导出了二维情况下色散媒质中ADI-FDTD的完全匹配层(PML)公式。应用推导公式计算了色散土壤中目标的散射,并与色散媒质中FDTD结果对比,在大量减少计算时间的情况下,两者结果符合较好。     

Approximate Crank-Nicolson schemes for the 2-D finite-difference time-domain method for TE/sub z/ waves

Two implicit finite-difference time-domain (FDTD) methods are presented in this paper for a two-dimensional TE/sub z/ wave, which are based on the unconditionally-stable Crank-Nicolson scheme. To treat PEC boundaries efficiently, the methods deal with the electric field components rather than the magnetic field. The "approximate-decoupling method" solves two tridiagonal matrices and computes only one explicit equation for a full update cycle. It has the same numerical dispersion relation as the ADI-FDTD method. The "cycle-sweep method" solves two tridiagonal matrices, and computes two equations explicitly for a full update cycle. It has the same numerical dispersion relation as the previously-reported Crank-Nicolson-Douglas-Gunn algorithm, which solves for the magnetic field. The cycle-sweep method has much smaller numerical anisotropy than the approximate-decoupling method, though the dispersion error is the same along the axes as, and larger along the 45/spl deg/ diagonal than ADI-FDTD. With different formulations, two algorithms for the approximate-decoupling method and four algorithms for the cycle-sweep method are presented. All the six algorithms are strictly nondissipative, unconditionally stable, and are tested by numerical computation in this paper. The numerical dispersion relations are validated by numerical experiments, and very good agreement between the experiments and the theoretical predication is obtained.     

色散媒质中采用Z变换的ADI-FDTD方法

基于Z变换方法将ADI-FDTD推广应用于色散媒质,得到了二维情况下色散媒质中的迭代差分公式,同时给出了一种采用ⅡR滤波器结构来减少存储量的方法.本文方法适合于任意M阶色散媒质,最后,给出了一个算例,数据仿真结果表明,本文的算法与传统色散媒质中的FDTD相比,在计算结果吻合的情况下,存储量相当,计算效率却更高,时间步长仅仅由计算精度来决定.     

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.