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。     

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.     

基于辛算法的二维电磁场散射问题的研究

辛算法是保持Hamilton系统辛结构的一种新的数值方法,由于 Maxwell方程是一无穷维Hamilton系统,因此可将辛算法用于电磁场模拟中.本文提出一种基于辛分块Runge-Kutta(PRK)方法的显式辛算法,并将它成功应用于二维电磁散射问题的计算中.通过对金属方柱散射场的数值模拟,比较了FDTD法和低阶辛算法(一阶和二阶),结果表明低阶辛算法不仅与FDTD法精度相当,而且可以减少存储空间和计算时间,尤其是一阶辛算法节省了大约的CPU时间,提高了计算速度,体现了该算法的优越性.     

多时间步长时域有限差分法分析微波电路

提出在非均匀网格空间的粗网格区域采用大时间步长,细网格区域采用小时间步长的多时间步长时域有限差分(MTS -FDTD)法,并对其稳定性条件进行了分析。该方法通过应用多个时间步长替代传统非均匀时域有限差分(NU- FDTD)法的单一时间步长的算法来提高计算速度。通过应用MTS- FDTD方法模拟自由空间中给定激励下某点的场和微带低通滤波电路。数值结果表明,与传统NU- FDTD法相比,MTS- FDTD法在保持同等计算精度的条件下计算速度提高了46%以上。     

三维情况下平面介质交界面处二阶精度FDTD方程

提出了一种新的二阶精度时域有限差分法(FDTD)算法,针对研究区域介质填充不均匀,包含平面介质交界面的情况.新算法在交界面处利用非均匀网格建模,通过积分形式Maxwell方程的离散和交界面处连续场分量的泰勒级数展开,给出了平面介质交界面处三维情况下的二阶精度FDTD方程.该方法在保证介质交界面处电磁场量二阶精度的同时,合理划分不同介质区域粗细网格,在不增加计算容量和计算时间的基础上,有效地提高算法整体的计算精度.最后对介质谐振腔结构和微带电路进行模拟,验证了本文算法的精度高于标准的FDTD方法.     

基于Daubechies尺度函数的共形MRTD方法研究及其电磁散射应用

为了降低Yee氏蛙跳式网格划分的台阶误差,该文对3维曲面导体目标进行精确电磁建模,将时域多分辨(MRTD)算法与共形时域有限差分(CFDTD)算法结合,提出一种新的基于Daubechies尺度函数的共形时域多分辨(CMRTD)方法。该文提出将基于Daubechies尺度函数的MRTD迭代公式分解为若干传统FDTD迭代公式的线性组合,然后对最里面回路上的FDTD分解式运用局部共形技术,再将各个分解式进行线性组合,从而得到CMRTD结果。仿真结果表明,CMRTD方法既保持了MRTD方法节省计算资源、计算效率高等优点,同时明显提高了计算的精度。     

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-FDTD方法在乳腺癌检测正向计算中的应用

传统的时域有限差分(Finite-Difference Time-Domain, FDTD)算法受到稳定性条件的制约, 时间步长受限于空间网格的尺寸.医学应用讲究即时性, 为提高成像的速度, 文中采用无条件稳定的交替隐式时域有限差分(Alternating-Direction Implicit Finite-Difference Time-Domain, ADI-FDTD)算法替代传统的FDTD算法进行正向计算, 通过实验得出采用ADI-FDTD算法在保证精度的前提下, 计算时间可缩短为FDTD算法的四分之一, 为乳腺癌微波即时成像提供了可能.     

一种具有弱条件稳定的分裂式FDTD方法

近十几年来,时域有限差分算法(FDTD)得到了快速发展,然而该算法一直受稳定性条件(CFL)的限制.为突破这一限制一种具有弱条件稳定(WCS)的FDTD算法得到发展,提高了FDTD的计算效率,但陔方法存在精度不高的缺点.文中针对弱条件稳定FDTD方法精度不高这一弱点,提出了一种新的算法,该算法具有弱条件稳定性,且计算速度比ADI-FDTD方法有显著提高,并通过数值实验验证了该方法的准确性和有效性.     

PSTD算法及其吸收边界分析

在解时域电大尺寸电磁场问题时,由于受到有限差分格式二阶精度的限制,传统FDTD算法的效率很低,对内存的要求高.采用以伪谱方法离散Maxwell微分方程为核心的Pseudospectral time-domain(PSTD)算法计算电大尺寸电磁场时域问题,将大大提高计算效率,降低内存需求.本文重点探讨了在PSTD技术中,电大尺寸问题的高效实现,并和传统FDTD算法进行了比较.此外还分析了其吸收边界－完全匹配层(PML)所发挥的作用,PML的设置以及各参数对场吸收的影响.     

High-order accurate split-step FDTD method for solution of maxwell?s equations

The split-step finite difference time domain (SS-FDTD) method characterised by unconditional stability is becoming an important numerical method in computational electromagnetics. Proposed is a new high-order accurate unconditionally stable SS-FDTD method, which is derived from the exponential evolution operator. Compared with the conventional SS-FDTD method, the numerical dispersion of the new method is greatly reduced     

Three New Unconditionally-Stable FDTD Methods With High-Order Accuracy

Three novel finite-difference time-domain (FDTD) methods based on the split-step (SS) scheme with high-order accuracy are presented, which are proven to be unconditionally stable. In the first novel method, symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical Maxwell's equations into six sub-matrices. Accordingly, the time step is divided into six sub-steps. The second and third proposed methods are obtained by adjusting the sequence of the sub-matrices deduced in the first method, so all the novel methods presented in the paper have similar formulations, of which the numerical dispersion errors and the anisotropic errors are lower than the alternating direction implicit finite-difference time-domain (ADI-FDTD) method, the initial SS-FDTD method and the modified SS-FDTD method based on the Strang-splitting scheme. Specifically, for the second method, corresponding to a certain cell per wavelength (CPW), there is a Courant number value making the numerical anisotropic error to be zero, while in the third novel method, corresponding to a certain Courant number value, there exists a CPW making the numerical anisotropic error to be zero. In order to demonstrate the high-order accuracy and efficiency of the proposed methods, numerical results are presented.     

Compact higher-order split-step FDTD method

A compact higher-order split-step FDTD (SS-FDTD) method is developed, that achieves higher computation efficiency than the previous non-compact higher-order SS-FDTD by reducing the bandwidth of the system involved. From the stability and dispersion analysis, it can be concluded that this compact higher-order SS-FDTD is also unconditionally stable and has the same level of accuracy as the non-compact method.     

端接任意负载传输线的分步CN-FDTD分析方法

为了高效精确地求解端接任意负载的传输线结构电磁瞬态响应,该文提出了一种基于分裂时间步技术的Crank-Nicolson(CN)-FDTD方法,通过理论分析证明了该方法具有无条件稳定特性。与混合单端口等效模型相结合,有效地将传输线系统分解为分布参数子系统与集总电路子系统,采用改进节点分析法(Modified Nodal Analysis,MNA)能够快速求解复杂终端电路网络。与以往瞬态分析方法相比,该方法时间步长的选取不受稳定条件的限制,且通过采用精细子时间步技术极大地削减了因大时间步长引入的色散误差。利用该方法计算双导体传输系统的电磁暂态响应,计算结果表明该算法具有很好的稳定性,在保证数值精度的基础上有效地提高了计算效率。     

Second-order split-step envelope PML algorithm for 2D FDTD simulations

Unconditionally stable second-order split-step (SS) envelope perfectly matched layer (PML) formulations are presented for truncating finite-difference time-domain (FDTD) grids. The proposed method is based on the second-order SS-FDTD algorithm. Numerical examples carried out in two-dimensional domains are included to show the validity of the proposed formulations.     

An Iterative Unconditionally Stable LOD–FDTD Method

We present an iterative, unconditionally stable locally-one-dimensional (LOD) finite-difference time-domain (FDTD) method based on the use of an iterative fixed-point correction to reduce the splitting error. Numerical examples are used to illustrate the gain in accuracy of the proposed method versus the conventional LOD-FDTD method and the improved computational efficiency versus the iterative alternating-direction-implicit (ADI)-FDTD method.     

Fundamental Schemes for Efficient Unconditionally Stable Implicit Finite-Difference Time-Domain Methods

Generalized formulations of fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain (FDTD) methods are presented. The fundamental schemes constitute a family of implicit schemes that feature similar fundamental updating structures, which are in simplest forms with most efficient right-hand sides. The formulations of fundamental schemes are presented in terms of generalized matrix operator equations pertaining to some classical splitting formulae, including those of alternating direction implicit, locally one-dimensional and split-step schemes. To provide further insights into the implications and significance of fundamental schemes, the analyses are also extended to many other schemes with distinctive splitting formulae. Detailed algorithms are described for new efficient implementations of the unconditionally stable implicit FDTD methods based on the fundamental schemes. A comparative study of various implicit schemes in their original and new implementations is carried out, which includes comparisons of their computation costs and efficiency gains.     

An Improved Implicit Split-Step Algorithm for Dispersive Band-Limited FDTD Applications

An improved unconditionally stable envelope finite difference time domain (FDTD) algorithm is presented for modeling open region dispersive band-limited electromagnetic applications. The algorithm is based on incorporating the split-step implicit FDTD scheme into the stretched coordinates perfectly matched layer absorbing boundary conditions. Numerical examples carried out in 2-D domains are included to show the validity of the proposed formulations.      

一种改进的IC互连线3D电容提取快速层级算法

快速层级算法(FHM)是边界元法求解3D电容积分方程的一种加速方法,该方法基于分层近似对电势系数矩阵隐式表示,使求解的时间复杂度降低到O(n).改进算法对FHM做了两点改进:(1)给出了分层近似的理论依据,这种分层依据适用于所有导体结构而无需重复试验.(2)利用层级关系,直接计算面电荷,避免了迭代过程,加速了电荷求解.一系列典型3D互连线结构的测试显示:改进后的算法不仅提高了求解精度,而且计算时间也减少到改进前的1/3.     

基于AOS非线性扩散的SAR图像去噪研究

针对合成孔径雷达(SAR)图像的斑点噪声,介绍了一种基于非线性各向异性扩散的去噪方法,该方法经过加性算子分离(AOS)方案离散可以保证其扩散迭代过程中滤波结果的绝对稳定,并且利用其在消除噪声的同时锐化边界的特点,将之引入SAR图像的斑点噪声抑制问题当中.通过对一幅SAR图像的滤波处理,以及若干衡量滤波算法效果的评价指标,将其与传统的自适应局域统计滤波方法进行分析比较,并得出相关结论,从而证实了该研究提出的AOS非线性扩散滤波法(AOS ND法)抑制SAR图像相干斑的可行性和有效性.