快速MEI算法及其在电大尺寸电磁散射问题中的应用

本文基于不变性测试方程法（ＥＭＩ）提出一种快速算法,在二维散 表面建立菜形差分网格后,通过对节点的重新排序,将原问题中的稀疏矩阵变换为带状稀疏阵,从而使占用的计算机内存和计算时间均由Ｏ（Ｎ２）下降为Ｏ（Ｎ）,可以解决原来无法计算的问题,议事 成功地计算了最大周长为１００００个波长的几个电大尺寸二维柱体的电磁散射,并与矩量法、ＭＥＩ方法进行比较。     

介质涂敷电大尺寸导体柱电磁散射特性的有限元—快速多极混合？…

采用有限元－快速多极混合算法分析了介质涂层电大尺寸导体柱的电北散射特性。与有限元－矩量法相比,快速多极算法将计算复度从Ｏ（Ｎ＾２）降低到Ｏ（Ｎ＾１．５）,大大加快计算速度,减少存储量。计算表明该混合算法对电大复杂涂敷目标电磁我伯分析是灵活而有效的。     

MEI系数的快速算法

不变性测试方程法已被证明是解决电磁问题的一种有效方法。目前电大尺寸问题中ＭＥＩ系数的计算已成为一个瓶颈。提出了一个快速算法用于加速ＭＥＩ系数的计算,它使用快速多极子方法计算测试子的散射场,使得ＭＥＩ系数的计算速度从Ｏ（Ｎ＾２）变为Ｏ（Ｎ＾１．５Ｌｏｇ２Ｎ）。     

一种计算机快速二维DCT算法

二维离散余弦变换（２Ｄ－ＤＣＴ）广泛用于数字图像处理中，特别是图像的数据压缩，二维ＤＣＴ的常规算法是行一列法，对于计算（Ｎ×Ｎ）ＤＣＴ，需要计算２Ｎ个一维ＤＣＴ。本文利用三角函数的公式，并将二维输入数据划分为Ｎ个不同的数据集，提出了一种快速算法。该算法对于计算（Ｎ×Ｎ）ＤＣＴ只需要计算Ｎ个一维ＤＣＴ，运算量是常规算法的一半。该算法的计算结构具有高度规则性，只要求执行实数运算。     

二维离散余弦变换的一种新的快速算法

本文介绍了二维离散余弦变换（ＤＣＴ）的一种新的快速算法，对于Ｎ×Ｎ ＤＣＴ（Ｎ＝２＾ｍ），只需用Ｎ个一维ＤＣＴ和若干加法运算。与常规的行－列法相比，所需的乘法运算量减少了一半，也比其它的快速算法的乘法运算量要少，而加法运算量基本上是相同的。     

电大尺寸多柱体电磁散射问题的一种快速混合算法--MEI+FMM

本文提出了一种改进的快速迭代ＭＥＩ（不变性测试方程）算法用于分析电气大尺寸多柱体的散射问题,在此算法中我们首次将快速多极子技术（ＦＭＭ）用于加速多柱体之间多次散射场的计算。应用本算法计算了柱体周长为几千波长的多柱体散射场。实际计算结果显示,一方法与原有的直接计算方法具有几乎同样的精度,而速度提高了两个数量级。     

基于节点编码的区域分解算法及其在二维散射中的应用

研究了一种高效率的基于节点编码的区域分解算法.将原始的求解区域分割为若干个相对独立的子区域,使原问题转化为若干个相对独立的子问题,通过求解公共边界上的场值,可以快速获得整个求解区域上的场值,极大地减少了存储量和计算量.此外,这种区域分解算法不仅能够快速、高效、并行地计算电大尺寸柱体的电磁散射,还特别适合于求解具有几何重复性特征的结构,如天线阵列、有限周期频率选择表面、PBG/EBG等的电磁仿真问题.数值算例验证了该方法的准确性和有效性.     

区域分裂法及其在三维散射中的应用

基于区域分裂（ＤＤＭ）和频域有限差分（ＦＤＦＤ）提出了一种分析三维散射问题的精确高效算法。用区域分裂法可以把原问题分解成若干子问题,可以大大缩小稀疏矩阵的规模,使得求解大尺寸三维散射问题成为可能。文中首先在小尺寸下计算了三维立体柱的散射特性,并和没有进行区域分裂时的ＦＤＦＤ法进行了对比,验证了本算法的正确性;然后又计算了尺寸比较大的三维矩形柱的散射特性,验证了它的高效性。     

二维离散余弦变换的一种新的快速算法

介绍了二维离散余弦变换的一种新的快速算法，对于Ｎ×ＮＤＣＴ（Ｎ＝２ｍ），只需用Ｎ个一维ＤＣＴ和若干加法运算，与常规的行一列法相比，所需的乘法运算量减少了一半，也比其它快速算法的乘法运算量要少，而加法运算量基本上是相同的。     

埋地二维柱体的电磁散射

本文利用进域有限差分（ＦＤ－ＴＤ）方法分析计算了正弦平面波照射下埋地二维金属柱体的电磁散射特性，给出了柱体上的感就电流值和地面上方近场区的电磁场值。讨论了有耗介质中差分网格的数值色散特性和吸收边界条件。通过将本文用ＦＤ－ＴＤ计算结果与其它数值结果进行比较，证实了ＦＤ－ＴＤ方法在分析有耗介质中电磁散射问题的有效性。     

电磁耦合问题的区域分解算法

作为偏微分方程数值解新技术,区域分解算法对于大型复杂问题的求解表现出巨大的优越性。本文将其与频域有限差分法(FDFD)结合,对有限厚度导体平面上缝隙电磁耦合问题进行了分析。通过将所分析的结构划分为多个相对独立的规则子域,使原问题中差分方程的系数矩阵转换为各子域中带宽极窄的带状阵,从而使计算时间和计算所需内存分别下降为O(N)和O(max(Ni)),其中N为总网格点数,Ni为第i个子域的网格点数。数值结果与文献提供的结果吻合,证明了该法的有效性。同时,该法很容易实现并行计算,为进一步提高计算效率提供可能。     

圆形金属波导传输特性的2-D频域有限差分法分析

时域有限差分(FDTD)法和频域有限差分(FDFD)法用于处理传输系统的本征值问题非常有效。本文首先基于二维频域有限差分(2 -DFDFD)法,导出圆柱坐标系中2- DFDFD的一般分析公式,并提供了圆波导中不规则划分网格的相应场量表达式;然后将导出的2- DFDFD分析公式应用于圆波导的传播特性的分析。数值计算结果和理论结果吻合很好,从而证明本文分析思路的正确性。同时,所编制的2- DFDFD程序具有通用性,只要调整边界条件的设置同样适于分析其他柱形金属波导结构。     

Microwave Subsurface Imaging Using Direct Finite-Difference Frequency-Domain-Based Inversion

We have developed a new algorithm for electromagnetic inverse scattering problems in inhomogeneous media using finite-difference frequency-domain (FDFD) forward modeling, referred to as the FDFD-based inversion method. The key issue of this method is to build a linear expression for the inverse problem from an FDFD forward model by using Born approximation to neglect mutual coupling between scattered pixels and to then solve for the inverse coefficient matrix. An important advantage of this matrix-based method is that there is no need to specify a Green's function. As such, this inverse scattering algorithm is easily implemented and is robust to the heterogeneity in the background. We test the algorithm with a microwave subsurface object detection application using cross-well radar. The new method is compared with conventional inversion using Green's function-based Born approximation. Numerical experiments are presented for a 2-D borehole geometry for buried object detection in uniform soil and in multilayered soil backgrounds.      

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.     

A Two-dimensional Full-wave Finite-difference Frequency-domain Analysis of Ferrite Loaded Structures

A two-dimensional (2-D) full-wave finite-difference frequency-domain (FDFD) method is presented for analyzing the dispersion characteristics of transversely magnetized ferrite loaded structures. Results for a number of different ferrite loaded structures are presented. The accuracy of the FDFD formulation is verified by comparing the numerical results with analytical results and those obtained using the FDTD method, and very good agreement is obtained.     

Computer simulations of nonlinear propagation of an optical pulseusing a finite-difference in the frequency-domain method

To simulate propagation of an optical pulse in a nonlinear medium, a finite-difference in frequency-domain (FDFD) method was developed. In this method, Maxwell's equations were solved rigorously without introducing an electric-field envelope function commonly used in conventional methods. This method was used to calculate the propagation of an optical soliton in a fused-silica-like material, and results were compared with those of a finite-difference in time-domain (FDTD) method. It was found that the FDFD method was efficient and more robust than the FDTD method. Another advantage of the FDFD method is the case of incorporating arbitrary linear dispersion relations into the calculations     

A simple finite-difference frequency-domain (FDFD) algorithm for analysis of switching noise in printed circuit boards and packages

Simultaneous switching noise (SSN) compromises the integrity of the power distribution structure on multilayer printed circuit boards (PCB). Several methods have been used to investigate SSN. These methods ranged from simple lumped circuit models to full-wave (dynamic) three-dimensional Maxwell equations simulators. In this work, we present an efficient and simple finite-difference frequency-domain (FDFD) based algorithm that can simulate, with high accuracy, the capacity of a PCB board to introduce SSN. The FDFD code developed here also allows for simulation of real-world decoupling capacitors that are typically used to mitigate SSN effects at sub 1 GHz frequencies. Furthermore, the algorithm is capable of including lumped circuit elements having user-specified complex impedance. Numerical results are presented for several test boards and packages, with and without decoupling capacitors. Validation of the FDFD code is demonstrated through comparison with other algorithms and laboratory measurements.     

Efficient analysis of waveguide components using a hybrid PEE-FDFD algorithm

The partial eigenfunction expansion (PEE) method combined with the classical finite difference frequency domain (FDFD) algorithm is proposed to accelerate frequency domain analysis of waveguide components. Examples are shown validating the method both for eigenvalue and deterministic problems.     

The hybrid extended Born approximation and CG-FFT method forelectromagnetic induction problems

The authors propose the hybridization of the extended Born approximation (EBA) with the conjugate-gradient fast Fourier transform (CG-FFT) method to improve the efficiency of numerical solution of electromagnetic induction problems. This combination improves the solution efficiency in two ways. First, using the FFT in the extended Born approximation decreases the computational cost of the conventional EBA method from O(N²) to O(N log₂ N) arithmetic operations, where N is the number of unknowns in the problem. This approach, referred to as the FFT-EBA method, applies to problems with a fairly large contrast. Secondly, using the EBA as a partial preconditioner for the CG-FFT method increases the convergence speed of the conventional CG-FFT method. This second approach, referred to as the EBA-CGFFT method, is in principle applicable to all problems with a homogeneous background, but is particularly efficient for problems with a higher contrast. Numerical experiments suggest that the combination of these two methods is more accurate and more efficient for electromagnetic induction problems