基于COCG的组合迭代法求解电磁场FEM线性方程组

针对COCG算法在求解有限元法分析电磁场边值问题所得到的线性系统时存在的不稳定性问题,提出了一种基于COCG的组合迭代方法。该方法通过在低精度迭代阶段采用COCG,而在其易出现迭代崩溃问题的高精度迭代阶段采用其他相对更稳定的迭代法来进行联合求解。该方法不仅能有效避免COCG算法的不稳定性问题,同时也让其高效率的优点得到充分保留因而有利于整个迭代收敛过程。数值结果表明,提出的组合迭代法能将COCG的高效率和其他迭代法的稳定性进行优势互补,从而能获得比常规的单独迭代法更高的求解性能。     

求解波导问题FEM线性系统的RIC预条件算法

提出了一种新型RIC预条件COCG迭代技术,用于改善有限元法仿真分析光电工程问题所产生的高度非正定的线性系统的迭代求解.提出的RIC预条件子是针对基本IC算法可能出现的分解崩溃问题,通过对主元进行加强来获得稳定的分解过程,进而产生高效的预条件子.数值试验表明,提出的RIC预条件子不仅能有效避免COCG迭代等方性崩溃,而且比常用的预条件子更高效;此外,RIC对其他若干Krylov子空间迭代法求解性能的改善作用也相当明显.     

对称线性BiCG迭代法求解波导问题

提出了一种对称化线性双共轭梯度(BiCG)迭代算法,应用于光电工程领域中波导问题的分析。该算法是针对有限元线性系统系数矩阵的大型复对称特性,在常规BiCG迭代法基础上对其进行对称化所得到的快速迭代求解算法。数值结果表明,所提出的对称BiCG迭代法比若干常用方法更加有效。     

基于高阶叠层基函数的加速迭代求解方法

研究了高阶叠层矢量基函数的尺度因子对迭代法求解矩阵方程收敛性的影响,选择了可以有效降低矩阵条件数的尺度因子;在此基础上,详细阐述了求解基于高阶叠层矢量基函数阻抗矩阵方程的叠层共轭梯度方法(HCGM),并从理论上分析了叠层共轭梯度算法的收敛性能.通过计算实例表明,与共轭梯度方法(CGM)相比.使用HCGM可以大幅度减少矩阵方程的迭代求解时间.     

预条件共轭梯度法在辐射和散射问题的应用

用矩量法求解一些辐射和散射问题,如线天线辐射和线状体散射等问题时,可以产生一个Ｔｏｅｐｌｉｔｚ线性方程组,采用预条件共轭梯度法（ＰＣＧ）与快速富里叶变换（ＦＦＴ）的结合方法（ＰＣＧＦＦＴ）来求解该方程组,其中预条件器采用Ｔ．Ｃｈａｎ的优化循环预条件器。使用ＰＣＧＦＦＴ算法,可有效地节省内存,提高了计算速度。为说明其有效性,将ＰＣＧＦＦＴ算法与ＣＧＦＦＴ算法以及Ｌｅｖｉｎｓｏｎ递推算进行了对比。     

共轭梯度BP算法在Matlab 7.0中的实现

应用Matlab 7.0中神经网络工具箱建立BP神经网络的最优化求解方法,采用共轭梯度法对网络的权值和阚值进行优化计算,实现网络权值和阈值的快速计算,为分析神经网络的合理结构提供了必要条件.对BP神经网络的传统梯度下降法与共轭梯度算法进行了仿真.这里通过对算法的训练速度,容错泛化能力等方面加以讨论,多方面印证共轭梯度算法的优越性,仿真结果凸显了训练速度的大幅提高,尤其对训练后网络受损情况下的泛化能力,采用线性回归的方法进行了仿真验证,同样得到满意结果,从新的角度支持了共轭梯度BP算法.     

一种基于共轭梯度最优化技术的三维时域扩散光学层析方法

扩散光学层析(DOT)中的图像重建是一个面向大参数集的非线性最优化问题,其标准求解方法为牛顿类迭代法,需要对整个Jacobian矩阵进行构建、求逆和存贮,这对大规模的三维问题是不可行的,为此常采用基于逐行线性逆策略的非创伤性填充(ART)技术,图像质量受到严重制约.采用共轭梯度算法,直接求解非线性目标函数梯度.可避免对Jacobian矩阵的操作,为有效降低步长因子求解引起的附加计算量,采用一维不精确搜索算法,通过对双非均匀目标体的平板模型进行模拟成像,与代数重建算法结果进行比较,表明共轭梯度法的重建质量、收敛速度和收敛性都优于ART算法.     

GPU加速混合场积分方程求解导体目标散射问题

利用图形处理单元（GPU）加速混合场积分方程（CFIE）分析导体目标电磁散射问题。较电场积分方程（EFIE）和磁场积分方程（MFIE）,CFIE消除了内谐振问题,并且具有更好的条件数。求解的数值方法为基于 RWG基函数的矩量法（MoM）。所有计算步骤均在 GPU上实现,包括：阻抗元素填充、电压向量填充、矩阵方程的共轭梯度（CG）求解、雷达散射截面（RCS）计算。在保证数值精确度的前提下获得了数十倍的速度提升。     

不完全乔列斯基分解共轭梯度法在磁感应成像三维有限元正问题中的应用

磁感应成像(MIT)3维正问题中,直接求解法计算有限元方程组时,计算速度慢且因舍入误差造成计算结果不正确。该文为了解决这一问题,采用不完全乔列斯基分解共轭梯度(ICCG)迭代求解法。基于ANSYS平台建立有限元数值模型,采用ICCG法迭代求解。通过仿真实验获得设定收敛容差的最优值。对仿真结果进行对比,与直接求解法、雅克比共轭梯度(JCG)法相比,ICCG法计算速度快、稳健性高。计算结果表明ICCG法受网格粗细影响小,能够正确求解磁感应成像3维正问题。     

一种病态线性系统求解的新算法

本文提出了一种病态线性系统求解的新算法,该算法将原线性系统求解的问题转化为极小值点的最优化问题,借助不对分寻优法进行迭代求解,并结合引入的伪误差来解决当方程组阶数非常大时出现的误差积累问题。文末算例实验表明,本文算法对于良态线性系统、病态线性系统均有较好的求解效果。该算法为病态线性系统利用计算机迭代求解提供了直接的参考方法。     

An Efficient MAINV Preconditioned COCG Method for FEM Analysis of Millimeter Wave Filters

The modified AINV (MAINV) sparse approximate inverse preconditioner is applied to the conjugate orthogonal conjugate gradient (COCG) iterative method for solving a large systems of linear equations resulting from the use of edge finite element method (FEM). The proposed preconditioner is derived from basic AINV process by adding pivots compensation strategy to avoid the potential breakdowns. Numerical experiments on several typical millimeter wave structrues demonstrate the effectiveness of the MAINV-COCG method, in comparison with other conventional methods.     

Diagonal preconditioners for the EFIE using a wavelet basis

The electric field integral equation (EFIE) has found widespread use and in practice has been accepted as a stable method. However, mathematically, the solution of the EFIE is an “ill-posed” problem. In practical terms, as one uses more and more expansion and testing functions per wavelength, the condition number of the resulting moment-method matrix increases (without bound). This means that for high-sampling densities, iterative methods such as conjugate gradients converge more slowly. However, there is a way to change all this. The EFIE is considered using a wavelet basis for expansion and for testing functions. Then, the resulting matrix is multiplied on both sides by a diagonal matrix. This results in a well-conditioned matrix which behaves much like the matrix for the magnetic field integral equation (MFIE). Consequences for the stability and convergence rate of iterative methods are described     

粗糙面下方金属目标复合电磁散射的快速算法

为快速有效计算粗糙面下金属目标的复合电磁散射,提出了一种基于前后向迭代算法(FBM)和共轭梯度(CG)法的快速互耦迭代算(CCIA).首先建立目标与粗糙面的耦合积分方程组,并采用矩量法将其离散为矩阵方程.其次针对得到的耦合积分方程,用FBM求解粗糙面表面电流分布,用CG法求解目标表面电流分布,目标和粗糙面的相互作用通过更新两方程的激励项完成.最后,计算了高斯粗糙面下方无限长金属圆柱目标的复合电磁散射系数,当目标尺寸趋于零或目标深度趋于无穷时的结果与单独介质粗糙面相一致,验证了该数值方法的正确性;同时,讨论了不同粗糙面情况下该方法的收敛性,并分析了不同粗糙面媒质、目标尺寸和目标位置对双站散射系数的影响.     

A numerical scheme to obtain the RCS of three-dimensional bodies ofresonant size using the conjugate gradient method and the fast Fouriertransform

A numerical scheme to obtain radar cross section (RCS) of three-dimensional bodies of resonant size (BRS) with arbitrary geometry and material composition is described. The RCS is obtained by solving the electric-field integral equation (EFIE) using the conjugate gradient-fast Fourier transform method (CG-FFT). The choice of a suitable set of basis and testing functions to discretize the EFIE leads to a very accurate and computationaly efficient CG-FFT procedure. This accuracy is checked by comparison with RCS measurements or predictions by other methods. As compared to the moment method, this CG-FFT scheme avoids the storage of large matrices and reduces the computer time by orders of magnitude     

Millimeter Wave Scattering of 2-D Frequency Selective Surface by Efficient Method of Lines with Preconditioned CG Technique

In this paper, both banded and symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) techniques are combined with method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. The electromagnetic wave scattering of 2-D frequency-selective surface is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, helmholtz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. Both banded and effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method are chosen to solve this matrix equation. Our numerical results show that PCG methods can converge to accurate solution in much fewer iteration steps for analysis of the electromagnetic wave scattering from 2-D frequency-selective surface.     

Complex Adaptive ICA Employing the Conjugate Gradient Technique for Signal Separation in Time-Varying Flat Fading Channels

The conjugate gradient method is a prominent technique for solving systems of linear equations and unconstrained optimization problems, including adaptive filtering. Since it is an iterative method, it can be particularly applied to solve sparse systems which are too large to be handled by direct methods. The main advantage of the conjugate gradient method is that it employs orthogonal search directions with optimal steps along each direction to arrive at the solution. As a result, it has a much faster convergence speed than the steepest descent method, which often takes steps in the same direction as earlier steps. Furthermore, it has lower computational complexity than Newton’s iteration approach. This unique tradeoff between convergence speed and computational complexity gives the conjugate gradient method desirable properties for application in numerous mathematical optimization problems. In this paper, the conjugate gradient principle is applied to complex adaptive independent component analysis (ICA) for maximization of the kurtosis function, to achieve separation of complex-valued signals. The proposed technique is called the complex block conjugate independent component analysis (CBC-ICA) algorithm. The CBC-ICA derives independent conjugate gradient search directions for the real and imaginary components of the complex coefficients of the adaptive system employed for signal separation. In addition, along each conjugate direction an optimal update is generated separately for the real and imaginary components using the Taylor series approximation. Simulation results confirm that in dynamic flat fading channel conditions, the CBC-ICA demonstrates excellent convergence speed and accuracy, even for large processing block sizes.     

Fast analysis of electromagnetic scattering of 3D dielectric bodies by use of the loose GMRES-FFT method

In this paper, electromagnetic wave scattering is analysed by the efficient Krylov subspace iterative fast Fourier transform (FFT) technique in terms of the electric field integral equation (EFIE) for a dielectric body of general shape, inhomogeneity and anisotropy. However, when the permittivity of the scatter becomes large, the convergence rate of Krylov subspace iterative methods slows down. The loose generalized minimum residual (LGMRES) method is therefore used to accelerate the iteration. As a result, good convergence improvement is achieved for high permttivity cases.     

Iterative implementation of linear multiuser detection for dynamicasynchronous CDMA systems

Several linear multiuser detectors for code-division multiple access (CDMA) systems can be characterized as an inverse of some form of correlation matrices. If the correlations change, the detectors must be redesigned. An ideal computation of the decorrelating or the linear minimum mean-squared-error (LMMSE) detector requires order K³ flops, where K is the number of users. To alleviate the computational complexity, iterative decorrelating and LMMSE detectors are proposed. The iterative detectors use steepest descent (SD), conjugate gradient (CG), and preconditioned conjugate gradient (PCG) algorithms, and require order K² flops per iteration. Their main advantages are the reduced number of flops and their suitability to highly parallel implementations. The correlation coefficient computation can also be embedded into the CG algorithm, which is an advantage with time-varying signature waveforms. The performance of the iterative algorithms is studied via computer simulations