共查询到19条相似文献,搜索用时 531 毫秒
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本文应用矩阵元素阶、阶矩阵及消去法的影响域等概念,给出了强主元多对角阵高阶近似求逆的一种快速算法。在强主元条件下,该法可应用于非对称阵和非正定阵。本文将该法与块预处理共轭梯度法相结合,应用于椭圆型方程数值解及类似问题的计算。数值结果表明,该法不仅适用范围较广,也具有较高的计算效率。 相似文献
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利用反弹平均的三维Fokker-Planck方程,对电子回旋波加热和电流驱动进行数值模拟.考虑超热电子径向扩散对电流驱动的影响,在方程中加入径向扩散输运项,采用九点格式的中心差分对方程进行数值离散得到系数矩阵,采用不完全LU分解对系数矩阵进行预处理,利用双共轭梯度稳定法求解得到分布函数.在不考虑电子径向扩散输运条件下,得到电子回旋波驱动电流密度与功率沉积密度的分布;考虑径向扩散输运的计算结果与BANDIT3D进行比较,驱动电流分布的趋势基本一致. 相似文献
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三维声波方程逆问题的共轭梯度法求解 总被引:3,自引:2,他引:1
考虑一个完整的三维声波方程的逆问题.通过构造一个表面声压偏差平方和形式的目标泛函,把声波方程的逆问题转化为一个控制声学特性参数分布使得目标泛函达到最小伍的优化问题.采用共轭梯度法来求解这个优化问题.通过引入一个对偶函数u(x,t),文中用微扰法求得了目标泛函梯度值的解析表达式,从而克服了以往用共轭梯度法求解偏微分方程控制的优化问题时计算目标活函梯度的困难,大大压缩了共轭梯度法计算目标泛函梯度的时间,而且提高了梯度值的计算精度.还进一步进行了反演声学特性参数三维分布的数值仿真计算.共轭梯度法完整解决了三维声波方程的逆问题. 相似文献
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高阶ICCG误差阵模与条件数的估计 总被引:1,自引:0,他引:1
文[1]针对模型问题,应用高阶近似LU分解法给出了阶为0,1,2时ICCG法的预处理阵表达式,进而估计了误差阵的无穷模及条件数。针对更复杂的高阶问题给出了三阶和四阶ICCG法误差阵无穷模的估计以及相应的条件数上限。在不同节点数的条件下,对实际计算的条件数与文中所给出的上限作了比较。 相似文献
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EBE技术在结构分析中的应用(Ⅲ)-EBE-PCG法 总被引:1,自引:0,他引:1
在建立单元向量、伪单元向量等概念的基础上,提出了当不形成总刚度矩阵时,预处理共轭梯度法(PCG)的一种高度并行的EBE计算方法,其基本思想是把PCG法各步的计算都单元化。文[3]中的数值试验结果表明了它的有效性。 相似文献
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本文从二维非线性Schrödinger方程出发,推导出五对角的复代数方程组,并应用高斯-赛德尔迭代法、SOR迭代法、复双共轭梯度法以及预处理复双共轭梯度法等对求解的计算量进行了比较。同时,又将复代数方程组化成七对角的实代数方程组,用高斯-赛德尔迭代法、SOR迭代法以及PCG法(预处理共轭梯度法)等进行了比较。结果表明,PCG法在上述几种方法中是最有效的。本文还对SOR松弛因子的选择进行了讨论。 相似文献
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基于通量重构形式的高阶算法,在保持间断Galerkin算法局部重构特性和非结构网格中任意高阶精度优点的同时,其计算量大大减小,且具有形式简单、灵活性高等特点。使用显式Runge-Kutta法,隐式非线性LU-SGS法,以及使用无矩阵预处理的广义极小残值法(generalized minimal residual,GMRES)进行求解,并使用p型多重网格在低阶次上光顺低频误差以加快求解。一至四阶精度结果显示使用p型多重网格对显式Runge-Kutta求解以及LU-SGS均具有明显的加速效果,而基于无矩阵预处理的GMRES解法具有更好的稳定性和更快的求解速度。本文提出的基于Gauss-Seidel迭代的无矩阵预处理方法,具有高效和稳定的特征,存储量大大小于ILU预处理。 相似文献
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利用块三对角矩阵的嵌套局部块分解构造了一个不完全分解预条件子,并考虑了其修正型变种,分析了两者的存在性及若干性质.针对标准七点差分矩阵,给出了预条件后的实际条件数.结果表明,采用局部块分解预条件时条件数与矩阵阶数的2/3次幂成正比,而采用修正型预条件时条件数与矩阵阶数的立方根成正比.最后考虑了预条件的高效实现并在主频为550MHz、内存为256M的微机上作了若干数值实验,并与其它较有效的预条件方法进行了比较. 相似文献
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预处理共轭梯度法的大量计算结果都表明,当迭代终止标准要求将余量的模减小某个倍数时,初值的选取对迭代次数仅有微弱影响。然而,本文给出的一类算例却表明,采用零初值或不同的随机初值,迭代次数之间会出现数倍的差别。同一种随机初值对不同参数模型问题的迭代次数也有很大差别。这种强初值效应对于方法的研究和比较是不利的。本文讨论和分析了这种现象。 相似文献
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L. Mo K. F. Tsang Edward K. N. Yung R. S. Chen D. G. Fang 《International Journal of Infrared and Millimeter Waves》2002,23(10):1529-1543
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. 相似文献
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The relationship between the object-plane phase and the intensity distribution in the Fresnel region can be described by the transport of intensity equation (TIE). The phase distribution can thus be uniquely determined by solving TIE. In this study, a full multigrid preconditioned conjugate gradient (FMG–CG) method is proposed to numerically solve the TIE for phase retrieval. The full multigrid method is a scalable algorithm, and can be parallelized readily and efficiently. By using this method as a preconditioner of the preconditioned conjugate gradient (PCG) method, fast convergence is obtained. The simulation experiments show that complicated phase distributions with fast convergence speed can be retrieved by this composite method. 相似文献
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Preconditioning for multidimensional TOMBO imaging 总被引:1,自引:0,他引:1
In this Letter, we propose a preconditioning method to improve the convergence speed of iterative reconstruction algorithms in a compact, multidimensional, compound-eye imaging system called the thin observation module by bound optics. The condition number of the system matrix is improved by using a preconditioner matrix. To calculate the preconditioner matrix, the system model is expressed in the frequency domain. The proposed method is simulated by using a compressive sensing algorithm called the two-step iterative shrinkage/thresholding algorithm. The results showed improved reconstruction fidelity with a certain number of iterations for high signal-to-noise ratio measurements. 相似文献
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Zhiyong Liu & Yinnian He 《advances in applied mathematics and mechanics.》2016,8(6):1072-1083
This paper provides a proof of robustness of the restricted additive Schwarz
preconditioner with harmonic overlap (RASHO) for the second order elliptic problems
with jump coefficients. By analyzing the eigenvalue distribution of the RASHO preconditioner,
we prove that the convergence rate of preconditioned conjugate gradient
method with RASHO preconditioner is uniform with respect to the large jump and
mesh size. 相似文献
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R. S. Chen K. F. Tsang Edward K. N. Yung 《International Journal of Infrared and Millimeter Waves》2000,21(8):1281-1301
In this paper, symmetric successive overrelaxation (SSOR) preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Millimeter wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, Helmholz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. An effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method, SSOR-PCG, is chosen to solve this matrix equation. With SSOR as the preconditioner as well as its efficient implementing in CG algorithm, PCG method can converge to accurate solution in much fewer iteration steps. 相似文献
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R. S. Chen X. W. Ping K. F. Tsang 《International Journal of Infrared and Millimeter Waves》2003,24(12):2139-2151
The Incomplete Cholesky factorizations preconditioning scheme is applied to the conjugate gradient (CG) method for solving a large system of linear equations resulting from finite element method (FEM) analysis of millimeter wave filters. As is well known, the convergence of CG method deteriorates with increasing EM wave number and in millimeter wave band the eigen-values of A are more and more scattered between both the right and the left half-plane. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for Complex coefficient matrix. With incomplete factorization preconditioning scheme in the conjugate gradient algorithm, this PCG approach can reach convergence in 20 times CPU time shorter than CG for several typical millimeter wave structures. 相似文献