High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

IMPROVED PRECONDITIONED CONJUGATE GRADIENT METHOD AND ITS APPLICATION IN F.E.A.FOR ENGINEERING

In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, ft is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.

The preconditioned conjugate gradient deconvolution method and its application

preconditioned 结合坡度 deconvolution 方法联合稀少的 deconvolution 和最佳的 preconditioned 的实现结合坡度方法转换到思考系数。这个方法能提高地震数据处理的频率并且拓宽有效频率带宽。就地震信号的变化时间的性质而言，我们在 deconvolution 期间用多尺度的变化时间的小浪代替经常的小浪。数字测试证明这个方法能获得好申请结果。

Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations

Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edge-preserving regularization functions, I.e., multiplicative half-quadratic regularizations, and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations. At each Newton iterate, the preconditioned conjugate gradient method, incorporated with a constraint preconditioner, is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix.The igenvalue bounds of the preconditioned matrix are deliberately derived, which can be used to estimate the convergence speed of the preconditioned conjugate gradient method. We use experimental results to demonstrate that this new approach is efficient,and the effect of image restoration is r0easonably well.

THE RESTRICTIVELY PRECONDITIONED CONJUGATE GRADIENT METHODS ON NORMAL RESIDUAL FOR BLOCK TWO-BY-TWO LINEAR SYSTEMS

The restrictively preconditioned conjugate gradient （RPCG） method is further developed to solve large sparse system of linear equations of a block two-by-two structure. The basic idea of this new approach is that we apply the RPCG method to the normal-residual equation of the block two-by-two linear system and construct each required approximate matrix by making use of the incomplete orthogonal factorization of the involved matrix blocks. Numerical experiments show that the new method, called the restrictively preconditioned conjugate gradient on normal residual （RPCGNR）, is more robust and effective than either the known RPCG method or the standard conjugate gradient on normal residual （CGNR） method when being used for solving the large sparse saddle point problems.

A Preconditioned Conjugate Gradient Method with Active Set Strategy for1-Regularized Least Squares

In the paper,we consider the l_(1)-regularized least square problem which has been intensively involved in the fields of signal processing,compressive sensing,linear inverse problems and statistical inference.The considered problem has been proved recently to be equivalent to a nonnegatively constrained quadratic programming(QP).In this paper,we use a recently developed active conjugate gradient method to solve the resulting QP problem.To improve the algorithm’s performance,we design a subspace exact steplength as well as a precondition technique.The performance comparisons illustrate that the proposed algorithm is competitive and even performs little better than several state-of-the-art algorithms.

A Two-Level Preconditioned Conjugate-Gradient Method in Distorted and Structured Grids

In this paper,we propose a new two-level preconditioned C-G method which uses the quadratic smoothing and the linear correction in distorted but topologically structured grid.The CPU time of this method is less than that of the multigrid preconditioned C-G method(MGCG)using the quadratic element,but their accuracy is almost the same.Numerical experiments and eigenvalue analysis are given and the results show that the proposed two-level preconditioned method is efficient.

PRECONDITIONED CONJUGATE GRADIENT METHODS FOR INTEGRAL EQUATIONS OF THE SECOND KIND DEFINED ON THE HALF-LINE

We consider solving integral equations of the second kind defined on the half-line [0, infinity) by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the associated integral operator. In this paper, we construct two different circulant integral operators to be used as preconditioners for the method to speed up its convergence rate. We prove that if the given integral operator is close to a convolution-type integral operator, then the preconditioned systems will have spectrum clustered around 1 and hence the preconditioned conjugate gradient method will converge superlinearly. Numerical examples are given to illustrate the fast convergence.

DOMAIN DECOMPOSITION PRECONDITIONERS FOR SECOND-ORDER HYPERBOLIC EQUATIONS ON L-SHAPED REGIONS

Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion preconditioner.s for the solution of linear systems via the preconditioned conjugate gradient method. For the constant-coefficient second-order hyperbolic equaions with initial and Dirichlet boundary conditions,we prove that the conditionnumber of the preconditioned interface system is bounded by 2+x2 2+0.46x2 where x is the quo-tient between the lime and space steps. Such condition number produces a convergence rale that is independent of gridsize and aspect ratios. The results could be extended to parabolic equations.

SINE TRANSFORM PRECONDITIONERS FOR SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS

In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.

Explicit Iterative Methods of Second Order and Approximate Inverse Preconditioners for Solving Complex Computational Problems

Explicit Exact and Approximate Inverse Preconditioners for solving complex linear systems are introduced. A class of general iterative methods of second order is presented and the selection of iterative parameters is discussed. The second order iterative methods behave quite similar to first order methods and the development of efficient preconditioners for solving the original linear system is a decisive factor for making the second order iterative methods superior to the first order iterative methods. Adaptive preconditioned Conjugate Gradient methods using explicit approximate preconditioners for solving efficiently large sparse systems of algebraic equations are also presented. The generalized Approximate Inverse Matrix techniques can be efficiently used in conjunction with explicit iterative schemes leading to effective composite semi-direct solution methods for solving large linear systems of algebraic equations.

汽化激光致声跨界通信的三维数值特性

激光致声技术可以将空气中的激光信号转化为水下的水声信号,将两种最佳信道高效地结合起来,从而解决空中-水下跨界通信问题。为了提高激光致声跨界通信的保密性和光声转化效率,采用了数值计算方法对不同条件下,激光在海面三维散射特性和透射特性进行了研究。首先,为了提高仿真计算的准确性,建立了三维激光海面散射场的数学模型。其次,采用数值计算方法求解三维激光海面散射的表面积分方程,并根据入射光波的特点,对入射界面进行强、弱区划分,以提高计算效率。最后,通过室内模拟试验对仿真结果进行了验证。研究结果表明,入射角度对于汽化激光致声通信的保密性和效率有着重要的影响,为后续的系统设计和相关应用研究提供了有意义的参考。

用有限元法优化高压电缆参数

提出了优化高压电缆的综合场数学模型 ,它包括电流场和静电场 ,推出了综合电场的边值问题 ,并用有限元法离散此数学模型。改进了传统的双共轭梯度法 ,并用此方法解离散的线性方程组 ,改善了解的收敛特性。优化了高压电缆参数 。

一种并行的大地电磁场非线性共轭梯度三维反演方法

本文改进并验证了大地电磁测深数据的三维反演算法和并行计算程序,程序对计算机物理内存和CPU速度及数量要求较低,使普通家用机进行三维反演计算成为可能.本文在Newman和Alumbaugh(2000)提出的三维非线性共轭梯度算法和Rodi和Mackie(2001)给出的大地电磁场二维NLCG反演预处理方法的基础上实现了大地电磁场NLCG三维反演算法,改进了的预处理方法,将反演计算对初始模型的依赖性降到最低,并且通过理论模型验证了程序的正确性,并根据日本KAYABE地区实测数据的反演结果验证了算法的实用性.

高分辨率阵列侧向测井的数学模型及有限元快速正演

对包含井眼、侵入带、围岩和目的层的轴对称地层模型,推导了无穷远截断边界上的Robin边界条件,建立了高分辨率阵列侧向测井的等值面边值问题模型.Robin边界条件较Dirichlet边界条件更加精确,可大大缩小求解区域而不影响计算精度.考虑到微分方程和边界条件为线性的,利用叠加原理简化了原微分方程边值问题的计算,克服了事先屏蔽电极上电流的不确定性.采用基于地址矩阵的稀疏存贮模式,大大减小了内存需求,且地址矩阵物理意义明确,方便迭代法调用求解有限元方程.引入预条件共轭梯度(PCG)法求解有限元计算形成的大型线性方程组,提高了测井响应的计算速度.利用本文方法定量考察了地层厚度、井径、侵入带等因素对阵列侧向测井响应的影响,为后续阵列侧向测井反演的研究奠定了基础,对实际测井工程具有一定的指导意义.

从瞬变电磁扩散场到拟地震波场的全时域反变换算法

将瞬变电磁满足的扩散方程转变为波动方程,然后利用地震类成像方法实现瞬变电磁虚拟波场成像,是实现瞬变电磁三维反演的有效手段之一.为了实现由扩散场到虚拟波场的转换,文中采用预条件正则化共轭梯度法求解波场反变换问题.首先,对几种离散方式进行比较,采用条件数最小的离散方式进行离散;然后选择最优的正则化参数,并利用超松弛预条件技术对系数矩阵进行预条件处理;最后,利用共轭梯度法进行迭代求解.超松弛预条件有效降低了系数矩阵的条件数,正则化方法使得反变换得到的波场稳定、可靠,共轭梯度法能够保证计算快速收敛.将反变换结果与已知虚拟波场函数对比,证明算法稳定、可信.将文中算法结果与前人研究结果进行对比,说明方法效果.通过实测数据的波场变换处理给出了文中方法的实际应用效果.结合反变换算法,对不同参数模型进行分析,总结了虚拟波场在色散介质中的传播规律.

基于空域最小二乘法求解GOCE卫星重力场的模拟研究

论述最小二乘过程中有色噪声的处理方法,提出使用自回归模型对GOCE梯度观测值中的有色噪声进行时域滤波,数值模拟结果验证该方法的有效性。利用数值模拟验证直接求逆方法和PCCG法求解大型法方程的有效性,后者的效率远远高于前者。联合加入噪声(有色噪声和白噪声)的卫星重力梯度张量径向分量观测值Vzz和SST观测值,分别使用空域最小二乘法和半解析法恢复180阶全球重力场模型,前者求解重力场模型的大地水准面和重力异常在180阶次的精度分别为3.01 cm和0.75 mGal(1 mGal=10-5 m/s2),优于半解析法求解模型的精度。

电容层析成像图像重建中的迭代算法

电容层析成像技术中图像重建算法的准确与快速是其在工业实际中得以应用的关键。Landweber方法是一种简单、灵活的迭代算法,具有很好的正则化特性,它的投影变体能够提供非负的图像重建。Landweber算法实际应用的困难是其收敛速度太低。本文采用预处理方法来加快Landweber迭代方法的收敛速度,即通过较少的迭代次数,获得适当的重建结果。仿真实验表明,同经典的快速算法共轭梯度迭代方法相比,预处理Landweber迭代方法具有更好的重建图像质量。

基于预处理共轭梯度的大地电磁快速正演

针对大地电磁法有限元模拟中计算量大的特点,采用按行压缩存储方式的不完全LDLT预处理共轭梯度法快速求解大型复系数方程组。引入不完全LDLT预处理,提出快速求解(LDLT)-1r的方法,以加快预处理共轭梯度法的收敛速度。研究结果表明:当网格节点自由度超过1万时,压缩率达到99.9%,求解方程组时间在1 s以内,为进一步快速反演奠定了基础。

动态载荷时域识别的联合去噪修正和正则化预优迭代方法

系统响应可表示为单位脉冲响应函数与激励载荷的卷积,将其离散化一组线性方程组,则载荷识别问题即转化为求解线性方程组的反问题。针对响应中带有噪音时载荷识别的困难,提出了联合奇异熵去噪修正和正则化预优的共轭梯度迭代识别方法。一方面对含噪信号进行基于奇异熵的去噪处理,提高反问题求解中输入数据的精度。另一方面利用正则化方法对共轭梯度迭代算法进行预优,改善反问题的非适定性。由于从输入的响应数据去噪和正则化算法两方面同时改善动态载荷识别反问题的求解,因此可以有效地抑制噪声,提高识别精度。通过数值算例分析,表明在不同的噪声水平干扰下,其识别精度均优于常规的正则化方法,能够实现有效稳定地识别动态载荷。最后通过实验研究进一步验证了该方法的正确性和有效性。