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Online monitoring of gas-solid two-phase flow using projected CG method in ECT image reconstruction

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Particuology 2013年第2期11卷 204-215页

作者： Qi Wang Chengyi Yang Huaxiang Wang Ziqiang Cui Zhentao Gao School of Electrical Engineering & Automation Tianjin University Oil Production Technology Research Institute of Huabei Oilfield Co.

Electrical capacitance tomography （ECT） is a promising technique for multi-phase flow measurement due to its high speed, low cost and non-intrusive sensing. Image reconstruction for ECT is an inverse problem of finding the permittivity distribution of an object by measuring the electrical capacitances between sets of electrodes placed around its periphery. The conjugate gradient （CG） method is a popular image reconstruction method for ECT, in spite of its low convergence rate. In this paper, an advanced version of the CG method, the projected CG method, is used for image reconstruction of an ECT system. The solution space is projected into the Kryiov subspace and the inverse problem is solved by the CG method in a low-dimensional specific subspace. Both static and dynamic experiments were carried out for gas-solid two-phase flows. The flow regimes are identified using the reconstructed images obtained with the projected CG method. The results obtained indicate that the projected CG method improves the quality of reconstructed images and dramatically reduces computation time, as compared to the traditional sensitivity, Landweber, and CG methods. Furthermore, the projected CG method was also used to estimate the important parameters of the pneumatic conveying process, such as the volume concentration, flow velocity and mass flow rate of the solid phase. Therefore, the projected CG method is considered suitable for online gas-solid two-phase flow measurement,

关键词： Electrical capacitance tomography (ECT) Image reconstruction Conjugate gradient method (CG) krylov subspace

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A MODIFIED GMRES METHOD FOR SOLVING LARGE NONSYMMETRIC LINEAR SYSTEMS

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高等学校计算数学学报 2005年第S1期 193-199页

作者：牛强卢琳璋王瑞瑞 Department of Information and Computational Mathematics Xiamen University Department of Information and Computational Mathematics Xiamen University Xiamen 361005 PRC

A modified GMRES method is proposed in this paper, the method replaces the approximation xm obtained by the GMRES method with a new approximation xm which is a linear combination of xm and the wasted basis vector vm+1. The residual norm of the new approximation satisfies a small one-dimensional minimization problem. Relationships between the residual norms of xm and xm are given. We show that the resulting m-step modified GMRES method is better than the original m-step GMRES method in theory and is considerably more efficient than the (m+1)-step GMRES method by numerical experiments.

关键词： linear systems krylov subspace Arnoldi process the GMRES method.

求解带位移反对称矩阵方程的有效数值方法（英文）

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高等学校计算数学学报 2015年第1期37卷 81-96页

作者：李东平张秀英长春师范大学数学学院吉林大学数学系

In this paper,two CG-type algorithms for solving shifted skewsymmetric matrix equations are *** new methods are extracted from the modified global Lanczos algorithm presented in the *** experiments illustrate the conv... 详细信息

关键词： CG-type krylov subspace global Arnoldi algorithm shifted skewsymmetric matrix

A Reduced-Order Modeling of Multi-Port RC Networks by Means of Graph Partitioning

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Journal of Semiconductors 2002年第10期23卷 1037-1040页

作者：杨华中冒小建燕昭然汪蕙清华大学电子工程系北京100084

A modified reduced-order method for RC networks which takes a division-and-conquest strategy is *** whole network is partitioned into a set of sub-networks at first,then each of them is reduced by krylov subspace techniques,and finally all the reduced sub-networks are incorporated *** some accuracy,this method can reduce the number of both nodes and components of the circuit comparing to the traditional methods which usually only offer a reduced net with less *** can markedly accelerate the sparse-matrix-based simulators whose performance is dominated by the entity of the matrix or the number of components of the circuits.

关键词： interconnect reduced-order modeling graph partitioning krylov subspace

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GMRES方法的收敛率

高等学校计算数学学报 2003年第3期25卷 253-260页

作者：钟宝江南京航空航天大学理学院南京 210016

1 引言 GMRES方法是目前求解大型稀疏非对称线性方程组 Ax=b,A∈R;;x,b∈R;（1）最为流行的方法之一.设x;是（1）解的初始估计,r;=b-Ax;是初始残量,K;=span{r;,Ar;,…A;r;}为由r;和A产生的krylov子空间.GMRES方法的第k步

关键词： GMRES krylov subspace Ritz values convergence behaviour.

Researted FOM for Multiple Shifted Linear Systems

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Journal of Shanghai University(English Edition) 2005年第2期9卷 107-113页

作者：李占稳汪勇顾桂定 Department of Mathematics College of Sciences Shanghai University Shanghai 200444 P.R.China Department

The seed method is used for solving multiple linear systems A (i)x (i) =b (i) for 1≤i≤s, where the coefficient matrix A (i) and the right-hand side b (i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A (i). In this paper, the FOM method is employed to solve multiple linear sy stems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a krylov subspace, then the resi duals of other systems are projected onto the generated krylov subspace to get t he approximate solutions for the unsolved ones. The whole process is repeated u ntil all the systems are solved.

关键词： multiple linear systems seed method krylov subspace FOM shifted systems.

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Fast Transient Simulation of Output Voltage for Piezoresistive Microaccelerometers Using Model Order Reduction

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Fast Transient Simulation of Output Voltage for Piezoresisti...