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On the comparisons of the multisplitting unsymmetric aor methods for M-matrices

Calcolo 1995年第3-4期32卷 207-220页

作者： Bai, Zhong-Zhi State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing 100080 P.O. Box 2719 China

This paper reveals the inner links between two known frameworks of multisplitting relaxation methods as completely as possible. By meticulously investigating the specific structures of these two frameworks, the asymptotic convergence rates as well as the monotone convergence rates of them are compared theoretically. This then definitely answers the question that which converges faster between these two frameworks of parallel matrix multisplitting relaxation methods from the standpoint of pure mathematics. At last, an example further confirms the correctness of the theoretical results. © 1995 Instituto di Elaborazione della Informazione del CNR.

关键词： asymptotic convergence rate Matrix multisplitting monotone convergence rate relaxation method

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A Restarted Conjugate Gradient Method for Ill-posed Problems

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Acta Mathematicae Applicatae Sinica 2003年第1期19卷 31-40页

作者： Yan-fei Wanglaboratory of Remote Sensing Information Sciences, Institute of Remote Sensing Applications, Chinese Academy of Sciences, P.O. Box 9718, Beijing 100101, Chinastate key laboratory of scientific and engineering computing, Institute of Computational Mathematics and scientific/engineering computing, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, China Laboratory of Remote Sensing Information Sciences Institute of Remote Sensing Applications Chinese Academy of Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering computing Chinese Academy of Sciences Beijing China

Abstract This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are give... 详细信息

关键词： keywords Ill-posed problems restarted CG damped discrepancy principle.

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Numerical simulation of Richtmyer-Meshkov instability

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Science China Mathematics 2004年第z1期47卷 234-244页

作者： FU Dexun, MA Yanwen, ZHANG Linbo & TIAN Baolinstate key laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China state key laboratory of scientific and engineering computing, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China 1. State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences 100080 Beijing China2. State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Chinese Academy of Sciences 100080 Beijing China

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

关键词： R-M instability, direct numerical simulation, shock-interface interaction.

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Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

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Chinese Physics B 2008年第11期17卷 3942-3952页

作者：傅景礼陈本永唐贻发付昊 Institute of Mathematical Physics Zhejiang Sci-Tech University Faculty of Mechanical-Engineering & Automation Zhejiang Sci-Tech University State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences China Jingye Engineering Corporation Limited Shenzhen Brach

A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler-Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.

关键词： total variation symplectic-energy-momentum integrator mechanico-electrical system

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Some perspective on the Large Scale scientific Computation Research

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Science China Mathematics 2004年第Z1期47卷 1-3页

作者： DU Qiang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080China

　　The "Large Scale scientific Computation (LSSC) Research"project is one of the state Major Basic Research projects funded by the Chinese Ministry of Science and Technology in the field ofinformation scien... 详细信息

关键词： LSSC Some perspective on the Large Scale scientific Computation Research

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A trust region method based on a new affine scaling technique for simple bounded optimization

A trust region method based on a new affine scaling techniqu...

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作者： Wang, Xiao Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences PO Box 2719 Beijing 100190 China

In this paper, we propose a new trust region affine scaling method for nonlinear programming with simple bounds. Our new method is an interior-point trust region method with a new scaling technique. The scaling matrix depends on the distances of the current iterate to the boundaries, the gradient of the objective function and the trust region radius. This scaling technique is different from the existing ones. It is motivated by our analysis of the linear programming case. The trial step is obtained by minimizing the quadratic approximation to the objective function in the scaled trust region. It is proved that our algorithm guarantees that at least one accumulation point of the iterates is a stationary point. Preliminary numerical experience on problems with simple bounds from the CUTEr collection is also reported. The numerical performance reveals that our method is effective and competitive with the famous algorithm LANCELOT. It also indicates that the new scaling technique is very effective and might be a good alternative to that used in the subroutine fmincon from Matlab optimization toolbox. © 2013 Copyright Taylor and Francis Group, LLC.

关键词： Nonlinear programming

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A NONMONOTONE CONJUGATE GRADIENT ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

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Journal of Systems Science & Complexity 2002年第2期15卷 139-145页

作者： Dai Yuhong Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences State Key Laboratory of Scientific and Engineering Computing 北京 100080

Abstract. Conjugate gradient methods are very important methods for unconstrainedoptimization, especially for large scale problems. In this paper, we propose a new conjugategradient method, in which the technique of nonmonotone line search is used. Under mildassumptions, we prove the global convergence of the method. Some numerical results arealso presented.

关键词： Unconstrained optimization conjugate gradient nonmonotone line search global convergence.

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High Order Mass-Lumping Finite Elements on Simplexes

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高等学校计算数学学报（英文版） 2017年第2期10卷 331-350页

作者： Tao Cui Wei Leng Deng Lin Shichao Ma Linbo Zhang State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of SciencesNo.55 East Zhongguancun Road Beijing 100190 China State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of SciencesNo.55 East Zhongguancun Road Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049 China

This paper is concerned with the construction of high order mass-lumping finite elements on simplexes and a program for computing mass-lumping finite elements on triangles and *** polynomial spaces for mass-lumping finite elements,as proposed in the literature,are presented and *** particular,the unisolvence problem of symmetric point-sets for the polynomial spaces used in mass-lumping elements is addressed,and an interesting property of the unisolvent symmetric point-sets is observed and *** its theoretical proof is still lacking,this property seems to be true in general,and it can greatly reduce the number of cases to consider in the computations of mass-lumping elements.A program for computing mass-lumping finite elements on triangles and tetrahedra,derived from the code for computing numerical quadrature rules presented in [7],is *** mass-lumping finite elements on triangles found using this program with higher orders,namely 7,8 and 9,than those available in the literature are reported.

关键词： Finite element mass-lumping simplex numerical quadrature multivariate polynomial interpolation unisolvence

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Conjugate Gradient Methods with Armijo-type Line Searches

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Acta Mathematicae Applicatae Sinica 2002年第1期18卷 123-130页

作者： Yu-Hong DAIstate key laboratory of scientific and engineering computing, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods. Under these line searches, global convergence results are established for several famous conjugate gradient methods, i... 详细信息

关键词： Unconstrained optimization conjugate gradient method line search global convergence

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On the clean numerical simulation(CNS) of chaotic dynamic systems

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Journal of Hydrodynamics 2017年第5期29卷 729-747页

作者：廖世俊 State Key Laboratory of Ocean Engineering Shanghai Jiao Tong UniversityShanghai 200240China MOE Laboratory of Scientific and Engineering Computing Shanghai Jiao Tong UniversityShanghai 200240China School of Naval Architecture Ocean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

According to Lorenz, chaotic dynamic systems have sensitive dependence on initial conditions（SDIC）, i.e., the butterfly-effect： a tiny difference on initial conditions might lead to huge difference of computer-generated simulations after a long time. Thus, computer-generated chaotic results given by traditional algorithms in double precision are a kind of mixture of ＂true＂（convergent） solution and numerical noises at the same level. Today, this defect can be overcome by means of the ＂clean numerical simulation＂（CNS） with negligible numerical noises in a long enough interval of time. The CNS is based on the Taylor series method at high enough order and data in the multiple precision with large enough number of digits, plus a convergence check using an additional simulation with even smaller numerical noises. In theory, convergent（reliable） chaotic solutions can be obtained in an arbitrary long（but finite） interval of time by means of the CNS. The CNS can reduce numerical noises to such a level even much smaller than micro-level uncertainty of physical quantities that propagation of these physical micro-level uncertainties can be precisely investigated. In this paper, we briefly introduce the basic ideas of the CNS, and its applications in long-term reliable simulations of Lorenz equation, three-body problem and Rayleigh-Bénard turbulent flows. Using the CNS, it is found that a chaotic three-body system with symmetry might disrupt without any external disturbance, say, its symmetry-breaking and system-disruption are ＂self-excited＂, i.e., out-of-nothing. In addition, by means of the CNS, we can provide a rigorous theoretical evidence that the micro-level thermal fluctuation is the origin of macroscopic randomness of turbulent flows. Naturally, much more precise than traditional algorithms in double precision, the CNS can provide us a new way to more accurately investigate chaotic dynamic systems.

关键词： Chaos reliable numerical simulation clean numerical simulation（CNS） three-body problem turbulence origin of randomness

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