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Multi-symplectic algorithm for 'Good' Boussinesq equation

Applied Mathematics and Mechanics (English Edition) 2002年第7期23卷 835-841页

作者： Wen-Ping, Zeng Lang-Yang, Huang Meng-Zhao, Qin Department of Mathematics Huaqiao University Quanzhou 362011 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing 100080 China

The multi-symplectic formulations of the Good Boussinesq equation were considered. For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman integrator was derived. The numerical experiments show that the multi-symplectic schemes have excellent long-time numerical behavior.

关键词： Nonlinear equations

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Message from the IWPAPS 2012 workshop chairs

Proceedings - 2012 IEEE International Conference on Cluster ...

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Proceedings - 2012 IEEE International Conference on Cluster computing Workshops, Cluster Workshops 2012 2012年 xiii页

作者： Zhang, Linbo Zhang, Yunquan State Key Laboratory of Scientific and Engineering Computing CAS China Institute of Software CAS China

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High order moment closure for Vlasov-Maxwell equations

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Frontiers of Mathematics in China 2015年第5期10卷 1087-1100页

作者： Yana DI Zhenzhong KOU Ruo LI The State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing 100190 China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing 100190 China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190 China HEDPS & CAPT LMAM & School of Mathematical Sciences Peking University Beijing 100871 China

The extended magnetohydrodynamic models are derived based on the moment closure of the Vlasov-Maxwell （VM） equations. We adopt the Grad type moment expansion which was firstly proposed for the Boltzmann equation. A new regularization method for the Grad＇s moment system was recently proposed to achieve the globally hyperbolicity so that the local well-posedness of the moment system is attained. For the VM equations, the moment expansion of the convection term is exactly the same as that in the Boltzmann equation, thus the new developed regularization applies. The moment expansion of the electromagnetic force term in the VM equations turns out to be a linear source term, which can preserve the conservative properties of the distribution function in the VM equations perfectly.

关键词： Moment closure Vlasov-Maxwell （VM） equations Boltzmannequation extended magnetohydrodynamics

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A Subspace Version of the Powell–Yuan Trust-Region Algorithm for Equality Constrained Optimization

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Journal of the Operations Research Society of China 2013年第4期1卷 425-451页

作者： Geovani Nunes Grapiglia Jinyun Yuan Ya-xiang Yuan Departamento de Matemática Universidade Federal do ParanáCentro PolitécnicoCx.postal 19.08181531-980CuritibaParanáBrazil The Capes Foundation Ministry of Education of BrazilCx.postal 25070.040-020BrasíliaDistrito FederalBrazil State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesZhongguancundonglu 55Beijing 100190P.R.China

This paper studied subspace properties of the Celis–Dennis–Tapia(CDT)subproblem that arises in some trust-region algorithms for equality constrained opti*** analysis is an extension of that presented by Wang and Yuan(***.104:241–269,2006)for the standard trust-region *** suitable conditions,it is shown that the trial step obtained from the CDT subproblem is in the subspace spanned by all the gradient vectors of the objective function and of the constraints computed until the current *** on this observation,a subspace version of the Powell–Yuan trust-region algorithm is proposed for equality constrained optimization problems where the number of constraints is much lower than the number of variables. The convergence analysis is given and numerical results arealso reported.

关键词： Constrained optimization Trust-region methods Subspace methods

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Construction and Analysis of Structured Preconditioners for Block Two-by-Two Matrices

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Journal of Shanghai University(English Edition) 2004年第4期8卷 397-405页

作者：白中治 State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P.R. China

For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications.

关键词： block two-by-two matrix preconditioner modified block relaxation iteration eigenvalue distribution positive definiteness.

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Teracluster LSSC-II--Its designing principles and applications in large scale numerical simulations

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中国科学A辑（英文版） 2004年第z1期47卷 53-68页

作者： Zhang Linbo Chen Shiyi LI Xinliang CAO Jianwen ZHANG Wensheng GONG Xingao State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of Mechanical Engineering The Johns Hopkins University and Center for Computational Science and Engineering Peking University Beijing 100875 China Institute of Mechanics Chinese Academy of SciencesBeijing 100080 China Parallel Computing Laboratory Institute of Software Chinese Academy of Sciences Beijing 100080 China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Surface Physics Laboratory National Key Laboratory Fudan University Shanghai 200433 Institute of Solid State Physics Chinese Academy of Sciences Hefei 230031 China

The teracluster LSSC-II installed at the state key laboratory of scientific and engineering computing, Chinese Academy of Sciences is one of the most powerful PC clusters in China. It has a peek performance of 2Tflops. With a Linpack performance of 1.04Tflops, it is ranked at the 43rd place in the 20th TOP500 List (November 2002), 51st place in the 21st TOP500 List (June 2003), and the 82nd place in the 22nd TOP500 List (November 2003) with a new Linpack performance of 1.3Tflops. In this paper, we present some design principles of this cluster, as well as its applications in some large-scale numerical simulations.

关键词： high performance computing PC cluster large scale numerical simulations

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A multi-scale geometric flow method for molecular structure reconstruction

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Computational Science and Discovery 2015年第1期8卷

作者： Xu, Guoliang Li, Ming Chen, Chong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and Systems Science Beijing100190 China

We have previously reported an L2-gradient flow (L2GF) method for cryo-electron tomography and single-particle reconstruction, which has a reasonably good performance. The aim of this paper is to further upgrade both the computational efficiency and accuracy of the L2GF method. In a finite-dimensional space spanned by the radial basis functions, a minimization problem combining a fourth-order geometric flow with an energy decreasing constraint is solved by a bi-gradient method. The bi-gradient method involves a free parameter As β increases from 0 to 1, the structures of the reconstructed function from coarse to fine are captured. The experimental results show that the proposed method yields more desirable results. © 2015 IOP Publishing Ltd.

关键词： Gradient methods

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Taking Myopic Best Response Against the Hedge Algorithm 42

Taking Myopic Best Response Against the Hedge Algorithm

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42nd Chinese Control Conference, CCC 2023

作者： Guo, Xinxiang Mu, Yifen School of Mathematical Sciences University of Chinese Academy of Sciences Beijing China Academy of Mathematics and Systems Science The State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China Academy of Mathematics and Systems Science The Key Laboratory of Systems and Control Chinese Academy of Sciences Beijing China

ISBN: (纸本)9789887581543

With the rapid development of artificial intelligence (AI), the game between the human and machine/AI becomes more and more common. The related theoretical analysis becomes significant and necessary, which however is still rare. This problem involves evolution analysis and optimal control of dynamic game systems driven by learning algorithms. In this paper, we consider a finitely repeated two-player zero-sum game. We study the dynamic evolution process of the game system, in which one player employs the Hedge algorithm and the other player takes the myopic best response. By the updating formula of the Hedge algorithm, we define a quantity called the state and construct the state Transition Triangle Graph (STTG). Then, we prove that the game system is periodic after o(T) stages. © 2023 Technical Committee on Control Theory, Chinese Association of Automation.

关键词： Artificial intelligence

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Fast algorithm for beamforming problems in distributed communication of relay networks

Fast algorithm for beamforming problems in distributed commu...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Cong Sun Yaxiang Yuan State Key Laboratory of Scientific and Engineering Computing ICMSEC AMSS Chinese Academy and Sciences Beijing China

A sequential quadratic programming (SQP) method is pro posed to solve the distributed beamforming problem in multiple relay networks. The problem is formulated as the minimization of the total relay transmit power, subject to individual signal-to-interference-and-noise ratio constraints at each receiver, which is a nonconvex quadratic constraint quadratic programming. Rather than solving its semi-definite programming (SDP) relaxation, we apply the SQP method to solve its tightened form to replace its inequality constraints with equalities. Its global convergence is guaranteed. Simulations show that it not only runs much faster, but also performs as good as SDP for calculation results.

关键词： Relays Array signal processing Quadratic programming Interference Signal to noise ratio Peer to peer computing

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A New Fully Polynomial Time Approximation Scheme for the Interval Subset Sum Problem

arXiv

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arXiv 2017年

作者： Diao, Rui Liu, Ya-Feng Dai, Yu-Hong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The interval subset sum problem (ISSP) is a generalization of the well-known subset sum problem. Given a set of intervals {[ai,1, ai,2]}ni=1 and a target integer T, the ISSP is to find a set of integers, at most one from each interval, such that their sum best approximates the target T but cannot exceed it. In this paper, we first study the computational complexity of the ISSP. We show that the ISSP is relatively easy to solve compared to the 0-1 Knapsack problem (KP). We also identify several subclasses of the ISSP which are polynomial time solvable (with high probability), albeit the problem is generally NP-hard. Then, we propose a new fully polynomial time approximation scheme (FPTAS) for solving the general ISSP problem. The time and space complexities of the proposed scheme are O (n max {1/ǫ, log n}) and O (n + 1/ǫ), respectively, where ǫ is the relative approximation error. To the best of our knowledge, the proposed scheme has almost the same time complexity but a significantly lower space complexity compared to the best known scheme. Both the correctness and efficiency of the proposed scheme are validated by numerical simulations. In particular, the proposed scheme successfully solves ISSP instances with n = 100, 000 and ǫ = 0.1% within one second. Copyright © 2017, The Authors. All rights reserved.

关键词： Computational complexity

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