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IEEE International Conference on High Performance computing and Communications (HPCC)

作者： Tao Cui State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy and Sciences Beijing China

PHG (parallel hierarchical grid) is a scalable parallel adaptive finite element toolbox under active developmentat the State key laboratory of scientific and engineering computing, Chinese Academy of Sciences. This paper demonstrates its application to adaptive finite element computations of electromagnetic problems. Two examples on solving the time harmonic Maxwell's equations are shown. Results of some large scale adaptive finite element simulations with up to 1 billion degrees of freedom and using up to 2048 CPUs are presented.

关键词： Finite element methods Equations Mathematical model Linear systems Harmonic analysis Algorithm design and analysis Laboratories

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Preconditioners for higher order edge finite element discretizations of Maxwell's equations

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Science China Mathematics 2008年第8期51卷 1537-1548页

作者： ZHONG LiuQiang1,2,SHU Shi1,2,SUN DuDu3&TAN Lin4 1School of Mathematical and Computational Sciences,Xiangtan University,Xiangtan 411105,China 2Hunan key laboratory for Computation and Simulation in Science and engineering,Xiangtan 411105,China 3Institute of Computational Mathematics and scientific/engineering computing,Academy of Mathematicsand Systems Science,Graduate University of Chinese Academy of Sciences,Chinese Academy Sciences,P.O.Box 2719,Beijing 100190,China 4Department of Math-Physics,Nanhua University,Hengyang 421001,China 1. School of Mathematical and Computational Sciences Xiangtan University Xiangtan 411105 China 2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan 411105 China 3. Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Graduate University of Chinese Academy of Sciences Chinese Academy Sciences P.O. Box 2719 Beijing 100190 China 4. Department of Math-Physics Nanhua University Hengyang 421001 China

In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's *** present the preconditioners for the first family and second family of higher order N′ed′elec element equations,*** combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform *** also present some numerical experiments to demonstrate the theoretical results.

关键词： preconditioner higher order edge finite element stable decomposition

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On the use of simplex methods in constructing quadratic models

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Science China Mathematics 2007年第7期50卷 913-924页

作者： Qing-hua ZHOU 1 College of Mathematics and Computer,Hebei University,Baoding 071002,China 2 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,Beijing 100080,China College of Mathematics Computer Hebei University Baoding 071002 China State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics Scientific/Engineering Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China

In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of functions evaluations have been reduced obviously through our algorithms.

关键词： unconstrained optimization trust region method quadratic model Lagrange function simplex methods direct methods 90C56

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Explicit Multi-Symplectic Methods for Hamiltonian Wave Equations

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Communications in Computational Physics 2007年第4期2卷 662-683页

作者： Jialin Hong Shanshan Jiang Chun Li Hongyu Liu State Key Laboratory of Scientific and Engineering Computing Institute of Computational MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100080P.R.China Graduate School Chinese Academy of SciencesBeijing 100080P.R.China Department of Mathematics The Chinese University of Hong KongShatinN.T.Hong Kong.

In this paper,based on the multi-symplecticity of concatenating symplectic Runge-Kutta-Nystrom(SRKN)methods and symplectic Runge-Kutta-type methods for numerically solving Hamiltonian PDEs,explicit multi-symplectic schemes are constructed and investigated,where the nonlinear wave equation is taken as a model *** comparisons are made to illustrate the effectiveness of our newly derived explicit multi-symplectic integrators.

关键词： Hamiltonian wave equations multi-symplectic integration symplectic Runge-Kutta methods symplectic Runge-Kutta-Nystrom methods.

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Splitting iteration methods for non-Hermitian positive definite systems of linear equations

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Hokkaido Mathematical Journal 2007年第4期36卷 801-814页

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

For large sparse system of linear equations with a non-Hermitian positive definite coefficient matrix, we review the recently developed Hermitian/skew-Hermitian splitting (HSS) iteration, normal/skew-Hermitian splitting (NSS) iteration, positive-definite/ skew-Hermitian splitting (PSS) iteration, and block triangular/skew-Hermitian splitting (BTSS) iteration. These methods converge unconditionally to the exact solution of the linearsystem, with the upper bounds of their convergence factors being only dependent on the spectrum of the Hermitian (or normal, or positive-definite) splitting matrix, but independent of the spectrum of the skew-Hermitian splitting matrix as well as the eigenvectors of all matrices involved. © 2007 by the University of Notre Dame. All rights reserved.

关键词： Block triangular matrix Hermitian and skew-Hermitian splitting Non-Hermitian matrix Normal/Skew-Hermitian splitting Positive definite matrix Positivedefinite/Skew-Hermitian splitting Splitting iteration method

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A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

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Chinese Physics B 2007年第3期16卷 599-604页

作者：刘鸿基傅景礼唐贻发 Institute of Mathematical Physics Shangqiu Teacher's College Shangqiu 476000 China Department of Physics Zhejiang Sci-Tech University Hangzhou 310018 China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing 100080 China Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.

关键词： Mei symmetry non-Noether conservative quantity Lutzky conservative quantity nonconservative system

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Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems

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Chinese Physics B 2007年第3期16卷 570-577页

作者：傅景礼戴桂冬萨尔瓦多·希梅尼斯唐贻发 Department of Physics Zhejiang Sci-Tech University Hangzhou 310018 China State Key Laboratory of Scientific and Engineering Computing ICMSEC Academy of Mathematies and System Science Chinese Academy of Sciences Beijing 100080 China Departament de Matematica Aplicáda TTII E. T.S.I. Telecomunicación Universidad Politécnica de Madrid 28040-Madrid Spain Graduate School of the Chinese Academy of Sciences Beijing 100080 China

This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.

关键词： discrete variational principle first integral mechanico-electrical systems

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Monotone projected gradient methods for large-scale box-constrained quadratic programming

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Science China Mathematics 2006年第5期49卷 688-702页

作者： ZHOU Bin, GAO Li & DAI Yuhong School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, China 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, Beijing 100080, China School of Mathematical Sciences LMAM Peking University Beijing 100871 China State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics Scientific/Engineering Computing Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing 100080 China

Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.

关键词： projected gradients, monotone gradient methods, box-constrained quadratic programming, large-scale problems.

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Conformal Invariant Asymptotic Expansion Approach for Solving （3＋1）-Dimensional JM Equation

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Communications in Theoretical Physics 2006年第6期45卷 979-984页

作者： LI Zhi-Fang RUAN Hang-Yu Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.

关键词：（3＋1）-dimensional Jimbo-Miwa （JM） equation conformal invariant asymptotic expansion approach Painlevé property approximate and exact solutions

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Two-step iterative methods for solving the stationary convection-diffusion equation with a small parameter at the highest derivative on a uniform grid

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Computational Mathematics and Mathematical Physics 2006年第2期46卷 282-293页

作者： Bai, Z.-Z. Krukier, L.A. Martynova, T.S. State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing 100080 P.O. Box 2719 China Computer Center Rostov State University Rostov-on-Don 344090 pr. Stachki 200/1 bld. 2 Russian Federation

A stationary convection-diffusion problem with a small parameter multiplying the highest derivative is considered. The problem is discretized on a uniform rectangular grid by the central-difference scheme. A new class of two-step iterative methods for solving this problem is proposed and investigated. The convergence of the methods is proved, optimal iterative methods are chosen, and the rate of convergence is estimated. Numerical results are presented that show the high efficiency of the methods. © MAIK "Nauka/Interperiodica" (Russia), 2006.

关键词： Convergence Dissipative matrix Iterative methods Optimal iterative parameters Transition operator

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