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Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science China Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1.& GUO Boling2.1. Department of {2., Beijing Normal University, Beijing 1.0875, China 2. {1. of Applied Physics and computational {2., Beijing 1.0080, China Department of mathematics Beijing Normal University Beijing China institute of Applied Physics and {1. {2. Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

Two-dimensional simulation of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect

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Progress in Natural Science:Materials International 2007年第12期17卷 1389-1396页

作者： Hu Jun1.and Yin Xieyuan2.1. {2. of Applied Physics and {1. mathematics, Beijing 1.0088, China 2. Department of Modern Mechanics, University of Science and Technology of China, Hefei 2.002., China) institute of Applied Physics and {1. {2. Beijing 100088 China Department of Modern Mechanics University of Science and Technology of China Hefei 230027 China

Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect are directly simulated by a mixed finite element method. A temperature perturbation is used as an initial disturbed source for the basic parallel flows. The whole spatio-temporal evolution of the binary fluid flows is exhibited: initially only the disturbed mode with the wavenumber k=π is amplified while others are damped, and continuously the amplified mode grows further and the nonlinear effect becomes important; after a nonlinear evolution transition the flow system evolves finally into a periodic right traveling wave.

关键词： Poiseuille-Rayleigh-Bénard flow Soret effect through-flow.

Theoretical and experimental researches on C-band three-cavity transit-time effect oscillator

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Science China(Physics,Mechanics & Astronomy) 2004年第3期47卷 310-329页

作者： FAN Zhikai1. LIU Qingxiang1. CHEN Daibing1. TAN Jie1.& ZHOU Haijing2.1. institute of Applied Electronics, Chinese Academy of Engineering Physics, Mianyang 62.0}00, China 2. institute of Applied Physics and computational mathematics, Beijing 1.0088, China institute of Applied Electronics Chinese Academy of Engineering Physics Mianyang China institute of Applied Physics and {1. {2. Beijing China

The C-band three-cavity transit-time effect oscillator (3C TTTO) is a novel high power microwave device based on the transit-time effect of the three-cavity (3C) resonator. The operational principle of this device is briefly expounded in this paper, and the theoretical and experimental researches on the radial insulation diode, the 3C resonator, the double-gap output cavity and the circular waveguide bevel cut radiation antenna are presented in detail. By using the analytic method, the eigen modes and their field distributions of the 3C resonator are developed, and some basic laws of the transit-time effect are obtained in non-π mode field of the 3C resonator. At last, the experimental results are given. This device generated RF peak power in excess of 400MW with 1.ns FWHM, and its beam-wave power conversion efficiency is about 1.%.

关键词： C-band, three-cavity (3C) resonator, transit-time effect, high power microwave, oscillator.

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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Chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1.and ZHU Lixing 2.1. {2. Lab, China University of Mining & Technology, Beijing 1.0083, China 2. Probability Lab, {1. of Applied {2., Chinese Academy of Sciences, Beijing 1.0080, China mathematics Lab China University of Mining & Technology Beijing China Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1. Guo Boling2.and Cheng Caozong1.1. College of Applied Sciences, Beijing University of Technology, Beijing 1.002., China 2. Center for Nonlinear Studies, institute of Applied Physics and {1. mathematics, Beijing 1.0088, China) College of Applied Sciences Beijing University of Technology Beijing 100022 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method

Parallel implementation of fast multipole method based on JASMIN

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Science China(Information Sciences) 2011年第4期54卷 757-766页

作者： CAO XiaoLin 1.2.MO ZeYao 1.2.LIU Xu 1.XU XiaoWen 1.& ZHANG AiQing 1.1.High Performance computational Center in {1. of Applied Physics and computational mathematics,Beijing 1.0094,China 2.Laboratory of computational Physics in {1. of Applied Physics and computational mathematics,Beijing 1.0094,China High Performance computational Center in {1. of Applied Physics and computational mathematics Beijing China Laboratory of computational Physics in {1. of Applied Physics and computational mathematics Beijing China

Fast multipole method (FMM) may reduce the complexity of N-body problems from O(N 2.) to O(N log N) or O(N).It was applied in problems ranging from electromagnetic scattering to dislocation *** can be divided into two parts: commonness and individuality.A parallel solver of FMM commonly used in various applications has been designed and implemented in JASMIN *** solver encapsulates the ***,it supplies users with abstract interfaces required to implement the individuality with serial *** commonness contains distributed storage of multi-levels,intra-level and inter-level data communication,and arrangement of computation,*** individuality contains various expansion and translation *** give here two applications that have used the *** was demonstrated with a parallel efficiency above 80% on 1.2. processors.

关键词： fast multipole method N-body problems JASMIN infrastructure parallel solver

A complex variable meshless method for fracture problems

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Science China(Physics,Mechanics & Astronomy) 2006年第1期49卷 46-59页

作者： CHENG Yumin1.& LI Jiuhong2.1. Shanghai {2. of Applied {1. and Mechanics, Shanghai University, Shanghai 2.0072. China 2. Department of Building Engineering, Xi’an University of Technology, Xi’an 71.048, China Shanghai institute of Applied {1. and Mechanics Shanghai University Shanghai China Department of Building Engineering Xi’an University of Technology Xi’an China

Based on the moving least-square (MLS) approximation, the complex variable moving least-square approximation (CVMLS) is discussed in this paper. The complex variable moving least-square approximation cannot form ill-conditioned equations, and has greater precision and computational efficiency. Using the analytical solution near the tip of a crack, the trial functions in the complex variable moving least-square approxi- mation are extended, and the corresponding approximation function is obtained. And from the minimum potential energy principle, a complex variable meshless method for fracture problems is presented, and the formulae of the complex variable meshless method are obtained. The complex variable meshless method in this paper has greater precision and computational efficiency than the conventional meshless method. Some examples are given.

关键词： moving least-square approximation, complex variable moving least-square approximation, meshless method, complex variable meshless method, fracture.

Boundary element-free method for elastodynamics

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Science China(Physics,Mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1.& PENG Miaojuan2.1. Shanghai {2. of Applied {1. and Mechanics, Shanghai University, Shanghai 2.0072. China 2. Department of Civil Engineering, Shanghai University, Shanghai 2.0072. China Shanghai institute of Applied {1. and Mechanics Shanghai University Shanghai China Department of Civil Engineering Shanghai University Shanghai China

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

Economical cascadic multigrid method (ECMG)

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Science China mathematics 2007年第12期50卷 1765-1780页

作者： Zhong-ci SHI~1.Xue-jun XU~(1.) Yun-qing HUANG~2.~1.LSEC,institute of {1. mathematics,Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 1.0080,China ~2.Hunan Key Laboratory for Computation and Simulation in Science and Engineering,institute for {1. and Applied mathematics,Xiangtan University,Xiangtan 41.1.5,China LSEC Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Institute for Computational and Applied Mathematics Xiangtan University Xiangtan China

In this paper, an economical cascadic multigrid method is proposed. Compared with the usual cascadic multigrid method developed by Bornemann and Deuflhard, the new one requires less iterations on each level, especially on the coarser grids. Many operations can be saved in the new cascadic multigrid algorithms. The main ingredient is the control of the iteration numbers on the each level to preserve the accuracy without over iterations. The theoretical justification is based on the observations that the error reduction rate of an iteration scheme in terms of the smoothing property is no longer accurate while the iteration number is big enough. A new formulae of the error reduction rate is employed in our new algorithm. Numerical experiments are reported to support our theory.

关键词： economical cascadic multigrid method (ECMG), cascadic multigrid method (CMG)