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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 Mathematics, Beijing Normal University, Beijing 100875, china 2..institute of {2. physics and computational Mathematics, Beijing 100080, china 1. Department of Mathematics Beijing Normal University Beijing 100875 China 2..institute of applied {2. and computational Mathematics Beijing 100080 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. institute of applied {2. and computational Mathematics, Beijing 100088, china 2. Department of Modern Mechanics, University of Science and Technology of china, Hefei 2.002., china) institute of applied {2. and computational Mathematics 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.

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 institute of {2. physics and computational Mathematics,Beijing 100094,china 2.Laboratory of computational physics in institute of {2. physics and computational Mathematics,Beijing 100094,china 1. High Performance computational Center in institute of {2. physics and computational Mathematics Beijing 100094 China2. Laboratory of Computational Physics in Institute of Applied Physics and Computational Mathematics Beijing 100094 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 102. processors.

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

FINITE DIFFERENCE METHOD WITH NONUNIFORM MESHES FOR QUASILINEAR PARABOLIC SYSTEMS

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Journal of computational Mathematics 1997年第4期15卷 289-310页

作者： Yu-lin Zhou (Labomtory of computational physics, Center of Nonlinear Studies, {2. of applied physics and computational Mathematics, Beijing, china) 北京应用物理和计算数学所北京

The analysis of the finite difference schemes with nonuniform meshes for the problems of partial differential equations is extremely rare even for very simple problems and even for the method of fully heuristic character. In the present work the boundary value problem for quasilinear parabolic system is solved by the finite difference method with nonuniform meshes. By using of the interpolation formulas for the spaces of discrete functions with unequal meshsteps and the method of a priori estimation for the discrete solutions of finite difference schemes with nonuniform meshes, the absolute and relative convergence of the discrete solutions of the finite defference scheme are proved. The limiting vector function is just the unique generalized solution of the original problem for the parabolic system.

关键词： Boundary value problems Convergence of numerical methods Estimation Heuristic methods Interpolation Partial differential equations

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 {2., Mianyang 62.900, china 2..institute of applied {2. and computational Mathematics, Beijing 100088, china 1. institute of applied Electronics Chinese Academy of Engineering Physics 621900 Mianyang China 2..institute of applied {2. and computational Mathematics 100088 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 15ns FWHM, and its beam-wave power conversion efficiency is about 17%.

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

A MULTIGRID METHOD FOR NONLINEAR PARABOLIC PROBLEMS

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Journal of computational Mathematics 1996年第4期14卷 363-382页

作者： x.J. Yu(Laborutory of computational physics, {2. of applied physics and computationalMathematics, Beijing, china) INST APPL PHYS & COMPUTAT MATH LAB COMPUTAT PHYSBEIJINGPEOPLES R CHINA

The multigrid algorithm in [13] is developed for solving nonlinear parabolic equations arising from the finite element discretization. The computational cost of the algorithm is approximate O(NkN) where N-k is the dim... 详细信息

关键词： Th Math A MULTIGRID METHOD FOR NONLINEAR PARABOLIC PROBLEMS UC

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 10002., china 2. Center for Nonlinear Studies, {2. of applied physics and computational Mathematics, Beijing 100088, 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

AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS

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Journal of computational Mathematics 2003年第2期21卷 125-134页

作者： Xia Cui(Laboratory of computational physics, {2. of applied physics and computational Mathematics,P.O. Box 8009-2., Beijing 100088, china) institute of applied {2. and computational Mathematics National Laboratory of Computational Physics 北京 100088

AD (Alternating direction) Galerkin schemes for d-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized, and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations, difficulty coming from non-linearity is treated, and optimal H1 and L2.convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis.

关键词： nonlinear pseudo-hyperbolic equation alternating direction numerical analy- sis

GENERAL INTERPOLATION FORMULAS FOR SPACES OF DISCRETE FUNCTIONS WITH NONUNIFORM MESHES

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Journal of computational Mathematics 1995年第1期13卷 70-93页

作者： Zhou Yu-lin(institute of applied {2. and computational Mathematics, Beijing, china ) 北京应用物理和计算数学所北京

The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.

关键词： Discrete functions Interpolation Mathematical constants Partial differential equations Difference quotients Real lines Finite difference methods Mathematical theorems Ratios Engineering