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Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science china mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1 ZHANG Baolin~(1,2. & LIU Yang~1 1. Department of mathematics,Wuhan University,Wuhan 430072.china 2. Laboratory of {2. physics,institute of applied physics and {2. mathematics,Beijing 100088. china 1. Department of mathematics Wuhan University 430072 Wuhan China 2. Laboratory of computational physics Institute of Applied Physics and Computational Mathematics 100088 Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.

CONVERGENCE FROM AN ELECTROMAGNETIC FLUID SYSTEM TO THE FULL COMPRESSIBLE MHD EQUATIONS

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Acta Mathematica Scientia 2018年第3期38卷 805-818页

作者： Xin XU institute of applied {2. and computational mathematics institute of applied {2. and computational mathematics Beijing 100088China

We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t = 0. The strong convergence results only hold outside the initial layer.

关键词： Zero dielectric constant limit full compressible magnetohydrodynamic equation initial layer

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., Beijing 100080, china 1. Department of mathematics Beijing Normal University Beijing 100875 China 2. institute of applied physics 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.

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

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

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

A numerical study on Rayleigh-Taylor instability of aluminum plates driven by detonation

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Science china(physics,Mechanics & Astronomy) 2010年第2期53卷 195-198页

作者： HE ChangJiang,ZHOU HaiBing & HANG YiHong institute of applied {2. and computational mathematics,Laboratory of computational {2.,Beijing 100088,china 1. institute of applied {2. and computational mathematics Laboratory of Computational Physics Beijing 100088 China

The authors,using elastic-plastic hydrodynamic code,present the Rayleigh-Taylor (RT) instability of Al plates driven by high-explosive detonation. Our numerical study assumes the material is fluid,or it is an elastic-plastic solid,and we compare the results of these simulations with the experimental data. For the numerical simulation of Rayleigh-Taylor instability of the metal driven by high-explosive detonation,the elastic-plastic effect must be assumed. The result of the simulation is different from the experiment,using only equation of state. However,the growth of perturbation agrees well with the measured growth under the second assumption. There is a cutoff wavelength for RT instability of the metal. The growth of perturbation is stable for short wavelength. The growth increases rapidly as the wavelength increases.

关键词： interface instability elastic-plastic numerical simulation

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.

Dissipative Transitions between Bloch Bands

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Journal of Materials Science & Technology 1999年第4期15卷 363-365页

作者： Xangeng ZHAO(institute of applied {2. and computational mathematics, Beijing 100088, china)E-mail:zhaoxg@*** Inst Appl Phys & Computat Math Beijing 100088 Peoples R China

We study the effect of dissipative transport of two-band systems in a static electric field. With the help of numerical solutions of a stochastic Liouville equation for the density matrix, we find that the Markoffian dephasing will take electrons which are initially located in one band to equal population of the two bands, instead of undergoing Zener resonance, as they do in the absence of scattering.

关键词： Rev Dissipative Transitions between Bloch Bands