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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.

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, institute of {2. Physics and computational mathematics,P.O. Box 8009-2., beijing 100088, china) institute of applied Physics and {2. 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

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 applied Physics and computational mathematics, beijing 100080, china 1. Department of mathematics Beijing Normal University Beijing 100875 China 2. institute of applied Physics and {2. 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.

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 Physics and {2. mathematics,Laboratory of {2. Physics,beijing 100088,china 1. institute of applied Physics and {2. 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

The existence of global solution and their weak limit of generalized Ginzburg-Landau equations in two dimensions

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Progress in Natural Science:Materials International 2006年第5期16卷 458-463页

作者： YANG Ling'e and GUO Boling (Department of mathematics, Foshan University, Foshan 52.000, china {2. of applied Physics and computational mathematics, beijing 100088, china) [a]Department of mathematics Foshan University Foshan China [b]institute of applied Physics and {2. mathematics Beijing China

By the uniform a priori estimate of solution about parameters, we prove the existence of global solution and inviscid lim- it to a generalized Ginzburg-Landau equations in two dimensions. We also prove that the solution to the Ginzburg-Landau equations converges to the weak solution to the derivative nonlinear Schrodinger equations.

关键词： Ginzburg-Landau equation global solution inviscid limits.

DECAY OF GLOBAL SOLUTIONS OF TWO NONLINEAR EVOLUTION EQUATIONS

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Acta Mathematicae Applicatae Sinica 1997年第1期13卷 23-32页

作者： GUO BOLING ZHANG LINGHAI(institute of applied Physics and {2. mathematics, beijing 100088, china) institute of applied Physics and {2. mathematics Beijing China

We study the decay of solutions of two nonlinear evolution equations: the Benjamin-OnoBurgers and the Schrodinger-Burgers equations. We establish sharp rates of L2.decay of global solutions to these problems, with initial data Uo(x)∈L1∩L2. The decay results of the solutions follow from the a priori L2.integral estimstes and the Fourier transform. The standard argument relies on a technique that involves the splitting of the phase space into two time-dependent subdomains.

关键词： Decay estimates nonlinear evolution equations

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 Physics and {2. mathematics, beijing 100088, china 2. Department of Modern Mechanics, University of Science and Technology of china, Hefei 2.002., china) institute of applied Physics and {2. 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.

Ab initio study of a Y-doped Σ31 grain boundary in alumina

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Science china(Physics,Mechanics & Astronomy) 2008年第11期51卷 1607-1615页

作者： CHEN Jun, XU Yun, CHEN DongQuan & ZHANG JingLin Laboratory of computational Physics, institute of {2. Physics and computational mathematics, beijing 100088, china 1. Laboratory of computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China

The atomic structures and energetics of clean and Y-doped general grain boundary (GB) Σ31/(0001) models in α-Al2.3 are studied by a series of high precision ab initio calculations. A large supercell with 700 atoms and periodic boundary conditions is adopted for undoped and Y-doped GB with different substitution sites and con-centrations. It is shown that Y atoms preferably segregate to the central column of the 7-member Al ring. This is explained as more favorable bond formation for Y in this position and lower GB energy. The calculated GB formation energy for the clean and Y-doped cases is respectively 3.99 and 3.67 J/m2. On the average, the GB region in Σ31 has a slightly lower charge density than the bulk crystalline region. In addtition, the GB induces a long ranged asymmetric electrostatic potential distri-bution on each side of the grain boundary.

关键词： alumina grain boundary Y-doped ab initio

Global Attractors for the Initial Value Problems of Cohn-Hilliard Equations on Compact Manifolds

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Acta Mathematica Sinica,English Series 1996年第3期12卷 314-325页

作者： Guo Boling Wang Youde, institute of applied Physics and {2. mathematics beijing, 100088 china institute of applied Physics and {2. mathematics Beijing China

In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems we prove the existence of global attractors for the initial value problem of Cahn-Hilliard equations. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors are also obtained.

关键词： Global Attractors for the Initial Value Problems of Cohn-Hilliard Equations on Compact Manifolds