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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

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

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 Department of mathematics Wuhan University Wuhan China Laboratory of computational physics Institute of Applied Physics and Computational Mathematics 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, {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

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@*** institute of applied {2. and computational mathematics Beijing 100088 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

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 institute of applied {2. and computational mathematics Laboratory of Computational Physics Beijing 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

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 High Performance computational Center in institute of {2. physics and computational mathematics Beijing China Laboratory of computational physics in {2. 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 102. processors.

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

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, {2. of applied physics and computational mathematics, beijing 100088, china Laboratory of computational physics Institute of Applied Physics and Computational Mathematics Beijing 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

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) Laboratory of computational physics Institute of Applied Physics and Computational Mathematics Beijing 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