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Journal of computational mathematics 2000年第5期18卷 467-480页

作者： Hua-zhong Tang , Hua-mu Wu (state key laboratory of scientific and engineering computing, institute of computational mathematics, chinese academy of sciences, beijing 100080, china) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

This paper continues to construct and study the explicit compact (EC) schemes for conservation laws. First, we axtend STCE/SE method on non-staggered grid, which has same well resolution as one in [1], and just requires half of the computational works. Then, we consider some constructions of the EC schemes for two-dimensional conservation laws, and some 1D and 2D numerical experiments are also given.

关键词： Conservation laws Compact scheme Shock-Capturing method Euler equations.

Numerical simulation of Richtmyer-Meshkov instability

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Science china mathematics 2004年第Z1期47卷 234-244页

作者： FU Dexun, MA Yanwen, ZHANG Linbo & TIAN Baolinstate key laboratory of Nonlinear Mechanics, institute of Mechanics, chinese academy of sciences, beijing 100080, china state key laboratory of scientific and engineering computing, institute of computational mathematics, chinese academy of sciences, beijing 100080, china state key laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences Beijing China state key laboratory of scientific and engineering computing Institute of Computational Mathematics Chinese Academy of Sciences Beijing China

The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.

关键词： R-M instability, direct numerical simulation, shock-interface interaction.

CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS CASCADIC MULTIGRID FOR PARABOLIC PROBLEMS

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Journal of computational mathematics 2000年第5期18卷 551-560页

作者： Zhong-ci Shi, Xue-jun Xu (state key laboratory of scientific and engineering computing, institute of computational mathematics, chinese academy of sciences, beijing 100080, china) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

In this paper, we develop the cascadic multigrid method for parabolic problems. The optimal convergence accuracy and computation complexity are obtained.

关键词： Cascadic multigrid Finite element Parabolic problem.

ON THE ERROR ESTIMATE OF LINEAR FINITE ELEMENT APPROXIMATION TO THE ELASTIC CONTACT PROBLEM WITH CURVED CONTACT BOUNDARY

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Journal of computational mathematics 2000年第6期18卷 561-566页

作者： Lie-heng Wang (state key laboratory of scientific and engineering computing, institute of computational mathematics, academy of mathematics and System sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h[sup ?]) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while *** et. al. Obtained the error bound O(h[sup ?]) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2]). [ABSTRACT FROM AUTHOR]

关键词： contact problem finite element approximation

PARALLEL CHAOTIC MULTISPLITTING ITERATIVE METHODS FOR THE LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEM

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Journal of computational mathematics 2001年第3期19卷 281-292页

作者： Zhong-zhi Bai (state key laboratory of scientific/engineering Competing institute of computational mathematics and scientific/engineering computing, academy of mathematics and Systems sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学与工程计算数学所科学与工程计算国家重点实验室北京 100080

Focuses on a study which presented a parallel chaotic multisplitting method for solving the large sparse linear complementarity problem. Preliminaries of the study; Equations of the parallel chaotic multisplitting met... 详细信息

关键词： linear complementarity problem matrix multisplitting chaotic iteration relaxed method convergence property

A SCALED CENTRAL PATH FOR LINEAR PROGRAMMING

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Journal of computational mathematics 2001年第1期19卷 35-40页

作者： Ya-xiang Yuan (state key laboratory of scientific and engineering computing, institute of computational mathematics and scientific/engineering computing chinese academy of sciences, beijing 100080, china) 中科院计算数学与工程计算数学所科学与工程计算国家重点实验室北京 100080

Proposes a central path in interior point methods which scales the variables. Role of the central path in interior point methods; Methodology; Results and discussion.

关键词： central path interior point methods linear programming

CORRECTION METHODS FOR STEADY INCOMPRESSIBLE FLOWS

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Journal of computational mathematics 1999年第4期17卷 419-424页

作者： Jian Li(state key laboratory of scientific and engineering computing, ICMSEC, chinese academy of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京

Correction methods for the steady semi-periodic motion of incompressible fluid are investigated. The idea is similar to the influence matrix to solve the lack of vorticity boundary conditions. For any given boundary condition of the vorticity, the coupled vorticity-stream function formulation is solved. Then solve the governing equations with the correction boundary conditions to improve the solution. These equations are numerically solved by Fourier series truncation and finite difference method. The two numerical techniques are employed to treat the non-linear terms. The first method for small Reynolds number R equals 0-50 has the same results as that in M. Anwar and S.C.R. Dennis' report. The second one for R greater than 50 obtains the reliable results. (Author abstract) 4 Refs.

关键词： incompressible flow vorticity stream function numerical solution

EXPERIMENTAL STUDY OF THE ASYNCHRONOUS MULTISPLITTING RELAXATION METHODS FOR THE LINEAR COMPLEMENTARITY PROBLEMS

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Journal of computational mathematics 2002年第6期20卷 561-574页

作者： Zhong-zhi Bai(state key laboratory of scientific/engineering computing, institute of computational mathematicsand scientific/engineering computing, academy of mathematics and System sciences, chineseacademy of sciences, beijing 100080, china) institute of computational mathematics and scientific/engineering computing Academy of Mathematics and System Sciences Chinese Academy of Sciences State Key Laboratory of Scientific/Engineering ComputingCAS 北京 100080

Presents a study of the numerical behaviors of the relaxed asynchronous multisplitting methods for linear complementarity problems by solving typical problems from practical applications on a real multiprocessor system. Description of the tested problems and computing environment used in the computations; Description of the asynchronous multisplitting unsymmetric accelerated overrelaxation method; Discussion of results.

关键词： linear complementarity problem matrix multisplitting asynchronous iterative methods numerical experiment

THE OVERLAPPING DOMAIN DECOMPOSITION METHODFOR HARMONIC EQUATION OVER EXTERIORTHREE-DIMENSIONAL DOMAIN

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Journal of computational mathematics 2000年第1期18卷 83-94页

作者： Ji-ining Wu De-bao Yu(state key laboratory of scientific and engineering computing, institute of computationalmathematics and scientific/engineering computing, chinese academy of sciences, beijing100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents a study which applied the overlapping domain decomposition method based on the natural boundary reduction to solve the boundary value problem of harmonic equation over domain. Methods to solve boundary value ... 详细信息

关键词： DDM exterior harmonic problem natural boundary reduction

VARIATIONS ON A THEME BY EULER

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Journal of computational mathematics 1998年第2期16卷 97-106页

作者： Kang Feng Dao-liu Wang (state key laboratory of scientific and engineering computing, ICMSEC, chinese academy of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京

The oldest and simplest difference scheme is the explicit Euler method. Usually, it is not symplectic for general Hamiltonian systems. It is interesting to ask: Under what conditions of Hamiltonians, the explicit Euler method becomes symplectic? In this paper, we give the class of Hamiltonians for which systems the explicit Euler method is symplectic. In fact, in these cases, the explicit Euler method is really the phase how of the systems, therefore symplectic. Most of important Hamiltonian systems can be decomposed as the summation of these simple systems. Then composition of the Euler method acting on these systems yields a symplectic method, also explicit. These systems are called symplectically separable. Classical separable Hamiltonian systems are symplectically separable. Especially, we prove that any polynomial Hamiltonian is symplectically separable.

关键词： Hamiltonian systems symplectic difference schemes explicit Euler method nilpotent symplectically separable