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ON DISCRETE PROJECTION AND NUMERICAL BOUNDARY CONDITIONS FOR THE NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKESEQUATIONS

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Journal of Computational mathematics 2002年第1期20卷 35-56页

作者： Lan Chieh Huang (ICMSEC, academy of mathematics and system {3., chinese academy of sciences, beijing 100080, China) ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the fully implicit Crank Nicholson (CN) schemes and three projection methods for approximate preservation of component-consistency under projection. Transformation from incompressible Navier-Stokes equations to differential algebraic equations CN schemes; Local errors of CN projection methods; Numerical boundary conditions.

关键词： differential algebraic equations discrete projection numerical boundary conditions

THE DUAL MIXED METHOD FOR AN UNILATERAL PROBLEM

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Journal of Computational mathematics 2003年第6期21卷 733-746页

作者： Lie-heng Wang(LSEC, ICMSEC, academy of mathematics and system {3., chinese academy of sciences,beijing 100080, China) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h3.4) and O(h3.2) are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for k = 0 and k = 1 respectively.

关键词： Dual Mixed Method Unilateral Problem.

COMPOSITE-STEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS

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Journal of Computational mathematics 2003年第5期21卷 613-624页

作者： Pu-yan Nie(LSEC, ICMSEC, academy of mathematics and system {3., chinese academy of sciences, beijing 100080, China) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

In a composite-step approach, a step Sk is computed as the sum of two components Uk and hk. The normal component Vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, Sk is a composite step composed of normal component Uk, and tangential component hk.

关键词： Composite-step like approaches Filter methods Equality constraints Sequen- tial quadratic programming(SQP) algorithms Normal component Tangential component Convergence.

SYMPLECTIC COMPUTATION OF HAMILTONIAN systemS (I)

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Journal of Computational mathematics 2002年第3期20卷 267-276页

作者： Yi-fa Tang(LSEC,ICMSEC,academy of mathematics and system {3., chinese academy of sciences,beijing 100080, China) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

Presents information on a study which discussed a symplectic computation of hamiltonian systems. Terms of formal energy of mid-point rule; Analysis of the mathematical pendulum to test the convergence of the formal en... 详细信息

关键词： mid-point rule formal energy

A NOTE ON THE CONSTRUCTION OF SYMPLECTIC SCHEMES FOR SPLITABLE HAMILTONIAN H = H^((1)) + H^((2)) + H^((3.)

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Journal of Computational mathematics 2002年第1期20卷 89-96页

作者： Yi-fa Tang (LSEC ICMSEC academy of mathematics and system {3., chinese academy of sciences, beijing 100080, China) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

In this note, we will give a proof for the uniqueness of 4th-order time-reversible sym- plectic difference schemes of 13.h-fold compositions of phase flows φtH(1) , φtH(2) , φtH(3. with different temporal parameter... 详细信息

关键词： Time-Reversible symplectic scheme Splitable hamiltonian.

Poisson kernel and Cauchy formula of a non-symmetric transitive domain

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Science China mathematics 2010年第7期53卷 1678-1683页

作者： LU Qi-Keng Institute of mathematics, academy of mathematics and {3. Science, chinese academy of sciences, beijing 100190, China Institute of mathematics Academy of Mathematics and System Science Chinese Academy of Sciences Beijing China

In 1965, Lu Yu-Qian discovered that the Poisson kernel of the homogenous domain S m,p,q={Z∈Cm×m, Z1∈Cm×p,Z2 ∈Cq×m|2i1( Z-Z+)-Z1Z1′-Z2′Z2>0} does not satisfy the Laplace-Beltrami equation associated with the Bergman metric when S m,p,q is not symmetric. However the map T0:Z→Z, Z1→Z1 , Z2→Z2 transforms S m,p,q into a domain S I (m, m + p + q) which can be mapped by the Cayley transformation into the classical domains R I (m, m + p + q). The pull back of the Bergman metric of R I (m, m + p + q) to S m,p,q is a Riemann metric ds 2 which is not a Khler metric and even not a Hermitian metric in general. It is proved that the Laplace-Beltrami operator associated with the metric ds 2 when it acts on the Poisson kernel of S m,p,q equals 0. Consequently, the Cauchy formula of S m,p,q can be obtained from the Poisson formula.

关键词： Poisson kernel Cauchy formula

GAUSS-SEIDEL-TYPE MULTIGRID METHODS

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Journal of Computational mathematics 2003年第4期21卷 421-434页

作者： Zhao-hui Huang Qian-shun Chang (academy of mathematics and system {3., chinese academy of sciences, beijing 100080, China) academy of mathematics and system {3. Chinese Academy of Sciences 北京 100080

By making use of the Gauss-Seidel-type solution method, the procedure for computing the interpolation operator of multigrid methods is simplified. This leads to a saving of computational time. Three new kinds of interpolation formulae are obtained by adopting different approximate methods, to try to enhance the accuracy of the interpolatory operator. A theoretical study proves the two-level convergence of these Gauss-Seidel-type MG methods. A series of numerical experiments is presented to evaluate the relative performance of the methods with respect to the convergence factor, CPU-time(for one V-cycle and the setup phase) and computational complexity.

关键词： Multigrid methods Gauss-Seidel solution Interpolation formula Convergence.

CONVERGENCE OF VORTEX METHODS FOR 3.D EULER EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 239-250页

作者： Jia-fu Lin (Institute of system Science, academy of mathematics and system sciences, chinese academy of sciences, beijing, 100080, China School of Mathematical sciences, Peking University, beijing 100871, China) 中科院系统科学所北京 100080

Presents a study on the convergence of vortex methods for the three-dimensional Euler equations in bounded domains. Related studies on the convergence of vortex methods; Formulation of vortex methods; Convergence for ... 详细信息

关键词： Euler equations vortex methods convergence initial-boundary value problem

FOURIER-LEGENDRE PSEUDOSPECTRAL METHOD FOR THE NAVIER-STOKES EQUATIONS

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Journal of Computational mathematics 2000年第3期18卷 225-238页

作者： Jian Li (LSEC, Institute of Computational mathematics and Scientific/Engineering Computing, academy of mathematics and {3. sciences, 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 100080

Constructs a Fourier-Legendre pseudospectral scheme for Navier-Stokes equations with semi-periodic boundary condition. Equation of the scheme; Estimation of errors; Numerical results.

关键词： Navier-Stokes equations Fourier-Legendre pseudospectral method error estimation