2003年, 第21卷, 第1期　刊出日期：2003-01-15

  

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  CONGRATULATIONS TO ACADEMICIAN ZHOU YULIN ON HIS 80~(th) BIRTHDAY

  Journal of Computational Mathematics. 2003, 21(1): 1-004.

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  Editorial Committee of Journal of Computational Mathematics Editorial Committee of Mathematica Numerica Sinica Editorial Committee of Journal on Numerical Methods and Computer ApplicationsEditorial Committee of Chinese Journal of Numerical Mathematics
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  ARTIFICIAL BOUNDARY CONDITIONS FOR

  Li Juan DING(1),Hai Yan JIANG(1),Zhen Huan TENG(2)

  Journal of Computational Mathematics. 2003, 21(1): 5-014.

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  This paper mainly designs artificial boundary conditions for "vortex in cell" method in solving two-dimensional incompressible inviscid fluid under two conditions: one is with periodical initial value in one direction and the other with compact supported initial value. To mimic the vortex motion, Euler equation is transformed into vorticity-stream function and the technique of vortex in cell is applied incorporating with the artificial boundary conditions.
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  EXACT NONREFLECTING BOUNDARY CONDITIONS FOR AN ACOUSTIC PROBLEM IN THREE DIMENSIONS

  Hou De HAN,Chun Xiong ZHENG

  Journal of Computational Mathematics. 2003, 21(1): 15-024.

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  In this paper, nonreflecting artificial boundary conditions are considered for an acoustic problem in three dimensions. With the technique of Fourier decomposition under the orthogonal basis of spherical harmonics, three kinds of equivalent exact artificial oundary conditions are obtained on a spherical artificial boundary. A numerical test is presented to show the performance of the method.
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  NONCONFORMING QUADRILATERAL ROTATED ELEMENT FOR REISSNER-MINDLIN PLATE

  Jun HU,Ping Bing MING,Zhong Ci SHI

  Journal of Computational Mathematics. 2003, 21(1): 25-032.

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  In this paper, we extend two rectangular elements for Reissner-Mindlin plate [9] to the quadrilateral case. Optimal H and L error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition.
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  HIGH ACCURACY NUMERICAL METHOD OF THIN-FILM PROBLEMS IN MICROMAGNETICS

  Zhong Yi HUANG

  Journal of Computational Mathematics. 2003, 21(1): 33-040.

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  In this paper, a new high accuracy numerical method for the thin-film problems of micron and submicron size ferromagnetic elements is proposed. For the computation of stray field, we use the finite element method(FEM) by introducing a semi-discrete artificial boundary condition [1,2].In our numerical experiments about the domain patterns and their movement, we can see that the results are accordant to that of experiments and other numerical methods. Our method are very convenient to deal with arbitrary shape of thin films such as a polygon with high accuracy.
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  THE UNCONDITIONAL CONVERGENT DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR QUASILINEAR PARABOLIC SYSTEMS WITH TWO DIMENSIONS

  Long Jun SHEN,Guang Wei YUAN

  Journal of Computational Mathematics. 2003, 21(1): 41-052.

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  In the present work we are going to solve the boundary value problem for the quasilinear parabolic systems of partial differential equations with two space dimensions by the finite difference method with intrinsic parallelism. Some fundamental behaviors of general finite difference schemes with intrinsic parallelism for the mentioned problems are studied. By the method of apriori estimation of the discrete solutions of the nonlinear difference systems, and the interpolation formulas of the various norms of the discrete functions and the fixedpoint technique in finite dimensional Euclidean apace, the existence of the discrete vector solutions of the nonlinear difference system with inreinsic parallelism are proved. Moreover the convergence of the discrete vector solutions of these difference schemes to th eunique generalized solution of the original quasilinear parabolic problem is proved.
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  MULTIVARIATE FOURIER SERIES OVER A CLASS OF NON TENSOR-PRODUCT PARTITION DOMAINS

  Jia Chang SUN

  Journal of Computational Mathematics. 2003, 21(1): 53-062.

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  This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity, orthogonality of Fourier basis system, partial sum of Fourier siries and its approximation behavior, can be moved on the new non tensor-product partition case.
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  THE UNCONDITIONAL STABLE DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR TWO DIMENSIONAL SEMILINEAR PARABOLIC SYSTEMS

  Guang Wei YUAN,Long Jun SHEN

  Journal of Computational Mathematics. 2003, 21(1): 63-070.

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  In this paper we are going to discuss the difference schemes with intrinsic parallelism for the boundary value problem of the two dimensional semilinear parabolic systems. The unconditional stability of the general finite difference schemes with intrinsic parallelism is justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems in the discrete $W^{(1,2)}_2$ norms. Then the uniqueness of the discrete vector solution of this difference scheme follows as the consequence of the stability.
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  LINEAR SYSTEMS ASSOCIATED WITH NUMERICAL METHODS FOR CONSTRAINED OPITMIZATION

  Y. YUAN

  Journal of Computational Mathematics. 2003, 21(1): 71-084.

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  Linear systems associated with numerical methods for constrained optimization are discussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods or trust region methods for constrained optimization van be expressed as similar systems of linear epuations. All these linear systems can be viewed as some kinds of approximation to the linear system derived by the Lagrange-Newton method. Some properties of these linear systems are analyzed.
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  MULTI-SCALE METHODS FOR INVERSE MODELING IN 1-D MOS CAPACITOR

  Ping Wen ZHANG(1),Yi SUN(1),Hai Yan JIANG(1),Wei YAO(2)

  Journal of Computational Mathematics. 2003, 21(1): 85-100.

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  In this paper, we investigate multi-scale methods for the inverse modeling in 1-D Metal-Oxide-Silicon (MOS) capacitor. First, the mathematical model of the device is given and the numerical simulation for the forward problem of the model is implemented using finite element method with adaptive moving mesh. Then numerical analysis of these parameters in the model for the inverse problem is presented. Some matrix analysis tools are applied to explore the parameters' sensitivities. And third, the parameters are extracted using Levenberg-Marquardt optimization method. The essential difficulty arises from the effect of multi-scale physical difference of the parameters. We explore the relationship between the parameters' sensitivities and the sequence for optimization, which can seriously affect the final inverse modeling results. An optimal sequence can effivciently overcome the multi-scale problem of these parameters.Numerical experiments show the efficiency of the proposed methods.
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  HIGH-ORDER I-STABLE CENTERED DIFFERENCE SCHEMES FOR VISCOUS COMPRESSIBLE FLOWS

  Wei Zhu BAO(1),Shi JIN(2)

  Journal of Computational Mathematics. 2003, 21(1): 101-112.

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  In this paper we present high-order I-stable centered difference schemes for the numerical simulation of viscous compressible flows. Here I-stability refers to time discretizations whose linear stability regions contain part of the imaginary axis. This class of schemes has a numerical stability independent of the cell-Reynolds number Rc, thus allows one to simulate high Reynolds number flows with relatively larger Rc, or coarser grids for a fixed Rc. on the other hand, Rc cannot be arbitrarily large if one tries to obtain adequate numerical resolution of the iscous behavior. We investigate the behavior of high-order I-stable schemes for Burgers' equation and the compressible Navier-stokes equations. Wedemonstrate that, for the second order scheme, Rc$\leq$6. Our study indicates that the fourth order schemeis preferable: better accuracy, higher resolution, and larger cell-Reynolds numbers.