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Lattice Boltzmann simulation for the spiral waves in the excitable medium

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Communications in Nonlinear Science and Numerical Simulation 2000年第4期5卷 147-150页

作者： Guangwu YAN and Li YUAN (Institute of computational mathematics, academy of Mathamatics and {3. sciences, Chinese academy of sciences, Beijing 100080, china e-mail: lyuan＠*** department of mathematics, Jilin university, Chanychun 13.023. Ch Inst. of computational mathematics Acad. of Math. and System Sciences Chinese Academy of Sciences Beijing 100080 China department of mathematics Jilin University Changchun 130023 China

We propose lattice Boltzmann method for the spiral waves. Using Chapman-Enskog expansion and multiscales technique, we obtain equilibrium distribution functions of the model. As an example, we simulate the Selkov rea... 详细信息

关键词： lattice Boltzmann method excitable medium Selkov system spiral waveL

Central simple Poisson algebras

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Science china mathematics 2004年第2期47卷 245-263页

作者： SU Yucai & XU Xiaopingdepartment of mathematics, Shanghai Jiaotong university, Shanghai 20003.,{3. Institute of mathematics, academy of mathematics and system sciences, Chinese academy of sciences, Beijing 100080,{3. 1.department of mathematics Shanghai Jiaotong University 200030 Shanghai China 2.Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic *** Lie algebra structures of these Poisson algebras are in general not finitely-graded.

关键词： Poisson algebra, locally-finite operator, derivation, finitely-graded, isomorphism class.

On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R^(2*)

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Science china mathematics 2004年第z1期47卷 181-189页

作者： WU Zhengpeng, KANG Tong & YU DehaoInstitute of computational mathematics and Scientific/Engineering Computing, academy of mathematics and system sciences, Chinese {3. of sciences, Beijing 100080, china department of Applied mathematics, Beijing Broadcasting Institute, Beijing 100024, china Combinatorial and computational mathematics Center, Pohang university of Science and Technology, Phoang 790-784, Republic of Korea Chinese Acad Sci Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp Beijing 100080 Peoples R China Beijing Broadcasting Inst Dept Appl Math Beijing 100024 Peoples R China Pohang Univ Sci & Technol Combinatorial & Computat Math Ctr Phoang 790784 South Korea

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with *** provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.

关键词： natural boundary integral method, finite element method, coupling method, error estimate.

Local and global behavior for algorithms of solving equations

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Chinese Science Bulletin 2001年第6期46卷 441-448,529页

作者： WANG Xinghua & LI Chongdepartment of mathematics, Zhejiang university, Hangzhou 3.0028,{3. academy of mathematics and system sciences, Chinese academy of sciences, Beijing 100080,{3. department of Applied mathematics, Southeast university, Nanjing 210096,{3. department of mathematics Zhejiang University Hangzhou China academy of mathematics and system {3. Chinese Academy of Sciences Beijing China department of Applied mathematics Southeast University Nanjing China

The theory of 'point estimate' and the concept of 'general convergence', which were put forward by Smale in order to investigate the complexity of algorithms for solving equations, have been producing a deep impact on the research about the local behavior, the semi-local behavior and the global behavior of iteration methods. The criterion of point estimate introduced by him not only provides a tool for quantitative analysis of the local behavior but also motivates the establishing of the unified determination for the semi-local behavior. Studying the global behavior in the view of discrete dynamical system will lead to many profound research subjects and open up a rich and colorful prospect. In this review, we will make a summarization about the research progress and some applications in nonsmooth optimizations.

关键词： Banach space nonlinear operator equation point esti-mate Sullivan domain nonsmooth optimization.

CONVERGENCE RATES TO TRAVELLING WAVES FOR A RELAXATION MODEL WITH LARGE INITIAL DISTURBANCE

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Acta Mathematica Scientia 2004年第2期24卷 213-227页

作者：张辉赵引川 departmentofmathematics BeijingNormalUniversityBeijing100825China

This paper is concerned with the convergence rates to travelling waves for a relaxation model with general flux functions. Compared with former results in this direction, the main novelty in this paper lies in the fact that the initial disturbance can be chosen large in suitable norm. Our analysis is based on the L^1-stability results obtained by C. Mascia and R. Natalini in [12].

关键词： Convergence rate relaxation travelling waves large initial disturbance

Tree wavelet approximations with applications

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Science china mathematics 2005年第5期48卷 680-702页

作者： XU Yuesheng & ZOU Qingsong department of mathematics, Syracuse university, Syracuse, NY 13.44, USA Institute of mathematics, academy of mathematics and system sciences, Chinese academy of sciences, Beijing 100080, china department of Scientific Computing and Computer Science, Zhongshan university, Guangzhou 510275, china 1. department of mathematics Syracuse University 13244 Syracuse NY USA 2. Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 3. department of Scientific Computing and Computer Science Zhongshan University 510275 Guangzhou China

We construct a tree wavelet approximation by using a constructive greedy scheme (CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.

关键词： greedy algorithms tree wavelet approximations Besov spaces.

ON THE SOLVABILITY OF GENERAL LINEAR METHODS FOR DISSIPATIVE DYNAMICAL systemS

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Journal of computational mathematics 2000年第6期18卷 633-638页

作者： Ai-guo Xiao (department of mathematics, Xiangtan university, Xiangtan 411105,{3..) (Institute of computational mathematics and Scientific/Engineering Computing, Chinese academy of sciences, Beijing 100080,{3.) 湘潭大学湖南湘潭 4111105

The main purpose of the present paper is to examine the existence and local uniqueness of solutions of the implicit equations arising in the application of a weakly algebraically stable general linear methods to dissipative dynamical systems, and to extend the existing relevant results of Runge-Kutta methods by Humphries and Stuart(1994). [ABSTRACT FROM AUTHOR]

关键词： general linear methods dissipative dynamical systems weak algebraic stability solvability

SINE TRANSFORM MATRIX FOR SOLVING TOEPLITZ MATRIX PROBLEMS

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Journal of computational mathematics 2001年第2期19卷 167-176页

作者： Li-zhi Cheng (department of mathematics & system {3., National university of Defence Technology, Changsha 410073. china) 国防科技大学湖南长沙 410073

Provides information on a study which discussed the properties of eigenvalues for the solutions of symmetric positive definite Toeplitz systems, skew circulant and sine transform based properties. Eigenvalues of various preconditioners; Design of positive sine transform based preconditioners; Clustering property of the preconditioners; Numerical results.

关键词： preconditioner Toeplitz systems the fast sine transform conjugate gradient algorithm

A mixed finite element method for the unilateral contact problem in elasticity

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Science china mathematics 2006年第4期49卷 513-524页

作者： HUA Dongying & WANG Lieheng The First Fundamental department, Beijing Information Technology Institute, Beijing 100101, china Institute of computational {3. and Scientific/Engineering Computing, academy of mathematics and system sciences, Chinese academy of sciences, Beijing 100080, china 1. The First Fundamental department Beijing Information Technology Institute Beijing 100101 China 2. Institute of computational mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

In this paper, we provide a new mixed finite element approximation of the variational inequality resulting from the unilateral contact problem in elasticity. We use the continuous piecewise P2-P1 finite element to approximate the displacement field and the normal stress component on the contact region. Optimal convergence rates are obtained under the reasonable regularity hypotheses. Numerical example verifies our results.

关键词： unilateral contact problem, mixed finite element method.