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Boundary element-free method for elastodynamics

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Science China(physics,Mechanics & Astronomy) 2005年第6期48卷 641-657页

作者： CHENG Yumin1 & PENG Miaojuan2.1. Shanghai institute of applied{2. and Mechanics, Shanghai University, Shanghai 2.0072. China 2. Department of Civil Engineering, Shanghai University, Shanghai 2.0072. China Shanghai institute of applied{2. and Mechanics Shanghai University Shanghai China Department of Civil Engineering Shanghai University Shanghai China

The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.

关键词： moving least-square approximation, improved moving least-square approximation, elastodynamics, boundary integral equation, meshless method, boundary element-free method, Fourier eigen transform.

Numerical study on scanning radiation acoustic field in formations generated from a borehole

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Science China(physics,Mechanics & Astronomy) 2005年第2期48卷 247-256页

作者： CHE Xiaohua1, ZHANG Hailan1, QIAO Wenxiao2.& JU Xiaodong2.1. institute of Acoustics, Chinese Academy of Sciences, beijing 100080, China 2. Faculty of Natural Resources & Information Technology, University of Petroleum,{2. 102.49, China institute of Acoustics Chinese Academy of Sciences Beijing China Faculty of Natural Resources & Information Technology University of Petroleum Beijing China

Numerical study on scanning radiation acoustic field in formations generated by linear phased array transmitters in a fluid-filled borehole is carried out using a real axis integration (RAI) method. The main lobe width of the acoustic beams and the incident angle on the borehole wall can be controlled by means of adjusting parameters, such as the element number and the delay time between the neighboring array elements of linear phased array transmitter. The steered angle of longitudinal waves generated in the formation satisfies the Snell’s law for plane waves when the incident angle on the borehole wall is less than the first critical angle. When the lobe width of the acoustic beams is narrow and the steered angle is less than the first critical angle, the acoustic field in the formation can be approximately calculated given that the linear phased array is put in the formation without borehole. The technique of scanning radiation acoustic field can be applied to enhancing investigation resolution and signal-to-noise ratio in crosswell seismic survey and borehole acoustic reflection imaging.

关键词： formation, linear phased array transmitter, steered angle, RAI, scanning radiation.

Variation　of　Satellite　Intensity　Factors　with　n　in　the　1s~2.∈lc→1s~2.dnl→1s~2.nl　Dielectronic　Recombination　of　Lithiumlike　Ions

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原子与分子物理学报 1995年第1期 99-106页

作者： Zhao Libo(institute of physics Chinese Academy of Sciences P.O.Box 603{2.)Li Shichang(institute Of applied physics and computational mathematics P. O. Box 8009 beijing 100088)

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关键词： Autoionization Dielectronic recombination Satellite intensity factor

Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation

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Science China mathematics 2011年第3期54卷 555-572页

作者： DENG ShengFu1, GUO BoLing2.& WANG TingChun2.3 1Department of mathematics, Zhanjiang Normal University, Zhanjiang 52.048, China 2.1} of{2. physics and computational mathematics, beijing 100088, China 3 College of Math and physics, Nanjing University of Information Science and Technology, Nanjing 2.0044, China Department of mathematics Zhanjiang Normal University Zhanjiang China institute of applied{2. and computational mathematics Beijing China College of Math and physics Nanjing University of Information Science and Technology Nanjing China

The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

关键词： homoclinic orbits heteroclinic orbits peakon wave solutions compacton wave solutions periodic cusp wave solutions

DIELECTRONIC RECOMBINATION RATE COEFFICIENTS FOR NEONLIKE IONS

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原子与分子物理学报 1996年第1期13卷 17-23页

作者： Zhao Libo Li Shichang(institute of physics. Chinese Academy of Sciences, P. O. Box 603{2.)(Instiute of applied physics and computational mathematics, P. O. Box 8009{2.) 中科院物理所北京 100080 北京应用物理和计算数学所北京 100080

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关键词： dielectronic recombination autoionization rate coefficient

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{2. and Scientific/Engineering Computing, Academy of{2. and System Sciences, Chinese Academy of Sciences, beijing 100080, China Department of applied{2., beijing Broadcasting institute, beijing 10002., China Combinatorial and computational{2. Center, Pohang University of Science and Technology, Phoang 790-784, Republic of Korea institute of computational{2. and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Department of applied mathematics Beijing Broadcasting Institute Beijing China Combinatorial and computational mathematics Center Pohang University of Science and Technology Phoang Republic of 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.

Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

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Science China(physics,Mechanics & Astronomy) 2006年第3期49卷 257-272页

作者： XU Mingyu1 & TAN Wenchang2.1. institute of applied{2., School of Math & System Science, Shandong University, Jinan 2.0100, China 2. State Key Laboratory of Turbulence and Complex Systems & Department of Mechanics and Engineering Science, Peking University, beijing 100871, China institute of applied{2. School of Math & System Science Shandong University Jinan China State Key Laboratory of Turbulence and Complex Systems & Department of Mechanics and Engineering Science Peking University Beijing China

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equa- tions) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern me- chanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.

关键词： fractional operators,intermediate processes,critical phenomena,modern mechanics

NEW DESIGN AND ANALYSIS OF FINITE DIFFERENCE DOMAIN DECOMPOSITION ALGORITHM FOR THE TWO-DIMENSIONAL HEAT EQUATION

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Journal of Systems Science & Complexity 2010年第2期23卷 403-412页

作者： Zhengsu WAN Baolin ZHANG Guangnan CHENG Department of mathematics Itunan Institute of Science and Technology Yueyang 414006 China Laboratory of computational physics Institute of Applied Physics and Computational Mathematics Beijing100088 China.

It is presented in this paper that the new design and its analysis of finite difference domain decomposition algorithms for the two-dimensional heat equation, and the numerical results have shown the stability and accuracy of the algorithms, where SauFyev asymmetric schemes have been used at the interface points. The Algorithm II in this paper has further extended those developed by Dawson and the others, Zhang and Shen.

关键词： Domain decomposition finite difference Saul'yev schemes two-dimensional heat equation

Finite Dimensional Behavior of Global Attractors for Weakly Damping Ginzburg-Landau Equations Coupling with BBM Equations

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Communications in Nonlinear Science and Numerical Simulation 1998年第1期3卷 10-14页

作者： Boling GUO * and Murong JIANG + *(institute of applied{2. and computational mathematics,beijing,100088,China) +(Department of mathematics,Yunnan University,Kunming 650091,China) E mail:guobl@*** Inst. Appl. Phys. and Compl. Math. Beijing 100088 China Department of mathematics Yunnan University Kunming 650091 China

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关键词： dimension attractor Ginzburg Landau equation couped BBM equationIntroduction