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Cascadic multigrid methods for parabolic problems

Science China mathematics 2008年第8期51卷 1415-1439页

作者： DU Qiang MING PingBing Department of Mathematics Pennsylvania State UniversityUniversity ParkPA 16802USA LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesBeijing 100190China

In this paper,we consider the cascadic multigrid method for a parabolic type *** Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the *** new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular *** error bound sare derived for both smooth and non-smooth *** strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.

关键词： cascadic multigrid method parabolic problem finite element methods backward Euler scheme smoother stability optimal error order optimal complexity 65N30 65N55 65F10

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A New Kind of Multilevel Solver for Second Order Steklov-Poincaré Operators

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17th International Conference on Domain Decomposition Methods

作者： Hu, Qiya LSEC and Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Academy of Sciences Beijing China

ISBN: (纸本)9783540751984

In this paper we are concerned with the construction of a preconditioner for the Steklov-Poincaré operator arising from a non-overlapping domain decomposition method for second-order elliptic problems in three-dimensional domains. We first propose a new kind of multilevel decomposition of the finite element space on the interface associated with a general quasi-uniform triangulation. Then, we construct a multilevel preconditioner for the underlying Steklov-Poincaré operator. The new multilevel preconditioner enjoys optimal computational complexity, and almost optimal convergence rate.

关键词： Domain decomposition methods

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Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions

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Science China mathematics 2008年第8期51卷 1401-1414页

作者： DAI Xiaoying YANG Zhang ZHOU Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Graduate University of Chinese Academy of Sciences Beijing 100190China

Based on a linear finite element space,two symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions are constructed and *** relationships between the finite element method and the finite differe... 详细信息

关键词： eigenvalue finite difference finite element finite volume symmetric

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Interaction Between Line Soliton and Algebraic Soliton for Asymmetric Nizhnik-Novikov-Veselov Equation

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Communications in Theoretical Physics 2008年第6期49卷 1547-1552页

作者： RUAN Hang-Yu LI Zhi-Fang Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.

关键词： variable separation approach the interaction between line soliton and algebraic soliton （2＋1）-dimensional ANNV equation

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Orbital-Free Density Functional Theory for Molecular Structure Calculations

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Numerical mathematics(Theory,Methods and Applications) 2008年第1期1卷 1-28页

作者： Huajie Chen Aihui Zhou LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Graduate University of Chinese Academy of Sciences Beijing 100080 China

We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.

关键词： Density functional theory molecular structure numerical discretization orbital-free

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High-Order Binary Symmetry Constraints of a Liouville Integrable Hierarchy and Its Integrable Couplings

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Communications in Theoretical Physics 2008年第3期49卷 540-544页

作者： CHEN Lan-Xin SUN Ye-Peng ZHANG Jun-Xian China University of Mining and Technology Beijing 100083 China Department of Mathematics Shijiazhuang University Shijiazhuang 050035 China Institute of Computational Mathematics and Scientific Engineering Computing AMSS the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.

关键词： Liouville integrable hierarchy loop algebra symmetry constraint binary nonlinearization integrable coupling

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A Generalized Peierls-Nabarro Model for Curved Dislocations Using Discrete Fourier Transform

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Communications in computational Physics 2008年第7期4卷 275-293页

作者： He Wei Yang Xiang Pingbing Ming School of Mathematical Sciences Peking UniversityBeijing 100871China. Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayKowloonHong Kong. Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System SciencesChinese Academy of SciencesNo.55 Zhong-Guan-Cun East RoadBeijing 100080China.

In this paper,we present a generalized Peierls-Nabarro model for curved dislocations using the discrete Fourier *** our model,the total energy is expressed in terms of the disregistry at the discrete lattice sites on the slip plane,and the elastic energy is obtained efficiently within the continuum framework using the discrete Fourier *** model directly incorporates into the total energy both the Peierls energy for the motion of straight dislocations and the second Peierls energy for kink *** discreteness in both the elastic energy and the misfit energy,the full long-range elastic interaction for curved dislocations,and the changes of core and kink profiles with respect to the location of the dislocation or the kink are all included in our *** model is presented for crystals with simple cubic *** results on the dislocation structure,Peierls energies and Peierls stresses of both straight and kinked dislocations are *** results qualitatively agree with those from experiments and atomistic simulations.

关键词： Dislocation Peierls-Nabarro model Peierls stress Peierls energy dislocation kink.

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Preconditioners for higher order edge finite element discretizations of Maxwell's equations

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Science China mathematics 2008年第8期51卷 1537-1548页

作者： ZHONG LiuQiang1,2,SHU Shi1,2,SUN DuDu3&TAN Lin4 1School of Mathematical and computational Sciences,Xiangtan University,Xiangtan 411105,China 2Hunan Key Laboratory for Computation and Simulation in Science and engineering,Xiangtan 411105,China 3institute of computational mathematics and Scientific/engineering computing,Academy of mathematicsand Systems Science,Graduate University of Chinese Academy of Sciences,Chinese Academy Sciences,P.O.Box 2719,Beijing 100190,China 4Department of Math-Physics,Nanhua University,Hengyang 421001,China 1. School of Mathematical and Computational Sciences Xiangtan University Xiangtan 411105 China 2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan 411105 China 3. Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Graduate University of Chinese Academy of Sciences Chinese Academy Sciences P.O. Box 2719 Beijing 100190 China 4. Department of Math-Physics Nanhua University Hengyang 421001 China

In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's *** present the preconditioners for the first family and second family of higher order N′ed′elec element equations,*** combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform *** also present some numerical experiments to demonstrate the theoretical results.

关键词： preconditioner higher order edge finite element stable decomposition

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Efficient Parallel Adaptive Computation of 3D Time-Harmonic Maxwell's Equations Using the Toolbox PHG

Efficient Parallel Adaptive Computation of 3D Time-Harmonic ...

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IEEE International Conference on High Performance computing and Communications (HPCC)

作者： Tao Cui State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and Systems Science Chinese Academy and Sciences Beijing China

PHG (parallel hierarchical grid) is a scalable parallel adaptive finite element toolbox under active developmentat the State Key Laboratory of Scientific and engineering computing, Chinese Academy of Sciences. This paper demonstrates its application to adaptive finite element computations of electromagnetic problems. Two examples on solving the time harmonic Maxwell's equations are shown. Results of some large scale adaptive finite element simulations with up to 1 billion degrees of freedom and using up to 2048 CPUs are presented.

关键词： Finite element methods Equations Mathematical model Linear systems Harmonic analysis Algorithm design and analysis Laboratories

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Increasing engineering students' awareness to environment through innovative teaching of mathematical modelling

Increasing engineering students' awareness to environment th...

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作者： Klymchuk, Sergiy Zverkova, Tatyana Gruenwald, Norbert Sauerbier, Gabriele School of Computing and Mathematical Sciences Faculty of Design and Creative Technologies Auckland University of Technology Private Bag 92006 Auckland 1142 New Zealand Department of Computational Mathematics Institute of Mathematics Economics and Mechanics Odessa National University Odessa Ukraine Wismar University of Technology Department of Business and Design Wismar Germany Department for Mechanical Engineering/Process and Environmental Engineering Wismar University of Technology Department of Business and Design Wismar Germany

This article presents the results of two studies on using an innovative pedagogical strategy in teaching mathematical modelling and applications to engineering students. Both studies are dealing with introducing non-traditional contexts for engineering students in teaching/learning of mathematical modelling and applications: environment and ecology. The aims of using these contexts were: to introduce students to some of the techniques, methodologies and principles of mathematical modelling for ecological and environmental systems;to involve the students in solving real-life problems adjusted to their region emphasizing the aspects of both survival (short term) and sustainability (long term);to encourage students to pay attention to environmental issues. On one hand, the contexts are not directly related to engineering. On the other hand, the chances are that many graduates of engineering will deal with mathematical modelling of environmental systems in one way or another in their future work because nearly every engineering activity has an impact on the environment. The first study is a parallel study conducted in New Zealand and Germany simultaneously with first-year students studying engineering mathematics. The second study is a case study of the experimental course Mathematical Modelling of Survival and Sustainability taught to a mixture of year 2-5 engineering students in Germany by a visiting lecturer from New Zealand. The models used with the students from both studies had several special features. Analysis of students' responses to questionnaires, their comments and attitudes towards the innovative approach in teaching are presented in the article. © The Author 2008. Published by Oxford University Press on behalf of The institute of mathematics and its Applications. All rights reserved.

关键词： Students

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