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A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection

Numerical Mathematics(Theory,Methods and Applications) 2009年第1期2卷 65-89页

作者： Lin-Bo Zhang State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China.

Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.

关键词： Adaptive refinement bisection tetrahedral mesh parallel algorithm MPI.

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Noether conserved quantities and Lie point symmetries of difference Lagrange-Maxwell equations and lattices

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Chinese Physics B 2009年第7期18卷 2634-2641页

作者：傅景礼聂宁明黄健飞 Jiménez Salvador 唐贻发 Vzquez Luis 赵维加 Institute of Mathematical Physics Zhejiang Sci-Tech University State Key Laboratory of Scientific and Engineering Computing ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of Sciences Department of Mathematics Qingdao University Departamento de Matema'tica Aplicada TTII E.T.S.I.Telecomunicacio'nUniversidad Polit'ecnica de Madrid28040-MadridSpain Departamento de Matemática Aplicada Facultad de MatemáticasInstituto de Matemática Interdisciplinar(IMI)Universidad Complutense de Madrid28040-MadridSpain Departamento de Matemática Aplicada Facultad de InformáticaInstituto de Matemática Interdisciplinar(IMI)Universidad Complutense de Madrid28040-MadridSpain

This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems,which leave invuriant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange Maxwell equations in differences which correspond to mechanico-electrical systems,by adapting existing differential *** particular,it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical *** an application,it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.

关键词： Lagrange Maxwell equation Lie point symmetry discrete mechanico-electrical system conserved quantity

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Several splittings for non-Hermitian linear systems

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Science China Mathematics 2008年第8期51卷 1339-1348页

作者： BAI Zhong-Zhi state key laboratory of scientific/engineering computing,Institute of Computational Mathematics and scientific/engineering computing,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,P.O.Box 2719,Beijing 100080,China 1. State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

For large sparse non-Hermitian positive definite system of linear equations, we present several variants of the Hermitian and skew-Hermitian splitting (HSS) about the coefficient matrix and establish correspondingly several HSS-based iterative schemes. Theoretical analyses show that these methods are convergent unconditionally to the exact solution of the referred system of linear equations, and they may show advantages on problems that the HSS method is ineffective.

关键词： Hermitian and skew-Hermitian splitting non-Hermitian linear system splitting iterative scheme convergence 65F10 65F15 65F50 65N22

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Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

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Chinese Physics B 2008年第11期17卷 3942-3952页

作者：傅景礼陈本永唐贻发付昊 Institute of Mathematical Physics Zhejiang Sci-Tech University Faculty of Mechanical-Engineering & Automation Zhejiang Sci-Tech University State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences China Jingye Engineering Corporation Limited Shenzhen Brach

A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler-Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.

关键词： total variation symplectic-energy-momentum integrator mechanico-electrical system

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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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A posteriori error estimates of constrained optimal control problem governed by convection diffusion equations

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中国高等学校学术文摘·数学 2008年第3期3卷 415-442页

作者： Ningning YAN Zhaojie ZHOU State Key Laboratory of Scientific and Engineering Computing Institute of Systems cienceAcademy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100190China

In this paper,we study a posteriori error estimates of the edge stabilization Galerkin method for the constrained optimal control problem governed by convection-dominated diffusion *** residual-type a posteriori error estimators yield both upper and lower bounds for control u measured in L2-norm and for state y and costate p measured in energy *** numerical examples are presented to illustrate the effectiveness of the error estimators provided in this paper.

关键词： Constrained optimal control problem convection dominated diffusion equation edge stabilization Galerkin method a posteriori error estimate

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A Stochastic Approximation Frame Algorithm with Adaptive Directions

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Numerical Mathematics(Theory,Methods and Applications) 2008年第4期1卷 460-474页

作者： Zi Xu Yu-Hong Dai Department of Mathematics College of Sciences Shanghai University Shang-hai 200444 PR. China. State Key Laboratory of Scientific and Engineering Computing Institute of Com-putational Mathematics and Scientific/Engineering Computing The Academy ofMathematics and Systems Science Chinese Academy of Sciences P.O.Box 2719Beijing 100190 P.R. China.

Stochastic approximation problem is to find some root or extremum of a nonlinear function for which only noisy measurements of the function are available. The classical algorithm for stochastic approximation problem is the Robbins-Monro （RM） algorithm, which uses the noisy evaluation of the negative gradient direction as the iterative direction. In order to accelerate the RM algorithm, this paper gives a flame algorithm using adaptive iterative directions. At each iteration, the new algorithm goes towards either the noisy evaluation of the negative gradient direction or some other directions under some switch criterions. Two feasible choices of the criterions are proposed and two corresponding frame algorithms are formed. Different choices of the directions under the same given switch criterion in the frame can also form different algorithms. We also proposed the simultanous perturbation difference forms for the two frame algorithms. The almost surely convergence of the new algorithms are all established. The numerical experiments show that the new algorithms are promising.

关键词： Stochastic approximation conjugate gradient adaptive directions.

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Message from the IWPAPS 2008 workshop chair

Proceedings - 10th IEEE International Conference on High Per...

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Proceedings - 10th IEEE International Conference on High Performance computing and Communications, HPCC 2008 2008年 xxiv页

作者： Linbo, Zhang State Key Laboratory of Scientific and Engineering Computing CAS China

No abstract available

ISBN: (纸本)9780769533520

No abstract available

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Dynamic Load Balancing on Adaptive Unstructured Meshes

Dynamic Load Balancing on Adaptive Unstructured Meshes

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

作者： Hui Liu State Key Laboratory of Scientific and Engineering Computing CAS Beijing China

In this paper the work on implementing two mesh partitioning algorithms, the refinement-tree based partitioning algorithm and the space-filling curve partitioning algorithm, in the parallel adaptive finite element toolbox PHG (parallel hierarchical grid) is presented. These algorithms are used for both initial mesh partitioning and mesh repartitioning for dynamical load balancing in adaptive finite element computations. In the implementations improved algorithms are designed. Partitioning time and quality of our code are compared with existing publicly available mesh or graph partitioners, including ParMETIS and Zoltan, through some numerical examples.

关键词： Finite element methods Partitioning algorithms Indexes Face Complexity theory Algorithm design and analysis Classification algorithms

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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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