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Convergence analysis of the adaptive finite element method with the red-green refinement

Science China Mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2,? & SHI ZhongCi 1 1 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 100190, China 2 key laboratory of Mathematics and Applied Mathematics (Peking University), Ministry of Education and School of mathematical Sciences, Peking University, Beijing 100871, China 3 Graduate University of Chinese Academy of Sciences, Beijing 100190, China 1. 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 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Mathematics and Applied Mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

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Multicast grooming algorithm in waveband switching optical networks

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Journal of Lightwave Technology 2010年第19期28卷 2856-2864页

作者： Guo, Lei Wang, Xingwei Cao, Jiannong Hou, Weigang Pang, Lan College of Information Science and Engineering Northeastern University Shenyang 110819 China Department of Computing Hong Kong Polytechnic University Hong Kong Hong Kong State Key Laboratory of Advanced Optical Communication Systems and Networks Peking University Beijing 100871 China

In optical Wavelength-Division-Multiplexing (WDM) networks, multicast becomes more and more popular to provide high-speed communication between one point and multiple points. At the same time, the ports of Optical Cross-Connect (OXC) are greatly enhanced with the increasing number of wavelengths in fibers, and then the waveband switching technique is proposed to save the ports and reduce the cost of OXC. However, current waveband grooming algorithms are all limited in unicast. To achieve the multicast communication and meanwhile save the ports of OXC, we need to solve the multicast grooming, routing and wavelength/waveband assignment problem which is the HP-hard. In this paper, we propose a heuristic algorithm named Integrated Multicast Waveband Grooming (IMWG) based on Multicast Layered Auxiliary Graph (MLAG) that includes a Virtual Topology Layer (VTL) and multiple Waveband-Plane Layers (WPLs) to support the single-hop, multi-hop and hybrid multicast waveband grooming. For each demand, IMWG first computes a single-hop or multi-hop grooming waveband-tree on VTL. If the grooming waveband-tree cannot be found on VTL, IMWG computes a new waveband-tree on WPL. If the new waveband-tree cannot be found on WPL, IMWG computes a hybrid grooming waveband-tree on MLAG. Simulation results show that, compared with other algorithms, IMWG is able to obtain better performances. © 2010 IEEE.

关键词： Multicasting

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Mammalian target of rapamycin regulates murine and human cell differentiation through STAT3/p63/Jagged/Notch cascade

Mammalian target of rapamycin regulates murine and human cel...

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第一届国家癌症中心学术年会

作者： Jianhui Ma Yanling Jing Shu Zhang Rongrong Chen Lianmei Wang Erxi Wu Guifang Cai Izabela Malinowska-Kolodziej Qi Liao Yuqin Liu Yi Zhao Yan Meng Qiang Sun Kaifeng Xu Jianwu Dai Jiahuai Han Lizi Wu Robert Chunhua Zhao Huangxuan Shen Hongbing Zhang David J.Kwiatkowski Xinxin Chen Haiyong Peng Qian Sun Xiaojun Zha Fang Wang Ying Wang Center of Excellence in Tissue Engineering Institute of Basic Medical Sciences and School of Basic MedicineChinese Academy of Medical Sciences and Peking Union Medical CollegeBeijingPeople ''s Republic of China Division of Breast SurgeryDepartment of SurgeryPeking Union Medical College HospitalChinese Academy of Medical Sciences and Peking Union Medical CollegeBeijingPeople ''s Republic of China Division of Respiratory MedicineDepartment of MedicinePeking Union Medical College HospitalChinese Academy of Medical Sciences and Peking Union Medical CollegeBeijingPeople''s Republic of China Key Laboratory of Molecular Developmental BiologyInstitute of Genetics and Developmental BiologyChinese Academy of SciencesBeijingPeople''s Republic of China Key Laboratory of the Ministry of Education for Cell Biology and Tumor Cell EngineeringSchool of Life SciencesXiamen UniversityXiamenFujianPeople ''s Republic of China Department of Molecular Genetics and MicrobiologyShands Cancer CenterUniversity of FloridaGainesvilleFloridaUSA Center of Excellence in Tissue EngineeringInstitute of Basic Medical Sciences and School of Basic MedicineChinese Academy of Medical Sciences and Peking Union Medical CollegeBeijingPeople ''s Republic of China State Key Laboratory of OphthalmologyLaboratory of Ocular GeneticsZhongshan Ophthalmic CenterSun Yat-Sen UniversityGuangzhouPeople''s Republic of China Division of Breast Surgery Department of SurgeryPeking Union Medical College HospitalChinese Academy of Medical Sciences and Peking Union Medical CollegeBeijingPeople ''s Republic of China Department of Physiology and PathophysiologyNational Laboratory of Medical Molecular BiologyInstitute of Basic Medical Sciences and School of Basic MedicineChinese Academy of Medical Sciences and Peking Union Medical CollegeBeijingPeople ''s Republic of China Department of Physiology and Pathophysiology National Laboratory of Medical Molecular BiologyInstitute of Basic Medical Sciences and School of Basic MedicineCh

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A collaborative framework for privacy protection in online social networks

A collaborative framework for privacy protection in online s...

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International Conference on Collaborative computing: Networking, Applications and Worksharing (CollaborateCom)

作者： Yan Zhu Zexing Hu Huaixi Wang Hongxin Hu Gail-Joon Ahn Key Laboratory of Network and Software Security Assurance Ministry of Education Peking University China Institute of Computer Science and Technology Peking University Beijing China School of Mathematical Sciences Peking University Beijing China Laboratory of Security Engineering for Future Computing (SEFCOM) Arizona State University Tempe AZ USA

With the wide use of online social networks (OSNs), the problem of data privacy has attracted much attention. Several approaches have been proposed to address this issue. One of privacy management approaches for OSN leverages a key management technique to enable a user to simply post encrypted contents so that only users who can satisfy the associate security policy can derive the key to access the data. However, the key management policies of existing schemes may grant access to unauthorized users and cannot efficiently determine authorized users. In this paper, we propose a collaborative framework which enforces access control for OSN through an innovative key management focused on communities. This framework introduces a community key management based on a new group-oriented convergence cryptosystem, as well as provides an efficient privacy preservation needed in a private OSN. To prove the feasibility of our approach, we also discuss a proof-of-concept implementation of our framework. Experimental results show that our construction can achieve the identified design goals for OSNs with the acceptable performance.

关键词： Cryptography Servers Kernel Data privacy Social network services Communities Collaboration

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An analytical solution to Boltzmann equation of dilute granular flow with homotopy analysis method

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Chinese Science Bulletin 2009年第23期54卷 4365-4370页

作者： ZHANG Li WANG GuangQian FU XuDong SUN QiCheng School of Mathematical Sciences and Computing Technology Central South University Changsha 410075 China State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China

The homotopy analysis method (HAM), as a new mathematical tool, has been employed to solve many nonlinear problems. As a fundamental equation in non-equilibrium statistical mechanics, the Boltzmann integro-differential equation (BE) describing the movement of particles is of strong nonlinearity. In this work, HAM is preliminarily applied to dilute granular flow which is relatively simple. By choosing the Maxwell velocity distribution function as the initial solution, the concrete expression of the first-order approximate solution to BE with collision term being the BGK model is given. Furthermore it is consistent with the solution using Chapman-Enskog method but does not rely on little parameters.

关键词：颗粒流玻尔流方程稀释积分微分方程速度分布函数非线性问题一阶近似解

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The quantization of river network morphology based on the Tokunaga network

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Science China Earth Sciences 2009年第10期52卷 1724-1731页

作者： Li Zhang BinXiang Dai GuangQian Wang TieJian Li Hao Wang School of Mathematical Sciences and Computing Technology Central South University Changsha 410075 China State Key Laboratory of Hydroscience and Engineering Tsinghua University Beijing 100084 China

River network morphology not only reflects the structure of river stream but also has great effects on hydrological process, soil erosion, river evolution, and watershed topography. Here we propose and define a new sequence of self-similar networks and corresponding parameters for the generated Tokunaga network. We also discuss the topological and numerical characteristics of self-similar networks with different iteration rules by utilizing links and fractal dimension. Application results indicate that the proposed method could be used to generate river network, which is much consistent with natural river network. The proposed parameter λ could well reflect the river network morphology.

关键词： fractal dimension river network morphology Tokunaga network

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A porous cell method for the simulation of fluid-solid interactions

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水道港口 2010年第5期31卷 318-318页

作者： H. B. Gu D. M. Causon C. G. Mingham L. Qian P. Z. Lin Centre for Mathematical Modelling and Flow Analysis Department of Computing and Mathematics Manchester Metropolitan UniversityManchester M 1 5GD UK State Key Laboratory of Hydraulics and Mountain River Engineering Sichuan University Chengdu 610065 China

There are many ways of describing a solid,porous or fluid region of the computational domain when solving the Navier-Stokes equations(NSE)for flow *** these the porous cell method is one of the most flexible *** this method,a parameter is defined as a ratio of the volume open to water and air in a calculation cell to its cell *** the calculation,the same numerical procedure is applied to every cell and no explicit boundary conditions are needed at solid *** method is used to simulate flow through porous media,around solid bodies and over a moving *** results compare well with experimental data and other numerical *** our future work the porous cell method will be applied to more complex fluid-solid interaction situations.

关键词： porous cell method Navier-Stokes equations sediment permeable dam level set method

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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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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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A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

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Chinese Physics B 2007年第3期16卷 599-604页

作者：刘鸿基傅景礼唐贻发 Institute of Mathematical Physics Shangqiu Teacher's College Shangqiu 476000 China Department of Physics Zhejiang Sci-Tech University Hangzhou 310018 China State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing 100080 China Shanghai University Shanghai Institute of Applied Mathematics and Mechanics Shanghai 200072 China

In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.

关键词： Mei symmetry non-Noether conservative quantity Lutzky conservative quantity nonconservative system

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