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Asymptotic expansions of finite element solutions to Robin problems in H^3 and their application in extrapolation cascadic multigrid method

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Science China Mathematics 2014年第4期57卷 687-698页

作者： HU HongLing CHEN ChuanMiao PAN KeJia College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China)Hunan Normal University School of Mathematics and Statistics Central South University Key Laboratory of Metallogenic Prediction of Nonferrous Metals Ministry of EducationSchool of Geosciences and Info-PhysicsCentral South University

For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈*** on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems ***,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is ***,some numerical experiments that confirm the theoretical analysis are presented.

关键词： finite element Richardson extrapolation Robin problem asymptotic expansion cascadic multi-grid method

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The 5th International Conference on Biomedical Engineering and Biotechnology (ICBEB 2016) Abstracts

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BMC MEDICAL IMAGING 2016年第SUPPL 1期16卷 65-65页

作者： [Anonymous] Department of MRI Shandong Medical Imaging Research Institute Affiliated to Shandong University Jinan Shandong 250021 People’s Republic of China Department of Interventional Radiology Shandong Provincial Hospital Affiliated to Shandong University Jinan Shandong 250021 People’s Republic of China College of Information Science and Technology Engr. Research Center of Digitized Textile & Fashion Tech. for Ministry of Education Donghua University Shanghai 201620 China Intelligent multimedia information processing Lab College of Software Northeastern University Shenyang Liaoning Province 110004 China Institute of Biomedical and Health Engineering Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen 518055 China School of Computer Science and Technology Nanjing Normal University Nanjing China Department of Electrical Engineering The City College of New York CUNY New York USA Jiangsu Key Laboratory of 3D Printing Equipment and Manufacturing Nanjing China School of Electronic Science and Engineering Nanjing University Nanjing Jiangsu 210046 China College of Engineering Nanyang Technological University Singapore 639798 Singapore School of Electronic Information Shanghai Dianji University Shanghai China School of Natural Sciences and Mathematics Shepherd University Shepherdstown WV 25443 USA Davis College of Agriculture Natural Resources and Design West Virginia University Morgantown WV 26505 USA State Key Laboratory of Millimeter Waves Southeast University Nanjing 210096 China Center of Medical Physics and Technology Hefei Institutes of Physical Science Chinese Academy of Sciences Hefei China College of Agricultural and Life Sciences University of Florida Gainesville FL 32611 USA Courant Institute of Mathematical Sciences New York University New York NY 10012 USA Translational Imaging Division & MRI Unit Columbia University and New York State Psychiatric Institute New York NY 10032 USA Guangxi Key Laboratory of Manufacturing System & Adv

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Necessity of Oversampling Theorem for Affine Frames

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Journal of Applied Mathematics and Physics 2014年第2期2卷 18-23页

作者： Qiquan Fang Xianliang Shi Weicai Li College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China) Hunan Normal University Changsha China Department of Mathematics Zhejiang University of Science and Technology Hangzhou China

In this paper we prove that n is relatively prime to a which is also necessary.

关键词： Affine Frame Oversampling

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Three methods and three conjectures in numerical computations for Hamilton systems

Three methods and three conjectures in numerical computation...

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4th International Conference on Numerical Analysis of Differential Equations (2014第四届微分方程数值分析国际会议)

作者： Chuanmiao Chen Institute of Computation Hunan Normal UniversityChangshaHunanPRC Key Laboratory of High performance Computation and Stochastic Information ProcessingMinistry of Education of China

We shall discuss three classes of numerical methods for Hamilton systems and three conjectures: Feng Kang's conjecture(i.e.,the deviation of computational orbits grows linearly with time: |z(tn)-Zn| ≤ C1tnh2m),quasi-symplecticity(i.e.,the deviation of symplecticity doesn't grow with time: |(DZn/DZo)TJ(DZn/DZo)-J|≤C2h2m),and quasi-preservation of energy(i.e.,the deviation of energy doesn't grow with time: |H(Zn)-H(Z(tn))|≤ C3h2m),where the constants Ci are independent of time *** experiments exhibit several important facts as *** algorithms always preserve symplecticity,then Feng Kang's conjecture and quasi-conservation of energy *** finite elements always are of conservation of energy,then Feng Kang's conjecture and quasi-symplecticity ***,if we define a broad class of regular algorithms which preserve Feng Kang's conjecture,we find that both quasi-symplecticity and quasi-conservation of energy still ***,in the generalized sense,all these algorithms are equivalent or twin-brothers.

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McKay quivers and absolute n-complete algebras

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Science China Mathematics 2013年第8期56卷 1607-1618页

作者： GUO JinYun College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information ProcessingMinistry of EducationHunan Normal University

In this paper,we show that the McKay quiver of a finite subgroup of a general linear group is a regular covering of the McKay quiver of its intersection with the special linear *** this and our results on "returning arrows" in McKay quiver,we give an algorithm to construct the McKay quiver of a finite abelian *** this construction,we show how the cone and cylinder of an(n-1)-Auslander absolute n-complete algebra are truncated from the McKay quivers of abelian groups.

关键词： McKay quiver Nakayama translation absolute n-complete algebra

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An application of Chen's theorem to convergence of Fourier multiplier transforms

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Applied Mathematics(A Journal of Chinese Universities) 2013年第4期28卷 455-464页

作者： SHI Xian-liang CHEN Yang HU Lan College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) Hunan Normal University

Let V be a star shaped region. In 2006, Colzani, Meaney and Prestini proved that if function f satisfies some condition, then the multiplier transform with the characteristic function of tV as the multiplier tends to f almost everywhere, when t goes to∞. In this paper we use a Theorem established by *** to show that if we change their multiplier, then the condition on f can be weakened.

关键词： Fourier transform multiplier summability convergence almost everywhere

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Extrapolation cascadic multigrid method on piecewise uniform grid

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Science China Mathematics 2013年第12期56卷 2711-2722页

作者： CHEN ChuanMiao HU HongLing College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China)Hunan Normal University

The triangular linear finite elements on piecewise uniform grid for an elliptic problem in convex polygonal domain are discussed. Global superconvergence in discrete Hi-norm and global extrapolation in discrete L2-norm are proved. Based on these global estimates the conjugate gradient method （CG） is effective, which is applied to extrapolation cascadic multigrid method （EXCMG）. The numerical experiments show that EXCMG is of the global higher accuracy for both function and gradient.

关键词： linear finite element piecewise uniform grid superconvergence extrapolation extrapolation cas-cadic multigrid method

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EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

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Acta Mathematica Scientia 2013年第6期33卷 1639-1651页

作者：周杰明莫晓云欧辉杨向群 College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of ChinaHunan Normal University Department of Mathematics Hunan University of Finance and Economics

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.

关键词： compound binomial model main claim by-claim dividend random income

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Pointwise Convergence of Wavelets of Generalized Shannon Type

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Acta Mathematica Sinica,English Series 2013年第12期29卷 2343-2354页

作者： Xian Liang SHI Wei WANG College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China)Hu’nan Normal University School of Sciences Central South University of Forestry and Technology

In this paper, a new result on pointwise convergence of wavelets of generalized Shannon type is proved, which improves a theorem established by Zayed.

关键词： Shannon type wavelet wavelet expansions pointwise convergence

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DOUBLE-MARKOV RISK MODEL

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Acta Mathematica Scientia 2013年第2期33卷 333-340页

作者：莫晓云周杰明欧辉杨向群 College of Mathematics and Computer Science Hunan Normal University Hunan University of Finance and Economics College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Education Ministry of China)Hunan Normal University

Given a new Double-Markov risk model DM = （μ, Q, v, H; Y, Z） and Double-Markov risk process U = {U（t）, t 〉 0}. The ruin or survival problem is addressed. Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained. Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained. The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.

关键词： Q process Markov chain Double-Markov risk characterization survival prob-ability recursion formula

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