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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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Spectral Petrov-Galerkin Methods for the Second Kind Volterra Type Integro-Differential Equations

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Numerical Mathematics(Theory,Methods and Applications) 2011年第2期4卷 216-236页

作者： Xia Tao Ziqing Xie Xiaojun Zhou Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of ChinaHunan Normal UniversityChangshaHunan 410081P.R.China School of Mathematics and Computer Science Guizhou Normal UniversityGuiyangGuizhou 550001P.R.China

This work is to provide general spectral and pseudo-spectral Jacobi-Petrov-Galerkin approaches for the second kind Volterra integro-differential *** Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical *** some spectral and pseudo-spectral Jacobi-Petrov-Galerkin methods,a rigorous error analysis in both L2_(ω^(α,β))^(2),and L^(∞)norms is given provided that both the kernel function and the source function are sufficiently *** experiments validate the theoretical prediction.

关键词： Volterra integro-differential equation spectral Jacobi-Petrov-Galerkin pseudo-spectral Jacobi-Petrov-Galerkin spectral convergence

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A Compact Difference Scheme for an Evolution Equation with a Weakly Singular Kernel

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Numerical Mathematics(Theory,Methods and Applications) 2012年第4期5卷 559-572页

作者： Hongbin Chen Da Xu Institute of Mathematics and Physics College of ScienceCentral South University of Forestry and TechnologyChangsha410004HunanChina Key Laboratory of High Performance Computing and Stochastic Information Processing(Ministry of Education of China) College of Mathematics and Computer ScienceHunan Normal UniversityChangsha410081HunanChina

This paper is concerned with a compact difference scheme with the truncation error of order 3/2 for time and order 4 for space to an evolution equation with a weakly singular *** integral term is treated by means of the second order convolution quadrature suggested by *** stability and convergence are proved by the energy method.A numerical experiment is reported to verify the theoretical predictions.

关键词： Evolution equation weakly singular kernel compact difference scheme stability convergence numerical experiment

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Ergodicity of the 2D Navier-Stokes Equations with Degenerate Multiplicative Noise

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Acta Mathematicae Applicatae Sinica 2018年第1期34卷 97-118页

作者： Zhao DONG Xu-hui PENG RCSDS Academy of Mathematics and Systems Science Chinese Academy of Sciences China Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China) College of Mathematics and Computer Science Hunan Normal University Changsha 410081. China School of Mathematics Sciences University of Chinese Academy of Sciences Beijing 100190 China

Consider the two-dimensional, incompressible Navier-Stokes equations on torus T^2= [-π, π]^2 driven by a degenerate multiplicative noise in the vorticity formulation（abbreviated as SNS）： dwt = ν？w_tdt ＋B（Kw_t, w_t）dt ＋ Q（w_t）dW t. We prove that the solution to SNS is continuous differentiable in initial value. We use the Malliavin calculus to prove that the semigroup{P_t}_t≥0 generated by the SNS is asymptotically strong Feller. Moreover, we use the coupling method to prove that the solution to SNS has a weak form of *** almost the same Hypotheses as that given by Odasso, Prob. Theory Related Fields, 140： 41–82（2005）with a different method, we get an exponential ergodicity under a stronger norm.

关键词： tochastic Navier-Stokes equation asymptotically strong Feller property ergodicity

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Variable 2-Microlocal Besov–Triebel–Lizorkin-Type Spaces

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Acta Mathematica Sinica,English Series 2018年第4期34卷 699-748页

作者： Su Qing WU Da Chun YANG Wen YUAN Ci Qiang ZHUO Laboratory of Mathematics and Complex Systerns (Ministry of Education) School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China Key Laboratory of High Performance Computing and Stochastic Information Processing ( HPCSIP) (Ministry of Education of China) College of Mathematics and Computer Science Hu'nan Normal University Changsha 410081 P. R. China

This article is devoted to the study of variable 2-microlocal Besov-type and Triebel- Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of Q-transforms, Peetre maximal functions, smooth atoms, ball means of differences and approximations by analytic functions. As applications, some re- lated Sobolev-type embeddings and trace theorems of these spaces are Mso established. Moreover, some obtained results, such as characterizations via approximations by analytic functions, are new even for the classical variable Besov and Triebel-Lizorkin spaces.

关键词： 2-Microlocal Besov space 2-Microlocal Triebel-Lizorkin space variable exponent φ-transform Peetre maximal function difference atom embedding

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Advances in simulated modeling of vibration systems based on computational intelligence

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自然科学进展(英文版) 2002年第12期12卷 881-886页

作者： LIANG Yanchun LEE Heow Pueh LIN Wuzhong LIM Siak Piang LEE Kwok Hong Zhou Chunguang College of Computer Science and Technology Jilin University Changchun 130012 China Institute of High Performance Computing Singapore 117528 Key Laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sci Institute of High Performance Computing Singapore 117528 Department of Mechanical Engineering National University of Singapore Singapore 119260 Singapore College of Computer Science and Technology Jilin University Changchun 130012 China

Computational intelligence is the computational simulation of the bio-intelligence, which includes artificial neural networks, fuzzy systems and evolutionary computations. This article summarizes the state of the art in the field of simulated modeling of vibration systems using methods of computational intelligence, based on some relevant subjects and the authors' own research work. First, contributions to the applications of computational intelligence to the identification of nonlinear characteristics of packaging are reviewed. Subsequently, applications of the newly developed training algorithms for feedforward neural networks to the identification of restoring forces in multi-degree-of-freedom nonlinear systems are discussed. Finally, the neural-network-based method of model reduction for the dynamic simulation of microelectromechanical systems (MEMS) using generalized Hebbian algorithm (GHA) and robust GHA is outlined. The prospects of the simulated modeling of vibration systems using techniques of computational intelligence are also indicated.

关键词： computational intelligence artificial neural network fuzzy system evolutionary computation vibration system

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Improved multi-objective evolutionary algorithm for multi-agent coalition formation

Journal of Software

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Journal of Software 2013年第12期8卷 2991-2995页

作者： Xu, Bo Zhang, Ruizhe Yu, Jian Ping Department of Computer Science and Technology of Guangdong University of Petrochemical Technology Guangdong Province China Computer Science and Technic Academy Department Pingdingshan University Henan Province China College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing Hunan Normal University Hunan Province China

One of the key problems in multi-agent coalition formation is to optimally assign and schedule resources. An improved multi-objective evolutionary Algorithm (IMOEA) is proposed to solve this problem. Compared with several well-known algorithms such as NSGA, MOEA, experimental results show the algorithm is very suitable for coalition formation problem. © 2013 Academy Publisher.

关键词： Multiobjective optimization

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An Extrapolation Cascadic MultigridMethod for Elliptic Problems on Reentrant Domains

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Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1347-1363页

作者： Kejia Pan Dongdong He Chuanmiao Chen School of Mathematics and Statistics Central South UniversityChangshaHunan 410083China School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai 200092China College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing(Ministry of Education of China)Hunan Normal UniversityChangshaHunan 410081China

This paper proposes an extrapolation cascadic multigrid(EXCMG)method to solve elliptic problems in domains with reentrant *** a class ofλ-graded meshes,we derive some new extrapolation formulas to construct a high-order approximation to the finite element solution on the next finer mesh using the numerical solutions on two-level of grids(current and previous grids).Then,this high-order approximation is used as the initial guess to reduce computational cost of the conjugate gradient *** application of this idea results in the EXCMG method proposed in this ***,numerical results for a crack problem and an L-shaped problem are presented to verify the efficiency and effectiveness of the proposed EXCMG method.

关键词： Richardson extrapolation Cascadicmultigrid gradedmesh elliptic problems corner singularity

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Online Optimization in Power Systems With high Penetration of Renewable Generation:Advances and Prospects

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IEEE/CAA Journal of Automatica Sinica 2023年第4期10卷 839-858页

作者： Zhaojian Wang Wei Wei John Zhen Fu Pang Feng Liu Bo Yang Xinping Guan Shengwei Mei Key Laboratory of System Control and Information Processing Ministry of Education of ChinaDepartment of AutomationShanghai Jiao Tong UniversityShanghai 200240China State Key Laboratory of Power System and the Department of Electrical Engineering Tsinghua UniversityBeijing 100084China Institute of High Performance Computing(IHPC) Agency for Science Technology and Research(A*STAR)Singapore 138632Singapore

Traditionally,offline optimization of power systems is acceptable due to the largely predictable loads and reliable *** increasing penetration of fluctuating renewable generation and internet-of-things devices allowing for fine-grained controllability of loads have led to the diminishing applicability of offline optimization in the power systems domain,and have redirected attention to online optimization ***,online optimization is a broad topic that can be applied in and motivated by different settings,operated on different time scales,and built on different theoretical *** paper reviews the various types of online optimization techniques used in the power systems domain and aims to make clear the distinction between the most common techniques *** particular,we introduce and compare four distinct techniques used covering the breadth of online optimization techniques used in the power systems domain,i.e.,optimization-guided dynamic control,feedback optimization for single-period problems,Lyapunov-based optimization,and online convex optimization techniques for multi-period ***,we recommend some potential future directions for online optimization in the power systems domain.

关键词： optimization Lyapunov optimization online convex optimization online optimization optimization-guided control

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Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

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Journal of Applied Mathematics and Physics 2019年第7期7卷 1463-1472页

作者： Qiufeng Chen Jianli Li Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) Changsha China School of Mathematics and Statistics Hunan Normal University Changsha China

In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.

关键词： Third-Order Three-Point Boundary Value Problem Fixed Point Theorem Three Positive Solutions

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