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Numerical Methods For Fractional Variational Problems Depending On Indefinite Integrals

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Numerical Methods For Fractional Variational Problems Depend...

第五届国际自动控制联合会分数阶导数及其应用会议

作者： Dongling Wang Aiguo Xiao Hunan Key Laboratory for Computation and Simulation in Scienceand Engineering Key Laboratory of Intelligent Computing &Information Processing of Ministry of Education University XiangtanHunan P.R.China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education University Xiangtan Hunan P.R.China

In this paper,the fractional variational integrators for fractional variational problems depending on indefinite integrals in terms of Caputo derivative are *** corresponding fractional discrete Euler-Lagrange equatio... 详细信息

关键词： Numerical Methods For Fractional Variational Problems Depending On Indefinite Integrals

Fully finite element adaptive algebraic multigrid method for time-space caputo-riesz fractional diffusion equations

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arXiv 2017年

作者： Yue, Xiaoqiang Bu, Weiping Shu, Shi Liu, Menghuan Wang, Shuai School of Mathematics and Computational Science Xiangtan University Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

The paper aims to establish a fully discrete finite element (FE) scheme and provide cost-effective solutions for one-dimensional time-space Caputo-Riesz fractional diffusion equations on a bounded domain Ω. Firstly, we construct a fully discrete scheme of the linear FE method in both temporal and spatial directions, derive many characterizations on the coefficient matrix and numerically verify that the fully FE approximation possesses the saturation error order under L2(Ω) norm. Secondly, we theoretically prove the estimation 1.+ O(ταh−2β) on the condition number of the coefficient matrix, in which τ and h respectively denote time and space step sizes. Finally, on the grounds of the estimation and fast Fourier transform, we develop and analyze an adaptive algebraic multigrid (AMG) method with low algorithmic complexity, reveal a reference formula to measure the strength-of-connection tolerance which severely affect the robustness of AMG methods in handling fractional diffusion equations, and illustrate the well robustness and high efficiency of the proposed algorithm compared with the classical AMG, conjugate gradient and Jacobi iterative methods. Copyright © 201., The Authors. All rights reserved.

关键词： computational complexity

Time-space finite element adaptive AMG for multi-term time fractional advection diffusion equations

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arXiv 2017年

作者： Yue, Xiaoqiang Xu, Yehong Shu, Shi Liu, Menghuan Bu, Weiping School of Mathematics and Computational Science Xiangtan University Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain Ω. Firstly, a fully discrete scheme is obtained by the linear FE method in both temporal and spatial directions, and many characterizations on the resulting matrix are established. Secondly, the condition number estimation is proved, an adaptive algebraic multigrid (AMG) method is further developed to lessen computational cost and analyzed in the classical framework. Finally, some numerical experiments are implemented to reach the saturation error order in the L2(Ω) norm sense, and present theoretical confirmations and predictable behaviors of the proposed algorithm.35R1., 65F1., 65F1., 65N55 Copyright © 201., The Authors. All rights reserved.

关键词： computational complexity

The improved upper solution bounds of the continuous coupled algebraic Riccati matrix equation

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International Journal of Control, Automation and Systems 2013年第4期11卷 852-858页

作者： Juan Zhang Jianzhou Liu Department of Mathematics and Computational Science Xiangtan University Xiangtan Hunan P. R. China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan China Hunan Key Laboratory for Computation & Simulation in Science & Engineering Xiangtan University Hunan China

In this paper, combining some special eigenvalue inequalities of matrix’s product and sum with the equivalent form of the continuous coupled algebraic Riccati equation (CCARE), we construct linear inequalities. Then, in terms of the properties of M-matrix and its inverse matrix, through solving the derived linear inequalities, we offer new upper matrix bounds for the solution of the CCARE, which improve some of the recent results. Finally, we present a corresponding numerical example to show the effectiveness of the given results.

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A Two-level Overlapping Schwarz Method Using Energy Minimizing Multiscale Finite Element Functions 25th

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A Two-level Overlapping Schwarz Method Using Energy Minimizi...

25th International Conference on Domain Decomposition Methods in science and {1., DD 201.

作者： Kim, Hyea Hyun Chung, Eric T. Wang, Junxian Department of Applied Mathematics and Institute of Natural Sciences Kyung Hee University Region Korea Republic of Department of Mathematics The Chinese University of Hong Kong SAR Hong Kong Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan China

In this paper, a two-level overlapping Schwarz algorithm is proposed for solving finite element discretization of the following model problem &#1.9; 2020, Springer Nature Switzerland AG.

ISBN: (纸本)9783030567491

关键词： Finite element method

High-density/efficient surface active sites on modified separators to boost Li-S batteries via atomic Co^(3+)-Se termination

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Nano Research 2022年第8期15卷 7199-7208页

作者： Shujie Liu Xiaofei Liu Manfang Chen Dong Wang Xin Ge Wei Zhang Xiyang Wang Chunhui Wang Tingting Qin Haozhe Qin Liang Qiao Dan Zhang Xing Ou Weitao Zheng Key Laboratory of Automobile Materials of MOE School of Materials Science and Engineeringand Electron Microscopy Centerand International Center of Future ScienceJilin UniversityChangchun 130013China Key Laboratory of Materials Design and Quantum Simulation College of ScienceChangchun UniversityChangchun 130022China National Base for International Science&Technology Cooperation School of ChemistryXiangtan UniversityXiangtan 411105China State Key Laboratory of Chem/Bio-Sensing and Chemometrics Advanced Catalytic Engineering Research Center of the Ministry of EducationCollege of Chemistry and Chemical EngineeringHunan UniversityChangsha 410082China Department of Mechanical and Mechatronics Engineering University of WaterlooWaterlooN2L 3G1Canada School of Metallurgy and Environment Central South UniversityChangsha 410083China

Various and critical electrocatalytic processes are involved during the redox reactions in the Li-S batteries,which extremely depend on the surface structure and chemical ***,single-atom concept unlocks a route to maximize the use of surface-active atoms,however,further increasing the density of active site is still strictly limited by the inherent structure that single-atoms are only highly-dispersed on ***,we provide a viewpoint that an elaborate facet design with singlecrystalline structure engineering can harvest high-density surface active sites,which can significantly boost the electrocatalyst performance for excellent Li-S ***,the single-crystal CoSe_(2)(scCS)exhibits three-types of terminated(01.)facet,efficiently obtaining the surface with a high-rich Co^(3+)–Se bond termination,in contrast with lots of surface grain boundaries and dangling bonds in polycrystalline CoSe_(2).Surprisingly,the surface active sites concentration can reach more than 69%.As anticipated,it can provide high-density and high-efficient active sites,enormously suppressing the shuttle effect and improving the reaction kinetics via accelerating the conversion and deposition of polysulfides and *** surface lattice strategy with element terminated mode is a promising approach for designing electrocatalyst effect-based energy system,not merely for Li-S batteries.

关键词： high-density surface active sites Co^(3+)-Se covalent bond atomic element terminated Li-S batteries single-crystalline strategy

Generalized Multiscale Finite Element Method for Multicontinuum Coupled Flow and Transport Model

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Lobachevskii Journal of Mathematics 2024年第11期45卷 5343-5356页

作者： Ammosov, D.A. Huang, J. Leung, W.T. Shan, B. Computational Technologies and Artificial Intelligence North-Eastern Federal University Yakutsk 677980 Russian Federation School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Hunan Xiangtan 411105 China Department of Mathematics City University of Hong Kong Hong Kong Department of Mathematics Texas A & M University College Station 77843 TX United States

Abstract: In this paper, we consider a coupled flow and transport process described by partial differential equations for pressure and concentration. We derive the multicontinuum coupled flow and transport model using the multicontinuum homogenization method. We formulate cell problems with constraints that take into account various homogenized effects. For the resulting multicontinuum model, we develop a multiscale solver based on the Generalized Multiscale Finite Element Method. The combined approach of multicontinuum and multiscale modeling makes it possible to consider complex heterogeneous media with high contrast. We present numerical results for a model problem with two continua and heterogeneous coefficients separable into microscopic and macroscopic parts. The results show the high efficiency of the proposed multiscale approach. © Pleiades Publishing, Ltd. 2024.

关键词： coupled flow and transport generalized multiscale finite element method homogenization miscible displacement multicontinuum

A NEURAL MULTIGRID SOLVER FOR HELMHOLTZ EQUATIONS WITH HIGH WAVENUMBER AND HETEROGENEOUS MEDIA

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arXiv 2024年

作者： Cui, Chen Jiang, Kai Shu, Shi Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Solving high-wavenumber and heterogeneous Helmholtz equations presents a longstanding challenge in scientific computing. In this paper, we introduce a deep learning-enhanced multigrid solver to address this issue. By conducting error analysis on standard multigrid applied to a discrete Helmholtz equation, we devise a strategy to handle errors with different frequencies separately. For error components with frequencies distant from the wavenumber, we perform simple smoothing based on local operations at different levels to eliminate them. On the other hand, to address error components with frequencies near the wavenumber, we utilize another multigrid V-cycle to solve an advection-diffusion-reaction (ADR) equation at a coarse scale. The resulting solver, named Wave-ADR-NS, involves parameters learned through unsupervised training. Numerical results demonstrate that Wave-ADR-NS effectively resolves heterogeneous 2D Helmholtz equation with wavenumber up to 2000. Comparative experiments against classical multigrid preconditioners and existing deep learning-based multigrid preconditioners reveals the superior performance of *** Codes 65N22, 65N55, 68T07 Copyright © 2024, The Authors. All rights reserved.

关键词： Helmholtz equation

Convergent analysis of algebraic multigrid method with data-driven parameter learning for non-selfadjoint elliptic problems

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arXiv 2024年

作者： Zhang, Juan Luo, Junyue Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and introduce a data-driven parameter learing method called Gaussian process regression (GPR) to predict optimal parameters. Numerical experimental results show that using GPR to predict parameters can save a significant amount of time cost and approach the optimal parameters accurately. © 2024, CC BY.

关键词： Algebra