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arXiv 2021年

作者： Jiang, Kai Si, Wei Xu, Jie School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China Chinese Academy of Sciences Beijing China

We propose a spectral viewpoint for grain boundaries that are generally quasiperiodic. To accurately capture the spectra computationally, it is crucial to adopt the projection method for quasiperiodic functions. Armed with the Lifshitz–Petrich free energy, we take the spectral viewpoint to examine tilt grain boundaries of the hexagonal phase. Several ingredients of grain boundaries are extracted, which are not easy to obtain from real-space profiles. We find that only a few spectra substantially contribute to the formation of grain boundaries. Their linear relation to the intrinsic spectra of the bulk hexagonal phase is independent of the tilt angle. By examining the feature of the spectral intensities, we propose a definition of the interface width. The widths calculated from this definition are consistent with visual *** Codes 65N35, 70H12, 82B24 © 2021, CC BY.

关键词： Grain boundaries

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Svgd: A Virtual Gradients Descent Method for Stochastic Optimization

arXiv

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arXiv 2019年

作者： Li, Zheng Shu, Shi School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has little memory requirements. We also analyze the theoretical convergence properties and implementation of the algorithm. Experimental results on multiple datasets and network models show that SVGD has advantages over other stochastic optimization methods. Copyright © 2019, The Authors. All rights reserved.

关键词： Machine learning

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Two-level additive preconditioners for edge element discretizations of time-harmonic Maxwell equations

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Computers & Mathematics with Applications 2013年第4期66卷 432-440页

作者： Liuqiang Zhong Chunmei Liu Shi Shu School of Mathematical Sciences South China Normal University Guangzhou 510631 China Department of Mathematics and Computational Science Hunan University of Science and Engineering Yongzhou 425199 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 China

Two-level additive preconditioners are presented for edge element discretizations of time-harmonic Maxwell equations. The key is to construct a special “coarse mesh” space, which adds the kernel of the curl -operator in a fine space to a coarse mesh space, to solve the original problem, and then uses the fine mesh space to solve the H ( curl ) -elliptic problem. It is shown that the generalized minimal residual (GMRES) method applied to the preconditioned system converges uniformly provided that the coarsest mesh size is reasonably small (but independent of the fine mesh size) and the parameter for the “coarse mesh” space solver is sufficiently large. Numerical experiments show the efficiency of the proposed approach.

关键词： Convergence GMRES method Edge finite element Time-harmonic Maxwell equations

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Free vibration exploration of axially functionally graded carbon nanotube-reinforced beams through an innovative perturbative methodology 3

Free vibration exploration of axially functionally graded ca...

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2024 3rd International Conference on Aerospace, Aerodynamics and Mechatronics engineering, AAME 2024

作者： Chen, Chen Zhou, Lilin Ye, Tianyu Li, Daokui College of Aerospace Science and Engineering National University of Defense Technology Hunan Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China Aviation Engineering Institute Civil Aviation Flight University of China Sichuan Guanghan618307 China

Axially functionally graded (AFG) carbon nanotube-reinforced composite (CNTRC) emerges as a promising solution for tailoring the stiffness and strength of various beam-like structures. Applications range from optimizing the weight-to-strength ratio of airplane wings to fine-tuning the frequency of micro-beam sensors, and even alleviating stresses induced by centrifugal forces or temperature gradients in turbine blades. However, the challenge of solving variable coefficient partial differential equations (VCPDEs) arising from the axial material gradient limits conventional methods to numerical and simulation techniques. In this study, a novel perturbation approach (PA) customized for AFG-CNTRC is highlighted for solving the problem analytically, simply, and precisely. First, the vibration model of an AFG-CNTRC beam is established according to the Euler-Bernoulli theory (EBT). Second, the vibration governing equations are solved by the PA and the state space method (SSM) analytically. Finally, the adaptivity and accuracy of the PA are validated and the effects of carbon nanotubes (CNTs) distribution patterns are analyzed. It is found that increasing CNT content at either end will increase the natural frequency for symmetric boundary conditions (BCs). The frequency decreases with the degree of nonlinearity distribution of CNTs. The frequency under the C-F BC exhibits low sensitivity to parameter effects. © Published under licence by IOP Publishing Ltd.

关键词： State space methods

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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(011)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

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Investigation on a quantum algorithm for linear differential equations

arXiv

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arXiv 2024年

作者： Dong, Xiaojing Peng, Yizhe Tang, Qili Yang, Yin Yu, Yue Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Ref. [BCOW17] introduced a pioneering quantum approach (coined BCOW algorithm) for solving linear differential equations with optimal error tolerance. Originally designed for a specific class of diagonalizable linear differential equations, the algorithm was extended by Krovi in [Kro23] to encompass broader classes, including non-diagonalizable and even singular matrices. Despite the common misconception, the original algorithm is indeed applicable to non-diagonalizable matrices, with diagonalisation primarily serving for theoretical analyses to establish bounds on condition number and solution error. By leveraging basic estimates from [Kro23], we derive bounds comparable to those outlined in the Krovi algorithm, thereby reinstating the advantages of the BCOW approach. Furthermore, we extend the BCOW algorithm to address time-dependent linear differential equations by transforming non-autonomous systems into higher-dimensional autonomous ones, a technique also applicable for the Krovi algorithm. © 2024, CC BY-NC-ND.

关键词： Consensus algorithm

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Preconditioners for higher order edge finite element discretizations of Maxwell's equations

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science China Mathematics 2008年第8期51卷 1537-1548页

作者： ZHONG LiuQiang1,2,SHU Shi1,2,SUN DuDu3&TAN Lin4 1School of Mathematical and computational sciences,Xiangtan University,Xiangtan 411105,China 2hunan key laboratory for computation and simulation in science and engineering,Xiangtan 411105,China 3Institute of computational Mathematics and Scientific/engineering Computing,Academy of Mathematicsand Systems science,Graduate University of Chinese Academy of sciences,Chinese Academy sciences,P.O.Box 2719,Beijing 100190,China 4Department of Math-Physics,Nanhua University,Hengyang 421001,China 1. School of Mathematical and Computational Sciences Xiangtan University Xiangtan 411105 China 2. Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan 411105 China 3. Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Graduate University of Chinese Academy of Sciences Chinese Academy Sciences P.O. Box 2719 Beijing 100190 China 4. Department of Math-Physics Nanhua University Hengyang 421001 China

In this paper,we are concerned with the fast solvers for higher order edge finite element discretizations of Maxwell's *** present the preconditioners for the first family and second family of higher order N′ed′elec element equations,*** combining the stable decompositions of two kinds of edge finite element spaces with the abstract theory of auxiliary space preconditioning,we prove that the corresponding condition numbers of our preconditioners are uniformly bounded on quasi-uniform *** also present some numerical experiments to demonstrate the theoretical results.

关键词： preconditioner higher order edge finite element stable decomposition

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A two-dimensional GeSe/SnSe heterostructure for high performance thin-film solar cells

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Journal of Materials Chemistry A 2019年第18期7卷 11265-11271页

作者： Yuliang Mao Congsheng Xu Jianmei Yuan Hongquan Zhao Hunan Key Laboratory for Micro-Nano Energy Materials and Devices School of Physics and Optoelectronics Xiangtan University Hunan 411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 China Chongqing Institute of Green and Intelligent Technology Chinese Academy of Sciences Chongqing 401120 China

Based on the first-principles calculations, we demonstrated that a GeSe/SnSe heterostructure has type-II band alignment and a direct band gap, which can effectively prevent the recombination of photogenerated electron–hole pairs. Moreover, the GeSe/SnSe heterostructure also exhibits strong optical absorption intensity, which can reach the order of 10⁵ cm⁻¹. Our predicted photoelectric conversion efficiency (PCE) for the GeSe/SnSe heterostructure reaches 21.47%. We also found that the hole carrier mobility of the GeSe/SnSe heterostructure along the x direction has been significantly improved to 6.42 × 10⁴ cm² V⁻¹ s⁻¹, which is higher than that of black phosphorus (1 × 10⁴ cm² V⁻¹ s⁻¹). By applying a vertical external electric field, we found that the band gap and band offset of the GeSe/SnSe heterojunction can be effectively tuned. The revealed type-II band alignment, strong optical absorption, superior PCE and superior hole carrier mobility of the GeSe/SnSe heterostructure imply that this new proposed material has broad application prospects in solar cells.

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The grad-div conforming virtual element method for the quad-div problem in three dimensions

arXiv

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arXiv 2024年

作者： Dong, Xiaojing Han, Yibing Huang, Yunqing Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Er huan Road Hunan Xiangtan411105 China

We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the H(grad-div)-conforming virtual element method of arbitrary approximation orders on polyhedral meshes. Three families of H(grad-div)conforming virtual elements are constructed based on the structure of a de Rham sub-complex with enhanced smoothness, resulting in an exact discrete virtual element complex. In the lowest-order case, the simplest element has only one degree of freedom at each vertex and face, respectively. We rigorously prove the interpolation error estimates, the stability of discrete bilinear forms, the well-posedness of discrete formulation and the optimal error estimates. Some numerical examples are shown to verify the theoretical results. © 2024, CC BY-NC-ND.

关键词： Mesh generation

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Influences of interpretations of boundary conditions on nonlinear finite element analysis of a concrete column under near-field blast loading 7

Influences of interpretations of boundary conditions on nonl...

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2022 7th International Conference on Information science, Computer Technology and Transportation, ISCTT 2022

作者： Xu, Jie Hendriks, Max A.N. Rots, Jan G. Tsouvalas, Apostolos College of Aerospace Science and Engineering National University of Defense Technology Hunan Changsha410073 China Hunan Key Laboratory of Intelligent Planning and Simulation for Aerospace Missions Hunan Changsha410073 China Faculty of Civil Engineering and Geosciences Delft University of Technology Zuid Holland Delft2628 CN Netherlands

ISBN: (纸本)9783800760565

Due to the accompanying severe consequences of explosions, the blast puts a great threat to public security. Nonlinear finite element analysis is a possible method for civil engineers to check the integrity of the structures under blast loading without underestimating the limit of the structures. However, different interpretations of the boundary conditions may lead to huge differences in computational expenses and analytical results. Therefore, how should civil engineers simulate the boundary conditions to gain relatively accurate numerical results with acceptable computational efforts is of great interest. In this article, 5 different interpretations of the same physical situations are discussed, and experimental results are used as the baseline for judgment, which could help to indicate the proper simplifications in the set-up of finite element models. © VDE VERLAG GMBH ∙ Berlin ∙ Offenbach.

关键词： Boundary conditions

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