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Corrigendum to “Curl recovery for the lowest order rectangular edge element” [Applied Mathematics and computation 371 (2020) 124897]

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Applied Mathematics and computation 2020年 372卷

作者： Peizhen Wang Yanping Chen Wei Yang School of Mathematics and Statistics North China University of Water Resources and Electric Power Zhengzhou Henan 450000 PR China School of Mathematical Sciences South China Normal University Guangzhou Guangdong 510631 PR China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 PR China

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A spatial sixth-order CCD-TVD method for solving multidimensional coupled Burgers' equation

arXiv

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arXiv 2018年

作者： Pan, Kejia Wu, Xiaoxin Yue, Xiaoqiang Ni, Runxin School of Mathematics and Statistics Central South University Changsha Hunan410083 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

In this paper, an efficient and high-order accuracy finite difference method is proposed for solving multidimensional nonlinear Burgers' equation. The third-order three stage Runge-Kutta total variation diminishing (TVD) scheme is employed for the time discretization, and the three-point combined compact difference (CCD) scheme is used for spatial discretization. Our method is third-order accurate in time and sixth-order accurate in space. The CCD-TVD method treats the nonlinear term explicitly thus it is very efficient and easy to implement. In addition, we prove the unique solvability of the CCD system under non-periodic boundary conditions. Numerical experiments including both two-dimensional and three-dimensional problems have been conducted to demonstrate the high efficiency and accuracy of the proposed method. Copyright © 2018, The Authors. All rights reserved.

关键词： Runge Kutta methods

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Multifractal temporally weighted detrended cross-correlation analysis of multivariate time series

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Chaos (Woodbury, N.Y.) 2020年第2期30卷 023134页

作者： Shan Jiang Bao-Gen Li Zu-Guo Yu Fang Wang Vo Anh Yu Zhou Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Xiangtan Hunan 411105 China. College of Information and Science Technology Hunan Agricultural University Changsha Hunan 410128 China. Faculty of Science Engineering and Technology Swinburne University of Technology PO Box 218 Hawthorn Victoria 3122 Australia. Institute of Future Cities and Department of Geography and Resource Management The Chinese University of Hong Kong Shatin Hong Kong China.

Fractal and multifractal properties of various systems have been studied extensively. In this paper, first, the multivariate multifractal detrend cross-correlation analysis (MMXDFA) is proposed to investigate the multifractal features in multivariate time series. MMXDFA may produce oscillations in the fluctuation function and spurious cross correlations. In order to overcome these problems, we then propose the multivariate multifractal temporally weighted detrended cross-correlation analysis (MMTWXDFA). In relation to the multivariate detrended cross-correlation analysis and multifractal temporally weighted detrended cross-correlation analysis, an innovation of MMTWXDFA is the application of the signed Manhattan distance to calculate the local detrended covariance function. To evaluate the performance of the MMXDFA and MMTWXDFA methods, we apply them on some artificially generated multivariate series. Several numerical tests demonstrate that both methods can identify their fractality, but MMTWXDFA can detect long-range cross correlations and simultaneously quantify the levels of cross correlation between two multivariate series more accurately.

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Design lithium storage materials by lithium adatoms adsorption at the edges of zigzag silicene nanoribbon: A first principle study

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Applied Surface Science 2017年 406卷 161-169页

作者： Guo, Gang Mao, Yuliang Zhong, Jianxin Yuan, Jianmei Zhao, Hongquan Hunan Key Laboratory for Micro–Nano Energy Materials and Devices School of Physics and Optoelectronic Engineering Xiangtan University Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan411105 China Chongqing Institute of Green and Intelligent Technology Chinese Academy of Sciences Chongqing401120 China

First-principles spin-polarized calculations are performed to design lithium storage materials using the active edges of zigzag silicene nanoribbon (ZSiNR). We predict that edge-adsorption of Li adatoms on zigzag silicene nanoribbon is preferred in energy to form new type lithium storage materials. Significant charge transfer from Li adatoms to Si atoms at the edges of ZSiNR is found, indicating the main ionic interactions. It is found that the band structures of ZSiNR with Li adsorptions are sensitive with the variation of sites of adatoms at the two edges. Ferro-magnetic to antiferro-magnetic change is found in ZSiNR with symmetrical adsorption of Li adatoms at its two edges. Other unsymmetrical Li adsorptions at the edges of ZSiNR prefer to stay in ferro-magnetic state as that in narrow pristine ZSiNR. © 2017 Elsevier B.V.

关键词： Adsorption

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Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations

arXiv

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arXiv 2018年

作者： Peng, Jie Wang, Junxian Shu, Shi School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

Balancing domain decomposition by constraints (BDDC) algorithms with adaptive primal constraints are developed in a concise variational framework for the weighted plane wave least-squares (PWLS) discritization of Helmholtz equations with high and various wave numbers. The unknowns to be solved in this preconditioned system are defined on elements rather than vertices or edges, which are different from the well-known discritizations such as the classical finite element method. Through choosing suitable "interface" and appropriate primal constraints with complex coefficients and introducing some local techniques, we developed a two-level adaptive BDDC algorithm for the PWLS discretization, and the condition number of the preconditioned system is proved to be bounded above by a user-defined tolerance and a constant which is only dependent on the maximum number of interfaces per subdomain. A multilevel algorithm is also attempted to resolve the bottleneck in large scale coarse problem. Numerical results are carried out to confirm the theoretical results and illustrate the efficiency of the proposed *** Codes 65N30, 65F10, 65N55 Copyright © 2018, The Authors. All rights reserved.

关键词： Helmholtz equation

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Inferring microRNA-disease association by hybrid recommendation algorithm and unbalanced bi-random walk on heterogeneous network

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Scientific reports 2019年第1期9卷 2474页

作者： Dong-Ling Yu Yuan-Lin Ma Zu-Guo Yu Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 P.R. China. Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education and Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 P.R. China. yuzuguo@***. School of Electrical Engineering and Computer Science Queensland University of Technology Brisbane Q4001 Australia. yuzuguo@***.

More and more research works have indicated that microRNAs (miRNAs) play indispensable roles in exploring the pathogenesis of diseases. Detecting miRNA-disease associations by experimental techniques in biology is expensive and time-consuming. Hence, it is important to propose reliable and accurate computational methods to exploring potential miRNAs related diseases. In our work, we develop a novel method (BRWHNHA) to uncover potential miRNAs associated with diseases based on hybrid recommendation algorithm and unbalanced bi-random walk. We first integrate the Gaussian interaction profile kernel similarity into the miRNA functional similarity network and the disease semantic similarity network. Then we calculate the transition probability matrix of bipartite network by using hybrid recommendation algorithm. Finally, we adopt unbalanced bi-random walk on the heterogeneous network to infer undiscovered miRNA-disease relationships. We tested BRWHNHA on 22 diseases based on five-fold cross-validation and achieves reliable performance with average AUC of 0.857, which an area under the ROC curve ranging from 0.807 to 0.924. As a result, BRWHNHA significantly improves the performance of inferring potential miRNA-disease association compared with previous methods. Moreover, the case studies on lung neoplasms and prostate neoplasms also illustrate that BRWHNHA is superior to previous prediction methods and is more advantageous in exploring potential miRNAs related diseases. All source codes can be downloaded from https://***/myl446/BRWHNHA .

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Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations

arXiv

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arXiv 2018年

作者： Yue, X.Q. Shu, S. Xu, X.W. Bu, W.P. Pan, K.J. School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Mathematics and Statistics Central South University Hunan410083 China

The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to discretize spatial and temporal derivatives to propagate solutions. Next, we present a non-intrusive time-parallelization and its two-level convergence analysis, where we algorithmically and theoretically generalize the MGRIT to time-dependent fine time-grid propagators. Finally, numerical illustrations show that the obtained numerical scheme possesses the saturation error order, theoretical results of the two-level variant deliver good predictions, and significant speedups can be achieved when compared to parareal and the sequential time-stepping approach. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite element method

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Convergence Analysis for the Chebyshev Collocation Methods to Volterra Integral Equations with a Weakly Singular Kernel

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Advances in Applied Mathematics and Mechanics 2017年第6期9卷 1506-1524页

作者： Xiong Liu Yanping Chen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Department of MathematicsXiangtan UniversityXiangtanHunan 411105China School of Mathematical Sciences South China Normal UniversityGuangzhouGuangdong 510631China School of Mathematics and Statistics Lingnan Normal UniversityZhanjiangGuangdong 524048China

In this paper,a Chebyshev-collocation spectral method is developed for Volterra integral equations(VIEs)of second kind with weakly singular *** first change the equation into an equivalent VIE so that the solution of the new equation possesses better *** integral term in the resulting VIE is approximated by Gauss quadrature formulas using the Chebyshev collocation *** convergence analysis of this method is based on the Lebesgue constant for the Lagrange interpolation polynomials,approximation theory for orthogonal polynomials,and the operator *** spectral rate of convergence for the proposed method is established in the L^(∞)-norm and weighted L^(2)-*** results are presented to demonstrate the effectiveness of the proposed method.

关键词： Chebyshev collocation method Volterra integral equations spectral rate of convergence H¨older continuity

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Enhancement of photoluminescence efficiency in GeSe ultrathin slab by thermal treatment and annealing: experiment and first-principles molecular dynamics simulations

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Scientific reports 2018年第1期8卷 17671页

作者： Yuliang Mao Xin Mao Hongquan Zhao Nandi Zhang Xuan Shi Jianmei Yuan Hunan Key Laboratory for Micro-Nano Energy Materials and Devices School of Physics and Optoelectronic Xiangtan University Hunan 411105 China. ylmao@***. Hunan Key Laboratory for Micro-Nano Energy Materials and Devices School of Physics and Optoelectronic Xiangtan University Hunan 411105 China. Chongqing institute of Green and Intelligent Technology Chinese Academy of Sciences Chongqing 401120 China. hqzhao@***. Chongqing institute of Green and Intelligent Technology Chinese Academy of Sciences Chongqing 401120 China. Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 China.

The effect of thermal treatment and annealing under different temperatures from 100 °C to 250 °C on the photoluminescence spectroscopy of the GeSe ultrathin slab is reported. After the thermal treatment and annealing under 200 °C, we found that the photoluminescence intensity of A exciton and B exciton in GeSe ultrathin slab is increased to twice as much as that in untreated case, while is increased by ~84% in the photoluminescence intensity of C exciton. Combined by our experimental work and theoretical simulations, our study confirms the significant role of thermal treatments and annealing in reducing surface roughness and removing the Se vacancy to form more compact and smoother regions in GeSe ultrathin slab. Our findings imply that the improved quality of GeSe surface after thermal treatments is an important factor for the photoluminescence enhancement.

关键词： Thermal Treatment First-principles Molecular Dynamics simulations Smoother Regions Reduced Surface Roughness GeSi Samples

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Numerical homogenization of elastoplastic deformations of composite material with small proportion of inclusions

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Journal of Physics: Conference Series 2019年第1期1392卷

作者： Petr V. Sivtsev Aleksandr E. Kolesov Petr E. Zakharov Ying Yang Research Laboratory 'Multiscale Matheatical Modeling and Computing' Ammosov North-Eastern Federal University 58 Belinskogo 677000 Yakutsk Russia Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 Hunan China

Numerical simulation of the stress-strain state of a composite material may be difficult due to large computational complexity associated with a grid resolution of a large number of inclusions. To overcome the problem one may use the homogenization method. But for material with plastic properties, proper modeling of yield stress and hardening may be overcomplicated. In this work we use some simplification associated with a small proportion of inclusions and restriction of stress values by matrix material strength. As model problem, we use deformation of concrete deep beam reinforced with steel or basalt fiber inclusions. For the numerical solution, the finite element method was applied using the FEniCS computing platform.

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