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High-order energy stable schemes of incommensurate phase-field crystal model

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arXiv 2018年

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

This article focuses on the development of high-order energy stable schemes for the multi-length-scale incommensurate phase-field crystal model which is able to study the phase behavior of aperiodic structures. These high-order schemes based on the scalar auxiliary variable (SAV) and spectral deferred correction (SDC) approaches are suitable for the L2.gradient flow equation, i.e., the Allen-Cahn dynamic equation. Concretely, we propose a second-order Crank-Nicolson (CN) scheme of the SAV system, prove the energy dissipation law, and give the error estimate in the almost periodic function sense. Moreover, we use the SDC method to improve the computational accuracy of the SAV/CN scheme. Numerical results demonstrate the advantages of high-order numerical methods in numerical computations and show the influence of length-scales on the formation of ordered structures. Copyright © 2.18, The Authors. All rights reserved.

关键词： Numerical methods

Recovery based finite element method for biharmonic equation in two dimensional

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arXiv 2018年

作者： Huang, Yunqing Wei, Huayi Yang, Wei Yi, Nianyu Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China

We design and numerically validate a recovery based linear finite element method for solving the biharmonic equation. The main idea is to replace the gradient operator ∇ on linear finite element space by G(∇) in the weak formulation of the biharmonic equation, where G is the recovery operator which recovers the piecewise constant function into the linear finite element space. By operator G, Laplace operator ∆ is replaced by ∇ · G(∇). Furthermore the boundary condition on normal derivative ∇u · n is treated by the boundary penalty method. The explicit matrix expression of the proposed method is also introduced. Numerical examples on uniform and adaptive meshes are presented to illustrate the correctness and effectiveness of the proposed *** Codes 65N30 Copyright © 2.18, The Authors. All rights reserved.

关键词： Finite element method

An Improved Third-order CWENO-Z Scheme at critical points

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IOP Conference Series: Materials science and engineering 2019年第3期569卷

作者： Shujiang Tang Mingjun Li Shuang Han School of mathematics and computational science Xiangtan University Xiangtan Hunan 411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan Hunan 411105 China

In this paper, by modifying the smoothness factor of the third-order CWENO scheme, we present the two-parameter CWENO-NZ3 scheme to improve accuracy at critical points. We selected some classical examples for numerical simulation, such as one-dimensional Sod shock tube, Shock-entropy wave interaction, Riemann problem with strong discontinuity and Rayleigh-Taylor instability problem. Numerically comparing with the classical third-order CWENO schemes, it is found that the improved schemes not only improve accuracy and resolution at the extreme points, but also reduce dissipation.

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

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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 © 2.18, The Authors. All rights reserved.

关键词： Runge Kutta methods

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

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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 © 2.18, The Authors. All rights reserved.

关键词： Helmholtz equation

Corrigendum to “Curl recovery for the lowest order rectangular edge element” [Applied Mathematics and computation 371 (2.2.) 12.897]

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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

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. © 2.17 Elsevier B.V.

关键词： Adsorption

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 2. 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 0.92.. 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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