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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 © 201., The Authors. All rights reserved.

关键词： Numerical methods

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Numerical methods for the mass-conserved Ohta-Kawasaki equation

arXiv

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arXiv 2019年

作者： Zhang, Juan Li, Shifeng Jiang, Kai School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

In this paper, we propose a numerical method to solve the mass-conserved Ohta-Kawasaki equation with finite element discretization. An unconditional stable convex splitting scheme is applied to time approximation. The Newton method and its variant are used to address the implicitly nonlinear term. We rigorously analyze the convergence of the Newton iteration methods. Theoretical results demonstrate that two Newton iteration methods have the same convergence rate, and the Newton method has a smaller convergent factor than the variant one. To reduce the condition number of discretized linear system, we design two efficient block preconditioners and analyze their spectral distribution. Finally, we offer numerical examples to support the theoretical analysis and indicate the efficiency of the proposed numerical methods for the mass-conserved Ohta-Kawasaki equation. Copyright © 201., The Authors. All rights reserved.

关键词： Newton-Raphson method

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The Parallel Generation of 2-D Hilbert Space-filling Curve on GPU

The Parallel Generation of 2-D Hilbert Space-filling Curve o...

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International Conference on Biomedical engineering and Informatics

作者： Chunsheng Feng Shi Shu Junxian Wang Zheng Li Hunan Key Laboratory for Computation & Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan China

ISBN: (纸本)9781467311830

In this paper, we propose two parallel Hilbert Space-filling Curve(HSFC) generation algorithms BMIMp and SDDMp based on block matrix iteration method(BMIM) and state diagrams driver method(SDDM) in the CUDA parallel programming mode. Numerical results show that both of them obtain high parallel speedup. Especially, the speedup of BMIMp and SDDMp can reach 207 and 290 respectively for the 1.-order HSFC. Furthermore, BMIMp outperforms SDDMp when considering the total computation time.

关键词： Hilbert Space-filling Curve block matrix iteration method state diagrams driver method CUDA C parallel computation

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Numerical prediction of inner turbulent flow in conical diffuser by using a new five-point scheme and DLR k-ε turbulence model

Numerical prediction of inner turbulent flow in conical diff...

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The 9th National Conference on Rheology

作者：蒋光彪何永森舒适肖映雄 College of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University

The internal turbulent flow in conical diffuser is a very complicated adverse pressure gradient *** k-ε turbulence model was adopted to study *** every terms of the Laplace operator in DLR k-ε turbulence model and pressure Poisson equation were discretized by upwind difference scheme.A new full implicit difference scheme of 5-point was constructed by using finite volume method and finite difference method.A large sparse matrix with five diagonals was formed and was stored by three arrays of one dimension in a compressed *** iterative methods do not work well with large sparse *** algebraic multigrid method(AMG),linear algebraic system of equations was solved and the precision was set at *** computation results were compared with the experimental *** results show that the computation results have a good agreement with the experiment *** precision of computational results and numerical simulation efficiency are greatly improved.

关键词： conical diffuser turbulent flow DLR k-ε turbulence model 5-point scheme algebraic multigrid method（AMG）

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Superconvergence and asymptotic expansion for semidiscrete bilinear finite volume element approximation of the parabolic problem

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Computers & Mathematics with Applications 2013年第1期66卷 91-104页

作者： Cunyun Nie Shi Shu Haiyuan Yu Yuyue Yang Department of Mathematics and Physics Hunan Institution of Engineering Hunan 411104 China Hunan Key Laboratory for Computation & Simulation in Science and Engineering Xiangtan University Hunan 411105 China Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education Xiangtan University Hunan 411105 China

We first derive the asymptotic expansion of the bilinear finite volume element for the linear parabolic problem by employing the energy-embedded method on uniform grids, and then obtain a high accuracy combination pointwise formula of the derivatives for the finite volume element approximation based on the above asymptotic expansion. Furthermore, we prove that the approximate derivatives have the convergence rate of order two. Numerical experiments confirm the theoretical results.

关键词： Linear parabolic problem Bilinear finite volume element Error asymptotic expansion Superconvergence

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Stability of three-dimensional icosahedral quasicrystals in multi-component systems

arXiv

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arXiv 2019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 411105 China

The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a phenomenological coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, Which provides a unified numerical framework to study periodic crystals and quasicrystals, Is used to compute free energy to high accuracy. Compared with traditional approaches, the advantage of the projection method has also been discussed in detail. A rigorous and systematic computation demonstrates that threedimensional icosahedral quasicrystal and two-dimensional decagonal quasicrystal are both stable phases in such a simple multi-component coupled-mode Swift-Hohenberg model. The result extends the two length-scales interaction mechanism of stabilizing quasicrystals from single-component to multi-component systems. Copyright © 201., The Authors. All rights reserved.

关键词： Quasicrystals

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A software cascading faults model

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science China(Information sciences) 2011年第11期54卷 2454-2458页

作者： LIU YanHeng 1.2,LIU XueLian 3 & WANG Jian 1.2 1.key {1. of Symbolic computation and Knowledge engineering of Ministry of Education,Jilin University,Changchun 1.001.,China 2 College of Computer science and Technology,Jilin University,Changchun 1.001.,China 3 College of Software,Jilin University,Changchun 1.001.,China 1. Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education Jilin University Changchun 130012 China2. College of Computer Science and Technology Jilin University Changchun 130012 China3. College of Software Jilin University Changchun 130012 China

Functions and call relations are extracted into nodes and edges,respectively,by which a novel topological model is *** directional edges and the corresponding weight values express the call relations and tightness *** introducing two concepts of function fault-tolerant capability and software fault intensity and by designing a allocation rule on fault-tolerant capability,a cascading fault model is built to explore fault propagation *** on practical software networks show that a weak fault intensity,a small number of initial faults,and a strong fault-tolerant capability can slow down the spreading *** functions with more call relations and more closer tightness contribute more to the stability of the whole system.

关键词： software fault tolerant cascading faults fault-tolerant capability fault intensity

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Recovery based finite element method for biharmonic equation in two dimensional

arXiv

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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 © 201., The Authors. All rights reserved.

关键词： Finite element method

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CONVERGENCE ANALYSIS OF THE JACOBI SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2014年第3期34卷 673-690页

作者： Yang Yin Chen Yanping Huang Yunqing Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan 411105 School of Mathematical Sciences South China Normal University Guangzhou 510631

We propose and analyze a spectral Jacobi-collocation approximation for frac- tional order integro-differential equations of Volterra type. The fractional derivative is de- scribed in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L~∞ norm and weighted L~2-norm. The numerical examples are given to illustrate the theoretical results.

关键词： Spectral Jacobi-collocation method fractional order integro-differential equa- tions Caputo derivative

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Identifying possible lncRNA-disease associations based on deep learning and positive-unlabeled learning

Identifying possible lncRNA-disease associations based on de...

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IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

作者： Lihong Peng Liangliang Huang Yuankang Lu Guangyi Liu Min Chen Guosheng Han School of Computer Science Hunan University of Technology Zhuzhou China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan China

ISBN: (数字)9781665468190

ISBN: (纸本)9781665468206

lncRNAs are involved in many biological processes, and their mutations and disorders are closely related to many diseases. Identification of LncRNA-Disease Associations (LDAs) helps us understand the pathogenesis of diseases and improve their diagnosis and treatment. However, experiments to determine LDAs are expensive, so it is essential to exploit effective computational methods to screen possible LDAs. In this study, we developed an LDA prediction model (LDA-DLPU) based on deep learning and positive-unlabeled (PU) learning. First, LDA-DLPU extracted features of lncRNAs and diseases based on singular value decomposition and regression model. Second, it selected negative LDAs based on PU learning and graph autoencoder. Finally, it classified unknown lncRNA-disease pairs based on deep neural network. LDA-DLPU obtained the best performance on two datasets. We predict that BCYRN1.and IFNG-AS1.may associate with leukemia.

关键词： Deep learning computational modeling Neural networks Biological processes Predictive models Feature extraction Bioinformatics

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