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A Coupled Immersed Interface and Level Set Method for Three-Dimensional Interfacial Flows with Insoluble Surfactant

Communications in computational Physics 2014年第2期15卷 451-469页

作者： Jian-Jun Xu Yunqing Huang Ming-Chih Lai Zhilin Li School of Mathematical and Computational Sciences Xiangtan UniversityHunan 410005China Department of Applied Mathematics National Chiao Tung UniversityHsinchu 30050Taiwan Department of Mathematics North Carolina State UniversityRaleighNC27695USA .4 Hunan Key Lab for Computation and Simulation in Science and Engineering Hunan 410005China School of Mathematical Sciences Nanjing Normal UniversityNanjingChina.

In this paper,a numerical method is presented for simulating the 3D interfacial flows with insoluble *** numerical scheme consists of a 3D immersed interface method(IIM)for solving Stokes equations with jumps across the interface and a 3D level-set method for solving the surfactant convection-diffusion equation along a moving and deforming *** 3D IIM Poisson solver modifies the one in the literature by assuming that the jump conditions of the solution and the flux are implicitly given at the grid points in a small neighborhood of the *** assumption is convenient in conjunction with the level-set *** allows standard Lagrangian interpolation for quantities at the projection points on the *** interface jump relations are re-derived accordingly.A novel rotational procedure is given to generate smooth local coordinate systems and make effective *** examples demonstrate that the IIM Poisson solver and the Stokes solver achieve second-order accuracy.A 3D drop with insoluble surfactant under shear flow is investigated numerically by studying the influences of different physical parameters on the drop deformation.

关键词： Multigrid method constrained Cauchy-Born elasticity nanoindentation CauchyBorn rule.

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Recovery based finite element method for biharmonic equation in two dimensional

arXiv

引用

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 © 2018, 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

引用

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...

引用

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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Multiscale Adaptive Multifractal Cross-Correlation Analysis of Multivariate Time Series

SSRN

引用

SSRN 2023年

作者： Jiang, Huanwen Wang, Xinyao Han, Guosheng Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

In the real world, most of the time series generated from complex systems are nonlinear. To effectively study its fractal properties, in this work, we first generalize the adaptive fractal analysis (AFA) to the adaptive multifractal cross-correlation analysis (AMFCCA), which can be used to study the multifractal cross-correlation between two time series. Considering the complexity of time series from complex systems, we extend AMFCCA to the case of multivariate time series, namely multivariate adaptive multifractal cross-correlation analysis (MV-AMFCCA). In order to detect the multifractality on different time scales, we propose multiscale adaptive multifractal cross-correlation analysis of multivariate time series (MMV-AMFCCA). By the numerical simulation on synthetic multivariate processes, our method shows the theoretical validity. Furthermore, we applied these methods to the multifractal analysis of three pollutants in urban and suburban areas in Beijing. After removing the seasonal trend, we find that the urban and suburban systems both have multifractality, especially the multifractality of the urban system are more evident than the suburban systems, the degree of multifractality in spring and winter stronger than that in summer and autumn. Therefore, our methods are suitable for systems with multiple outputs and provide more comprehensive methods for characterizing autocorrelation and cross-correlation in multivariate time series. © 2023, The Authors. All rights reserved.

关键词： Time series

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Numerical Methods For Fractional Variational Problems Depending On Indefinite Integrals

Numerical Methods For Fractional Variational Problems Depend...

引用

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

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

arXiv

引用

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 © 2017, The Authors. All rights reserved.

关键词： computational complexity

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

arXiv

引用

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.35R11, 65F10, 65F15, 65N55 Copyright © 2017, The Authors. All rights reserved.

关键词： computational complexity

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

引用

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

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

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25th International Conference on Domain Decomposition Methods in science and engineering, DD 2018

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

ISBN: (纸本)9783030567491

关键词： Finite element method

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