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Time-splitting finite difference method with the wavelet-adaptive grids for semiclassical Gross–Pitaevskii equation in supercritical case

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Journal of computational Physics 2014年 267卷 146-161页

作者： Xueyang Li Aiguo Xiao School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan 411105 PR China

The Gross–Pitaevskii equation is the model equation of the single-particle wave function in a Bose–Einstein condensation. A computation difficulty of the Gross–Pitaevskii equation comes from the semiclassical problem in supercritical case. In this paper, we apply a diffeomorphism to transform the original one-dimensional Gross–Pitaevskii equation into a modified equation. The adaptive grids are constructed through the interpolating wavelet method. Then, we use the time-splitting finite difference method with the wavelet-adaptive grids to solve the modified Gross–Pitaevskii equation, where the approximation to the second-order derivative is given by the Lagrange interpolation method. At last, the numerical results are given. It is shown that the obtained time-splitting finite difference method with the wavelet-adaptive grids is very efficient for solving the one-dimensional semiclassical Gross–Pitaevskii equation in supercritical case and it is suitable to deal with the local high oscillation of the solution.

关键词： Gross–Pitaevskii equation Wavelet-adaptive grids Time-splitting finite difference method Interpolating wavelet Lagrange interpolation method

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Protein folding kinetic order prediction from amino acid sequence based on horizontal visibility network

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Current Bioinformatics 2016年第2期11卷 173-185页

作者： Zhao, Zhi-Qin Yu, Zu-Guo Anh, Vo Wu, Jing-Yang Han, Guo-Sheng 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 XiangtanHunan411105 China School of Mathematical Sciences Queensland University of Technology GPO Box 2434 BrisbaneQ4001 Australia School of Science Xi’an Shiyou University 18 Second Dianzi Road Yanta District Xi’anShaanxi710065 China

Protein folding is one of the most important problems in molecular biology. The kinetic order of protein folding is one of the main aspects of the folding process. Previous methods for predicting protein folding kinetic order require to use the information on tertiary or predicted secondary structure of a protein. In this paper, based on physicochemical properties of amino acids, we propose an approach to predict the protein folding kinetic order from the primary structure of a protein using support vector machine combined with principal component analysis. The horizontal visibility network, Hilbert-Huang transform, global descriptor, and Lempel-Ziv complexity are used to extract features in our approach. To evaluate our approach, the leave-one-out cross-validation test is employed on two widely-used data sets ("IvankovData" and "ZhengData" data sets) consisting of two-state and multi-state proteins. The overall accuracies of prediction can reach 83.87% for "IvankovData" data set and 85% for "ZhengData" data set respectively. Comparisons with the existing methods show that the present approach performs better on the "IvankovData" data set. These results indicate that the present approach is effective and valuable for predicting protein folding kinetic order. Based on factor analysis, we find that the length of protein sequence, hydrophobicity and hydrophilicity of amino acids are important features in our approach. © 2016 Bentham science Publishers

关键词： Hilbert-Huang transform

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Finite element methods for fractional diffusion equations

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International Journal of Modeling, simulation, and Scientific Computing 2020年第4期11卷 32-52页

作者： Yue Zhao Chen Shen Min Qu Weiping Bu Yifa Tang LSEC ICMSECAcademy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190P.R.China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 P.R.China School of Mathematics and Computational Science&Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan 411105P.R.China

Due to the successful applications in engineering,physics,biology,finance,etc.,there has been substantial interest in fractional diffusion equations over the past few decades,and literatures on developing and analyzing efficient and accurate numerical methods for reliably simulating such equations are vast and fast *** paper gives a concise overview on finite element methods for these equations,which are divided into time fractional,space fractional and time-space fractional diffusion ***,we also involve some relevant topics on the regularity theory,the well-posedness,and the fast algorithm.

关键词： Fractional diffusion equation finite element method regularity theory well-posedness fast algorithm.

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Spectral collocation method for a class of fractional diffusion differential equations with nonsmooth solutions

Spectral collocation method for a class of fractional diffus...

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作者： Wang, Junjie Xiao, Aiguo Bu, Weiping Hunan Key Laboratory for Computation and Simulation in Science and Engineering & Key Laboratory for Intelligent Computing and Information Processing of Education Ministry Xiangtan University Hunan China School of Mathematics and Statistics Pu'er University Yunnan China

In this paper, we develop spectral collocation method for a class of fractional diffusion differential equations. Since the solutions of these fractional differential equations usually exhibit singularities at the end-points, it can not be well approximated by classical polynomial basis functions. We first give nonclassical interpolants based on the associated Jacobi-Gauss points and obtain the corresponding fractional differentiation matrices. Second, we prove the convergence for the developed spectral collocation method. Finally, several numerical examples are considered to demonstrate the validity and applicability of the developed basis functions. © 2020 John Wiley & Sons, Ltd.

关键词： Polynomials

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Underlying scaling relationships between solar activity and geomagnetic activity revealed by multifractal analyses

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Journal of Geophysical Research: Space Physics 2014年第9期119卷 7577-7586页

作者： Yu, Zu-Guo Anh, Vo Eastes, Richard Hunan Key Laboratory for Computation and Simulation in Science and Engineering Ministry of Education Xiangtan University Xiangtan Hunan China School of Mathematical Sciences Queensland University of Technology Brisbane QLD Australia Florida Space Institute University of Central Florida Orlando FL United States

This paper identifies some scaling relationships between solar activity and geomagnetic activity. We examine the scaling properties of hourly data for two geomagnetic indices (a_p and AE), two solar indices (solar X-rays X_l and solar flux F10.7), and two inner heliospheric indices (ion density Ni and flow speed Vs) over the period 1995-2001 by the universal multifractal approach and the traditional multifractal analysis. We found that the universal multifractal model (UMM) provides a good fit to the empirical K(q) and τ(q) curves of these time series. The estimated values of the Lévy index α in the UMM indicate that multifractality exists in the time series for a_p, AE, X_l, and Ni, while those for F10.7 and Vs are monofractal. The estimated values of the nonconservation parameter H of this model confirm that these time series are conservative which indicate that the mean value of the process is constant for varying resolution. Additionally, the multifractal K(q) and τ(q) curves, and the estimated values of the sparseness parameter C₁ of the UMM indicate that there are three pairs of indices displaying similar scaling properties, namely a_p and X_l, AE and Ni, and F10.7 and Vs. The similarity in the scaling properties of pairs (a_p,X_l) and (AE,Ni) suggests that a_p and X_l, AE and Ni are better correlated - in terms of scaling - than previous thought, respectively. But our results still cannot be used to advance forecasting of a_p and AE by X_l and Ni, respectively, due to some reasons. key Points The scaling properties of the geomagnetic and the solar indices are examinedThe results suggest that multifractality exists in a_p, AE, Xl, and ion densityThe scaling similarity of the a_p and Xl data suggests flare-storm dependence ©2014. American Geophysical Union. All Rights Reserved.

关键词： geomagnetic indices multifractal analysis scaling property solar indices universal multifractal model

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Anisotropic mesh generation methods based on ACVT and natural metric for anisotropic elliptic equation

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science CHINA Mathematics 2013年第12期56卷 2615-2630页

作者： HUANG YunQing SU YiFan WEI HuaYi YI NianYu Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China

Anisotropic meshes are known to be well-suited for problems which exhibit anisotropic solution features. Defining an appropriate metric tensor and designing an efficient algorithm for anisotropic mesh generation are two important aspects of the anisotropic mesh methodology. In this paper, we are concerned with the natural metric tensor for use in anisotropic mesh generation for anisotropic elliptic problems. We provide an algorithm to generate anisotropic meshes under the given metric tensor. We show that the inverse of the anisotropic diffusion matrix of the anisotropic elliptic problem is a natural metric tensor for the anisotropic mesh generation in three aspects: better discrete algebraic systems, more accurate finite element solution and superconvergence on the mesh nodes. Various numerical examples demonstrating the effectiveness are presented.

关键词： anisotropic mesh metric tensor superconvergence anisotropic elliptic equation

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An indirect convergent Jacobi spectral collocation method for fractional optimal control problems

An indirect convergent Jacobi spectral collocation method fo...

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作者： Yang, Yin Zhang, Jiaqi Liu, Huan O. Vasilev, Aleksandr 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 Xiangtan Hunan China Ammosov North-Eastern Federal University Yakutsk Russia

In this paper, we present a novel indirect convergent Jacobi spectral collocation method for fractional optimal control problems governed by a dynamical system including both classical derivative and Caputo fractional derivative. First, we present some necessary optimality conditions. Then we suggest a new Jacobi spectral collocation method to discretize the obtained conditions. By the proposed method, we get a system of algebraic equations by solving of which we can approximate the optimal solution of the main problem. Finally, we present a convergence analysis for our method and solve three numerical examples to show the efficiency and capability of the method. © 2019 John Wiley & Sons, Ltd.

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Parallelization of a DEM code based on CPU-GPU heterogeneous architecture

Parallelization of a DEM code based on CPU-GPU heterogeneous...

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26th International Conference on Parallel computational Fluid Dynamics, ParCFD 2013

作者： Yue, Xiaoqiang Zhang, Hao Luo, Congshu Shu, Shi Feng, Chunsheng School of Mathematics and Computational Science Xiangtan University 411105 Hunan China Heat and Mass Transfer Technological Center Technical University of Catalonia 08222 Terrassa Spain Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University 411105 Hunan China

ISBN: (纸本)9783642539619

Particulate flows are commonly encountered in both engineering and environmental applications. The discrete element method (DEM) has attracted plentiful attentions since it can predict the whole motion of the particulate flow by monitoring every single particle. However the computational capability of the method relies strongly on the numerical scheme as well as the hardware environment. In this study, a parallelization of a DEM based code titled Trubal was implemented. Numerical simulations were carried out to show the benefits of this research. It is shown that the final parallel code gave a substantial acceleration on the Trubal. By simulating 6,000 particles using a NVIDIA Tesla C2050 card together with Intel Core-Dual 2.93 GHz CPU, an average speedup of 4.69 in computational time was obtained. © Springer-Verlag Berlin Heidelberg 2014.

关键词： Finite difference method

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Two Physics-Based Schwarz Preconditioners for Three-Temperature Radiation Diffusion Equations in High Dimensions

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Communications in computational Physics 2022年第8期32卷 829-849页

作者： Xiaoqiang Yue Jianmeng He Xiaowen Xu Shi Shu Libo Wang National Center for Applied Mathematics in Hunan Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationHunan Key Laboratory for Computation and Simulation in Science and EngineeringXiangtan UniversityXiangtan 411105P.R.China Laboratory of Computational Physics Institute of Applied Physics and ComputationalMathematicsBeijing 100094P.R.China College of Information Science and Technology JinanUniversityGuangzhou 510632P.R.China

We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high *** this article,motivated by[***,***,***,SIAM *** ***.33(2012)653–680]and[***,***,***,***.442(2021)110513],we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain,and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear ***,computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.

关键词： Radiation diffusion equations Schwarz methods algebraic multigrid parallel and distributed computing

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A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 57-86页

作者： Yin Yang Jianyong Tao Shangyou Zhang Petr V.Sivtsev Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtanHunan 411105China Department of Mathematical Sciences University of DelawareNewarkDE 19716USA International Scientific and Research Laboratory of Multiscale Model Reduction and High Performance Computing Ammosov North Eastern UniversityKulakovskogo677013YakutskRussia

In this paper,we design a collocation method to solve the fractional Ginzburg-Landau equation.A Jacobi collocation method is developed and implemented in two ***,we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation(JGLC)method in one-and two-dimensional *** equation is then converted to a system of ordinary differential equations(ODEs)with the time variable based on *** second step applies the Jacobi-Gauss-Radau collocation(JGRC)method for the time ***,we give a theoretical proof of convergence of this Jacobi collocation method and some numerical results showing the proposed scheme is an effective and high-precision algorithm.

关键词： The fractional Ginzburg-Landau equation Jacobi collocation method convergence

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