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Efficient implementation of the Barnes-Hut octree algorithm for Monte Carlo simulations of charged systems

Science China mathematics 2014年第7期57卷 1331-1340页

作者： GAN ZeCheng XU ZhenLi Department of Mathematics Institute of Natural Sciencesand MoE Key Lab of Scientific and Engineering ComputingShanghai Jiao Tong University

Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many biological and soft matter materials solvable in *** appropriate treatment of long-range electrostatic interaction is essential for these charged systems,but remains a challenging problem for large-scale *** develop an efficient Barnes-Hut treecode algorithm for electrostatic evaluation in Monte Carlo simulations of Coulomb many-body *** algorithm is based on a divide-and-conquer strategy and fast update of the octree data structure in each trial move through a local adjustment *** test the accuracy of the tree algorithm,and use it to perform computer simulations of electric double layer near a spherical *** is shown that the computational cost of the Monte Carlo method with treecode acceleration scales as log N in each *** a typical system with ten thousand particles,by using the new algorithm,the speed has been improved by two orders of magnitude from the direct summation.

关键词： electrostatics Monte Carlo fast algorithms octree colloidal interfaces

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Orbital-Free Density Functional Theory for Molecular Structure Calculations

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Numerical mathematics(Theory,Methods and Applications) 2008年第1期1卷 1-28页

作者： Huajie Chen Aihui Zhou LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Graduate University of Chinese Academy of Sciences Beijing 100080 China

We give here an overview of the orbital-flee density functional theory that is used for modeling atoms and molecules. We review typical approximations to the kinetic energy, exchange-correlation corrections to the kinetic and Hartree energies, and constructions of the pseudopotentials. We discuss numerical discretizations for the orbital-free methods and include several numerical results for illustrations.

关键词： Density functional theory molecular structure numerical discretization orbital-free

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A Compact Scheme for Coupled Stochastic Nonlinear Schrodinger Equations

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Communications in computational Physics 2017年第1期21卷 93-125页

作者： Chuchu Chen Jialin Hong Lihai Ji Linghua Kong Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Institute of Applied Physics and ComputationalMathematics Beijing 100094China School of Mathematics and Information Science Jiangxi Normal UniversityNanchangJiangxi 330022China

In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger *** prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law,discrete charge conservation law and discrete energy evolution law almost *** experiments confirm well the theoretical analysis ***,we present a detailed numerical investigation of the optical phenomena based on the compact *** numerical experiments for various amplitudes of noise,we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to *** particular,if the noise is relatively strong,the soliton will be totally ***,we observe that the phase shift is sensibly modified by the ***,the numerical results present inelastic interaction which is different from the deterministic case.

关键词： Coupled stochastic nonlinear Schrodinger equations compact scheme stochastic multi-symplectic conservation law energy evolution law charge conservation law soliton evolution soliton interaction

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A POSITIVITY-PRESERVING FINITE ELEMENT METHOD FOR QUANTUM DRIFT-DIFFUSION MODEL

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Journal of computational mathematics 2023年第5期41卷 909-932页

作者： Pengcong Mu Weiying Zheng School of Mathematical Science University of Chinese Academy of SciencesBeijing 100049China LSEC NCMISInstitute of Computational Mathematics and Scientific ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion *** model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi *** propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction *** IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction ***,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi *** Poisson equation of electrical potential is solved with standard Lagrangian finite *** prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete *** experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.

关键词： Quantum drift-diffusion model Positivity-preserving finite element method Newton method FinFET device High bias voltage

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A computational framework for Carreau nanomaterial induced by stretchy regime considering Brownian diffusion, viscous dissipation, ferromagnetism and thermophoresis

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Partial Differential Equations in Applied mathematics 2025年 13卷

作者： Hussain, Iftikhar Khan, Waqar Azeem Tabrez, Muhammad Waqas, M. Ibrahim, Talib K. Saidani, Taoufik Kausar, M.S. Zamri, Nurnadiah Abdullaeva, Barno Garalleh, Hakim AL Department of Mathematics Mohi-ud-Din Islamic University Nerian Sharif Jammu and Kashmir Azad 12010 Pakistan School of Mathematics and Statistics Beijing Institute of Technology Beijing 100081 China NUTECH School of Applied Sciences and Humanities National University of Technology Islamabad 44000 Pakistan Faculty of Informatics and Computing Universiti Sultan Zainal Abidin Besut Campus Terengganu Besut 22200 Malaysia Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Department of Petroleum Engineering College of Engineering Knowledge University Erbil 44001 Iraq Department of Petroleum Engineering Al-Kitab University Altun Kupri Iraq Center for Scientific Research and Entrepreneurship Northern Border University Arar 73213 Saudi Arabia Faculty of Informatics and Computing Universiti Sultan Zainal Abidin (Kampus Gong Badak) Terengganu Kuala Terengganu 21300 Malaysia Department of Mathematics and Information Technologies Vice-Rector for Scientific Affairs Tashkent State Pedagogical University Tashkent Uzbekistan Department of Mathematical Science College of Engineering University of Business and Technology Jeddah 21361 Saudi Arabia

In recent decade, the research in nanotechnology brought the idea of nanofluids which are highly conducting materials. Some important applications of nanofluids are justified in pharmaceutical industry, coolants in vehicles engine, preparation process of various medicines for treatment of fatal diseases like cancer, aircraft industry, latest heat exchangers etc. The ferro particles are special class of nanomaterial which attract variety of interest from the researchers. The objective of current research is to perform the investigation for heat and mass transfer subject to Carreau nanofluid to observe the enhancement of heat transmission phenomena. The induction of magnetic dipole has been observed for thermal transport phenomenon. The flow is causing by stretched surface. A simplified system is obtained by utilizing the dimensionless variables. Physical interpretation of results have been presented. Result showed that temperature profile in presence of ferrofluid fluid boosts up with escalation in thermophoresis parameter, while opposite behavior is noted for power law index. The concentration of ferrofluid showing declining behavior for Schmidt numbers and rises for thermophoresis parameter. © 2024

关键词： Carreau ferrofluid Heat and mass transfer Magnetic dipole Numerical solution

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HETEROGENEOUS MULTISCALE METHODS FOR FOURTH-ORDER SINGULAR PERTURBATIONS

arXiv

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arXiv 2025年

作者： Liao, Yulei Ming, Pingbing Department of Mathematics Faculty of Science National University of Singapore 10 Lower Kent Ridge Road Singapore119076 Singapore LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models for architectured materials. We establish an error estimate for the homogenized solution applicable to general media and derive an explicit convergence for the locally periodic media with the fine-scale Ε. For cell problems of size δ = NΕ, the classical resonance error O(Ε/δ) can be eliminated due to the dominance of the higher-order operator. Despite the occurrence of boundary layer effects, discretization errors do not necessarily deteriorate for general boundary conditions. Numerical simulations corroborate these theoretical findings. Copyright © 2025, The Authors. All rights reserved.

关键词： Convergence of numerical methods

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Flexible alignment of images using B-spline reparameterization and L 2-gradient flows

Flexible alignment of images using B-spline reparameterizati...

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International Congress on Image and Signal Processing

作者： Xu, Guoliang Zheng, Yanmei State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China

ISBN: (纸本)9781424465149

In this paper, we present a new flexible alignment method to align two or more similar images. By minimizing an energy functional measuring the difference of the initial image and target image, a L2-gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and a semi-implicit Euler scheme in the temporal direction. The experimental results show that the proposed method is efficient, effective and capable of capturing large variation of the initial and the target images. ©2010 IEEE.

关键词： Finite element method

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A Review and Prospect for scientific and engineering computing in China

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Bulletin of the Chinese Academy of Sciences 2002年第1期16卷 49-52页

作者： Yu Dehao(CAS institute of computational mathematics & scientific/engineering computing) CAS Institute of Computational Mathematics & Scientific/Engineering Computing

The rise of scientific computing was one of the most important advances in the S&T progress during the second half of the 20th century. Parallel with theoretical exploration and scientific experiments,scientific computing has become the 'third means' for scientific activities in the world today. The article gives a panoramic review of the subject during the past 50 years in China and lists the contributions made by Chinese scientists in this field. In addition, it reveals some key contents of related projects in the national research plan and looks into the development vista for the subject in China at the dawning years of the new century.

关键词： Pro A Review and Prospect for scientific and engineering computing in China

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A Cone Constrained Convex Program:Structure and Algorithms

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Journal of the Operations Research Society of China 2013年第1期1卷 37-53页

作者： Liqun Qi Yi Xu Ya-Xiang Yuan Xinzhen Zhang Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomKowloonHong KongChina State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesZhong Guan Cun Donglu 55Beijing100190P.R.China Department of Mathematics School of ScienceTianjin UniversityTianjin300072China

In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and *** study defining functions,defining sequences and polyhedral outer approximations for this positive semidefinite space tensor cone,give an error bound for the polyhedral outer approximation approach,and thus establish convergence of three polyhedral outer approximation algorithms for solving this *** then study some other approaches for solving this structured convex *** include the conic linear programming approach,the nonsmooth convex program approach and the bi-level program *** numerical examples are presented.

关键词： Convex program Space tensor Positive semi-definiteness Cone Algorithms

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A Constrained Cauchy-Born Elasticity Accelerated Multigrid Method for Nanoindentation

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Communications in computational Physics 2014年第2期15卷 470-486页

作者： Jingrun Chen Pingbing Ming Jerry Zhijian Yang Institute of Computational Mathematics and Scientific/Engineering Computing AMSSChinese Academy of SciencesBeijing100190P.R.China. LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesNo.55 East Road Zhong-Guan-CunBeijing100190P.R.China. School of Mathematics and Statistics Wuhan UniversityWuhan430072P.R.China. South Hall 6705 Mathematics DepartmentUniversity of CaliforniaSanta BarbaraCA93106USA

We introduce a new multigrid method to study the lattice statics model arising from nanoindentation.A constrained Cauchy-Born elasticity model is used as the coarse-grid *** method accelerates the relaxation process and considerably reduces the computational *** particular,it saves quite a bit when dislocations nucleate and move,as demonstrated by the simulation results.

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

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