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Journal of Computational Mathematics 2020年第3期38卷 452-468页

作者： Jie Chen Zhengkang He Shuyu Sun Shimin Guo Zhangxin Chen School of Mathematics and Statistics Xi'an Jiaotong UniversityXi'an 710049China Computational Transport Phenomena Laboratory Division of Physical Science and EngineeringKing Abdullah University of Science and TechnologyThuwal 23955-6900Kingdom of Saudi Arabia School of Mathematics and Statistics Xi'an Jiaotong Universityy Xi'an 710049China Department of Chemical&Petroleum Engineering Schulich School of EngineeringUniversity of Calgary2500 University Drive N.W.CalgaryAlberta T2N 1N4Canada

In this paper,we study linearly first and second order in time,uniquely solvable and unconditionally energy stable numerical schemes to approximate the phase field model of solid-state dewetting problems based on the novel"scalar auxiliary variable"(SAV)approach,a new developed efficient and accurate method for a large class of gradient *** schemes are based on the first order Euler method and the second order backward differential formulas(BDF2)for time discretization,and finite element methods for space *** proposed schemes are proved to be unconditionally stable and the discrete equations are uniquely solvable for all time *** numerical experiments are presented to validate the stability and accuracy of the proposed schemes.

关键词： Phase field models Solid-state dewetting SAV energy stability Surface diffusion Finite element method

Improvement of the energy stability of the Single Ion Microbeam

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Plasma Science and Technology 2008年第2期10卷 250-253页

作者：詹福如齐学红许明亮陈连运余增亮 Institute of Plasma Physics Chinese Academy of Sciences Hefei 230031 China

energy instability strongly affects the state and the beam size of the single ion microbeam. A facility based on the Generating Voltmeter was developed to improve the energy stability of the CAS-LIBB （Chinese Academy of Sciences, key laboratory of ion beam bioengineering） single ion microbeam. This paper presents the analysis of the energy＇ instability of the single ion microbeam. A simplified theoretical model is set up to calculate the relationship between the energy instability and the beam spot size. By using this technique, the energy instability is adjusted to about 1%. Stable run-time is over 6 hours. The radius of the single ion beam is reduced by 10% compared to the previous olin.

关键词： single ion microbeam energy stability electrostatic accelerator

Fully-Decoupled and Second-Order Time-Accurate Scheme for the Cahn–Hilliard Ohta–Kawaski Phase-Field Model of Diblock Copolymer Melt Confined in Hele–Shaw Cell

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Communications in Mathematics and Statistics 2024年第3期12卷 479-504页

作者： Junying Cao Jun Zhang Xiaofeng Yang School of Data Science and Information Engineering Guizhou Minzu UniversityGuiyang 550025People’s Republic of China Guizhou Key Laboratory of Big Data Statistics Analysis Computational Mathematics Research CenterGuizhou University of Finance and EconomicsGuiyang 550025People’s Republic of China Department of Mathematics University of South CarolinaColumbiaSCUSA

In this work,we consider numerical approximations of the phase-field model of diblock copolymer melt confined in Hele–Shaw cell,which is a very complicated coupled nonlinear system consisting of the Darcy equations and the Cahn–Hilliard type equations with the Ohta–Kawaski *** the combination of a novel explicit-Invariant energy Quadratization approach and the projection method,we develop the first full decoupling,energy stable,and second-order time-accurate numerical *** introduction of two auxiliary variables and the design of two auxiliary ODEs play a vital role in obtaining the full decoupling structure while maintaining energy *** scheme is also linear and unconditional energy stable,and the practical implementation efficiency is also very high because it only needs to solve a few elliptic equations with constant coefficients at each time *** strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation *** experiments further verify the convergence rate,energy stability,and effectiveness of the developed algorithm.

关键词： Phase-field Explicit-IEQ Darcy Decoupled energy stability Diblock copolymer melt

Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation

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Science China Mathematics 2022年第10期65卷 2201-2218页

作者： Xiaoli Li Jie Shen School of Mathematics Shandong UniversityJinan 250100China Department of Mathematics Purdue UniversityWest LafayetteIN 47907USA

In this paper,we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase field crystal equation,which is a sixth-order nonlinear damped wave *** schemes are linear,conserve mass and unconditionally dissipate a pseudo *** prove rigorously second-order error estimates in both time and space for the phase field variable in discrete *** also present some numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy.

关键词： modified phase field crystal scalar auxiliary variable energy stability error estimate numerical experiments

Analysis of the second-order BDF scheme with variable steps for the molecular beam epitaxial model without slope selection

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Science China Mathematics 2021年第5期64卷 887-902页

作者： Hong-Lin Liao Xuehua Song Tao Tang Tao Zhou Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211101China Department of Mathematics and International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China Division of Science and Technology BNU-HKBU United International CollegeZhuhai 519087China NCMIS&LSEC Institute of Computational Mathematics and Scientific Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this work,we are concerned with the stability and convergence analysis of the second-order backward difference formula(BDF2)with variable steps for the molecular beam epitaxial model without slope *** first show that the variable-step BDF2 scheme is convex and uniquely solvable under a weak time-step *** we show that it preserves an energy dissipation law if the adjacent time-step ratios satisfy r_(k):=τ_(k)/τ_(k-1)stability and rigorous error estimates are established,under the same step-ratio constraint that ensures the energy stability,i.e.,0

关键词： molecular beam epitaxial growth variable-step BDF2 scheme discrete orthogonal convolution kernels energy stability convergence analysis

Highly efficient and unconditionally energy stable semi-discrete time-marching numerical scheme for the two-phase incompressible flow phase-field system with variable-density and viscosity

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Science China Mathematics 2022年第12期65卷 2631-2656页

作者： Chuanjun Chen Xiaofeng Yang School of Mathematics and Information Sciences Yantai UniversityYantai 264005China Department of Mathematics University of South CarolinaSC29208USA

For the variable-density/viscosity Cahn-Hilliard phase-field model of the binary-phase incompressible fluid flow system, the development of easy-to-implement numerical schemes has long been known as a challenging problem. We develop a novel fully-decoupled numerical technique in this article which can achieve unconditional energy stability while explicitly discretizing nonlinear coupling items. The idea is invented on the basis of combining the Strang operator splitting method and the novel decoupling method by using the zero-energy-contribution property. The scheme only needs to solve a series of completely independent linear elliptic equations at each time step, in which the Cahn-Hilliard equation and the pressure Poisson equation are with constant coefficients. To demonstrate the effectiveness of the scheme, we provide the rigorous proof of the energy stability/solvability, and also perform ample accuracy and stability tests and 2D/3D numerical simulations, including the Rayleigh-Taylor instability and bubble rising dynamics.

关键词： variable-density decoupled time marching Cahn-Hilliard equation Navier-Stokes equations energy stability

Two-Phase Image Segmentation by the Allen-Cahn Equation and a Nonlocal Edge Detection Operator

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Numerical Mathematics(Theory,Methods and Applications) 2022年第4期15卷 1147-1172页

作者： Zhonghua Qiao Qian Zhang Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomHong KongSARChina Research Institute for Smart energy The Hong Kong Polytechnic UniversityHung HomHong KongSARChina School of Science Harbin Institute of TechnologyShenzhenChina

Based on a nonlocal Laplacian operator,a novel edge detection method of the grayscale image is proposed in this *** operator utilizes the information of neighbor pixels for a given pixel to obtain effective and delicate edge *** nonlocal edge detection method is used as an initialization for solving the Allen-Cahn equation to achieve two-phase segmentation of the grayscale *** exponential time differencing(ETD)solvers are employed in the time integration,and finite difference method is adopted in space *** maximum bound principle and energy stability of the proposed numerical schemes are *** capability of our segmentation method has been verified in numerical experiments for different types of grayscale images.

关键词： Image segmentation Allen-Cahn equation nonlocal edge detection operator maximum principle energy stability

An energy Stable Monolithic Eulerian Fluid-Structure Numerical Scheme

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Chinese Annals of Mathematics,Series B 2018年第2期39卷 213-232页

作者： olivier pironneau Dedicated to Philippe G. Ciarlet on the occasion of his 80th birthda

The conservation laws of continuum mechanics, written in an Eulerian frame,do not distinguish fluids and solids, except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for hyperelastic solids. By taking the velocities as unknown monolithic methods for fluid structure interactions(FSI for short) are built. In this paper such a formulation is analysed when the solid is compressible and the fluid is incompressible. The idea is not new but the progress of mesh generators and numerical schemes like the Characteristics-Galerkin method render this approach feasible and reasonably robust. In this paper the method and its discretisation are presented, stability is discussed through an energy estimate. A numerical section discusses implementation issues and presents a few simple tests.

关键词： Fluid-Structure interactions Numerical method energy stability Finiteelement method

Hybrid Seagull and Whale Optimization Algorithm-Based Dynamic Clustering Protocol for Improving Network Longevity in Wireless Sensor Networks

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China Communications 2024年第10期21卷 113-131页

作者： P.Vinoth Kumar K.Venkatesh Department of Networking and Communications School of ComputingCollege of Engineering and TechnologySRM Institute of Science and TechnologyKattankulathur 603203India

energy efficiency is the prime concern in Wireless Sensor Networks(WSNs) as maximized energy consumption without essentially limits the energy stability and network lifetime. Clustering is the significant approach essential for minimizing unnecessary transmission energy consumption with sustained network lifetime. This clustering process is identified as the Non-deterministic Polynomial(NP)-hard optimization problems which has the maximized probability of being solved through metaheuristic *** adoption of hybrid metaheuristic algorithm concentrates on the identification of the optimal or nearoptimal solutions which aids in better energy stability during Cluster Head(CH) selection. In this paper,Hybrid Seagull and Whale Optimization Algorithmbased Dynamic Clustering Protocol(HSWOA-DCP)is proposed with the exploitation benefits of WOA and exploration merits of SEOA to optimal CH selection for maintaining energy stability with prolonged network lifetime. This HSWOA-DCP adopted the modified version of SEagull Optimization Algorithm(SEOA) to handle the problem of premature convergence and computational accuracy which is maximally possible during CH selection. The inclusion of SEOA into WOA improved the global searching capability during the selection of CH and prevents worst fitness nodes from being selected as CH, since the spiral attacking behavior of SEOA is similar to the bubble-net characteristics of WOA. This CH selection integrates the spiral attacking principles of SEOA and contraction surrounding mechanism of WOA for improving computation accuracy to prevent frequent election process. It also included the strategy of levy flight strategy into SEOA for potentially avoiding premature convergence to attain better trade-off between the rate of exploration and exploitation in a more effective manner. The simulation results of the proposed HSWOADCP confirmed better network survivability rate, network residual energy and network overall throughput on par wi

关键词： clustering energy stability network lifetime seagull optimization algorithm(SEOA) whale optimization algorithm(WOA) wireless sensor networks(WSNs)

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

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Acta Mathematica Scientia 2024年第2期44卷 650-670页

作者：司智勇 School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuo454003China

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau *** backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau *** this method,the system is decoupled and linearized to avoid solving the non-linear equation at each *** theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

关键词： time-dependent Ginzburg-Landau equation generalized scalar auxiliary variable algorithm maximum bound principle energy stability