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Journal of Computational Mathematics 2023年第3期41卷 370-394页

作者： Haishen Dai qiumei huang Cheng Wang School of Mathematics Faculty of ScienceBeijing University of TechnologyBeijing 100124China Department of Mathematics University of MassachusettsNorth DartmouthMA 02747USA

In this paper,ETD3-Padéand ETD4-PadéGalerkin finite element methods are proposed and analyzed for nonlinear delayed convection-diffusion-reaction equations with Dirichlet boundary conditions.An ETD-based RK is used for time integration of the corresponding equation.To overcome a well-known difficulty of numerical instability associated with the computation of the exponential operator,the Padéapproach is used for such an exponential operator approximation,which in turn leads to the corresponding ETD-Padéschemes.An unconditional L^(2) numerical stability is proved for the proposed numerical schemes,under a global Lipshitz continuity assumption.In addition,optimal rate error estimates are provided,which gives the convergence order of O(k^(3)+h^(r))(ETD3-Padé)or O(k^(4)+h^(r))(ETD4-Padé)in the L^(2)norm,respectively.Numerical experiments are presented to demonstrate the robustness of the proposed numerical schemes.

关键词： Nonlinear delayed convection diffusion reaction equations ETD-Pad´e scheme Lipshitz continuity L^(2)stability analysis Convergence analysis and error estimate

Exponential Time Differencing Schemes for the Peng-Robinson Equation of State with Preservation of Maximum Bound Principle

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 494-527页

作者： qiumei huang Kun Jiang Jingwei Li College of Mathematics Faculty of ScienceBeijing University of TechnologyBeijing 100124China Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China Laboratory of Mathematics and Complex Systems and School of Mathematical Science Beijing Normal UniversityBeijing 100875China

The Peng-Robison equation of state,one of the most extensively applied equations of state in the petroleum industry and chemical engineering,has an excel-lent appearance in predicting the thermodynamic properties of a wide variety of ma-terials.It has been a great challenge on how to design numerical schemes with preser-vation of mass conservation and energy dissipation law.Based on the exponential time difference combined with the stabilizing technique and added Lagrange multi-plier enforcing the mass conservation,we develop the efﬁcientﬁrst-and second-order numerical schemes with preservation of maximum bound principle(MBP)to solve the single-component two-phase diffuse interface model with Peng-Robison equation of state.Convergence analyses as well as energy stability are also proven.Several two-dimensional and three-dimensional experiments are performed to verify these theo-retical results.

关键词： Peng-Robinson equation of state diffuse interface model maximum bound principle exponential time differencing Lagrange multiplier

A NOTE ON RICHARDSON EXTRAPOLATION OF GALERKIN METHODS FOR EIGENVALUE PROBLEMS OF FREDHOLM INTEGRAL EQUATIONS

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Journal of Computational Mathematics 2008年第4期26卷 598-612页

作者： qiumei huang Yidu Yang LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China School of Mathematics and Computer Science Guizhou Normal University Guiyang 550001 China

In this paper, we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms. Using this extrapolation formula, we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues. Some numerical experiments ave carried out to demonstrate the effectiveness of our new method and to confirm our theoretical results.

关键词： Fredholm integral equations Semi-simple eigenvalues Asymptotic expansion,Galerkin method Richardson extrapolation Sloan iteration.

An accurate a posteriori error estimator for the Steklov eigenvalue problem and its applications

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Science China Mathematics 2021年第3期64卷 623-638页

作者： Fei Xu qiumei huang Beijing Institute for Scientific and Engineering Computing Faculty of ScienceBeijing University of TechnologyBeijing 100124China

In this paper, a type of accurate a posteriori error estimator is proposed for the Steklov eigenvalue problem based on the complementary approach, which provides an asymptotic exact estimate for the approximate eigenpair. Besides, we design a type of cascadic adaptive finite element method for the Steklov eigenvalue problem based on the proposed a posteriori error estimator. In this new cascadic adaptive scheme, instead of solving the Steklov eigenvalue problem in each adaptive space directly, we only need to do some smoothing steps for linearized boundary value problems on a series of adaptive spaces and solve some Steklov eigenvalue problems on a low dimensional space. Furthermore, the proposed a posteriori error estimator provides the way to refine meshes and control the number of smoothing steps for the cascadic adaptive method. Some numerical examples are presented to validate the efficiency of the algorithm in this paper.

关键词： Steklov eigenvalue problem a posteriori error estimator cascadic multigrid method adaptive finite element method complementary method

Numerical Investigations of a Class of Biological Models on Unbounded Domain

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Numerical Mathematics(Theory,Methods and Applications) 2019年第1期12卷 169-186页

作者： qiumei huang Dongfang Li Jiwei Zhang Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing 100124China School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratoryof Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China Beijing Computational Science Research Center Beijing1000193China

This paper is concerned with numerical computations of a class of biologi-cal models on unbounded spatial domains.To overcome the unboundedness of spatial domain,we first construct efficient local absorbing boundary conditions(LABCs)to re-formulate the Cauchy problem into an initial-boundary value(IBV)problem.After that,we construct a linearized finite difference scheme for the reduced IVB problem,and provide the corresponding error estimates and stability analysis.The delay-dependent dynamical properties on the Nicholson’s blowflies equation and the Mackey-Glass equa-tion are numerically investigated.Finally,numerical examples are given to demonstrate the efficiency of our LABCs and theoretical results of the numerical scheme.

关键词： Biological models artificial boundary method absorbing boundary conditions finite difference method stability,convergence

LOCAL SUPERCONVERGENCE OF CONTINUOUS GALERKIN SOLUTIONS FOR DELAY DIFFERENTIAL EQUATIONS OF PANTOGRAPH TYPE

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Journal of Computational Mathematics 2016年第2期34卷 186-199页

作者： Xiuxiu Xu qiumei huang Hongtao Chen Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124 China School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing Xiamen University Xiamen 361005 China

This paper is concerned with the superconvergent points of the continuous Galerkin solutions for delay differential equations of pantograph type. We prove the local nodal superconvergence of continuous Galerkin solutions under uniform meshes and locate all the superconvergent points based on the supercloseness between the continuous Galerkin solution U and the interpolation Hhu of the exact solution u. The theoretical results are illustrated by numerical examples.

关键词： Pantograph delay differential equations Uniform mesh Continuous Galerkinmethods Supercloseness Superconvergence.

Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations

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Advances in Applied Mathematics and Mechanics 2020年第1期12卷 189-211页

作者： Kun Jiang qiumei huang Xiuxiu Xu College of Applied Sciences Beijing University of TechnologyBeijing 100124China School of Mathematical Sciences Anhui UniversityHefei 230031China

In this paper,the discontinuous Galerkin method is applied to solve the multi-pantograph delay differential equations.We analyze the optimal global convergence and local superconvergence for smooth solutions under uniform meshes.Due to the initial singularity of the forcing term f,solutions of multi-pantograph delay differential equations are singular.We obtain the relevant global convergence and local superconvergence for weakly singular solutions under graded meshes.The numerical examples are provided to illustrate our theoretical results.

关键词： Multi-pantograph discontinuous Galerkin method global convergence local superconvergence,weakly singular graded meshes

Preparation and photocatalytic activity of Fe3O4@SiO2@ZnO:La

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Journal of Rare Earths 2020年第12期38卷 1288-1296页

作者： Xiaowei Lv Wenyi huang Xingcheng Ding Jiangwei He qiumei huang Jialin Tan Hao Cheng Jun Feng Lijun Li Guangxi Key Laboratory of Green Processing of Sugar Resources College of Biological and Chemical EngineeringGuangxi University of Science and TechnologyLiuzhou 545006China Zhejiang Runtu Co. Ltd.Shangyu 312300China

In this study,Fe3 O4@SiO2@ZnO:La microspheres were successfully prepared.The microspheres have the advantages of both ZnO doped with La and the Fe3 O4@SiO2 structure such that the former improves the photocatalytic activity of ZnO and the latter can be reused.The X-ray diffraction(XRD),a field emission scanning electron microscope(SEM),a field emission transmission electron microscope(TEM),X-ray photoelectron spectroscopy(XPS),and a vibrating sample magnetometer(VSM)were used to characterize Fe3 O4@SiO2@ZnO:La microspheres.Methyl orange was used as the model molecule to study the effect of the Zn2+concentration and the doping amount of La on the photocatalytic activity of Fe3 O4@SiO2@ZnO:La microspheres.Results show that in the synthesis of Fe3 O4@SiO2@ZnO:La microspheres,photocatalytic activity of the microspheres is enhanced first and weakened later with the increase of Zn2+concentration.In the La doping process,the photocatalytic activity of Fe3 O4@SiO2@ZnO:La microspheres is enhanced with the increase in the La doping amount.The magnetic photocatalysts not only have high photocatalytic activity,but also can be reused.After being reused five times,the photocatalyst’s degradation rate of methyl orange is still as high as 81%,which shows that magnetic photocatalysts have prospective wider applications in photocatalytic degradation of dye wastewater.

关键词： Fe3O4@SiO2 ZnO:La Photocatalysis Reuse Rare earths

基于开阖理论研究朱宗元教授治疗变应性鼻炎的临床经验

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中华中医药学刊 2024年第4期42卷 47-49页

作者：奥晓静董秋梅黄娟内蒙古医科大学中医学院内蒙古呼和浩特010010

介绍朱宗元教授治疗变应性鼻炎的临床经验,认为肺为华盖,居于人体最上部,容易受邪侵袭而致开阖失司,不能完成人体正常的气机升降出入,新陈代谢,津液布散。进而导致人体免疫功能失调发生此病。其认为治疗变应性鼻炎应以调节开阖、通调免... 详细信息

介绍朱宗元教授治疗变应性鼻炎的临床经验,认为肺为华盖,居于人体最上部,容易受邪侵袭而致开阖失司,不能完成人体正常的气机升降出入,新陈代谢,津液布散。进而导致人体免疫功能失调发生此病。其认为治疗变应性鼻炎应以调节开阖、通调免疫、祛邪开窍为主,只有从根本论治才能使机体的免疫功能恢复正常。选择过敏煎为主合用桂枝加葛根汤、苍耳子散加减作为治疗变应性鼻炎的主方,以达调节气机升降出入、恢复正常开阖之功效。

关键词：朱宗元变应性鼻炎开阖名医经验

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青少年早期学业成就对主观幸福感的影响:自尊和流动性的作用

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心理发展与教育 2024年第3期40卷 384-392页

作者：黄垣成袁湫嵋辛婷李彩娜陕西师范大学心理学院陕西(高校)哲学社会科学重点研究基地儿童青少年心理与行为健康研究中心西安710062

为考察学业成就对主观幸福感的影响以及自尊和流动性的作用,采用自尊量表和幸福感指数问卷对西安市两所中学的847名初中生(流动298人)进行三年的纵向追踪,同时收集青少年在初中三年的学业成绩(语数外)。结果表明:(1)青少年初一时的学业... 详细信息

为考察学业成就对主观幸福感的影响以及自尊和流动性的作用,采用自尊量表和幸福感指数问卷对西安市两所中学的847名初中生(流动298人)进行三年的纵向追踪,同时收集青少年在初中三年的学业成绩(语数外)。结果表明:(1)青少年初一时的学业成就可直接预测初三时的主观幸福感;(2)初二的自尊在初一的学业成就与初三的主观幸福感间起部分中介作用;(3)学业成就、自尊和主观幸福感间的纵向中介模型在流动与普通青少年间存在显著差异:结果(1)(2)仅适用于普通青少年,流动青少年初三时的主观幸福感仅受初二时自尊水平的影响。研究揭示了青少年早期学业成就与主观幸福感的关系及其作用机制,对提升初中生的主观幸福感具有一定的现实指导意义。

关键词：学业成就主观幸福感自尊青少年早期流动性