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Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

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Communications on Applied Mathematics and Computation 2024年第1期6卷 257-278页

作者： Xuechun Liu haijin wang Jue Yan Xinghui Zhong School of Mathematical Sciences Zhejiang UniversityHangzhou310027ZhejiangChina School of Science Nanjing University of Posts and TelecommunicationsNanjing210023JiangsuChina Department of Mathematics Iowa State UniversityAmes50011IAUSA

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

关键词： Direct discontinuous Galerkin(DDG)method with interface correction Symmetric DDG method Superconvergence Fourier analysis Eigen-structure

The Direct Discontinuous Galerkin Methods with Implicit-Explicit Runge-Kutta Time Marching for Linear Convection-Diffusion Problems

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Communications on Applied Mathematics and Computation 2022年第1期4卷 271-292页

作者： haijin wang Qiang Zhang School of Science Nanjing University of Posts and TelecommunicationsNanjing 210023China Department of Mathematics Nanjing UniversityNanjing 210093China

In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.

关键词： Direct discontinuous Galerkin method Implicit-explicit scheme Stability analysis Energy method Convection-diffusion problem

Thermal management for thermoset automated fiber placement based on infrared heater structure arrangement

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Chinese Journal of Aeronautics 2022年第1期35卷 173-183页

作者： Han wang Weiwei wang haijin wang Huiyue DONG Yinglin KE A State Key Laboratory of Fluid Power and Mechatronic System School of Mechanical EngineeringZhejiang UniversityHangzhou 310027China Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province School of Mechanical EngineeringZhejiang UniversityHangzhou 310027China

Layup temperature is a vital factor that affects the production quality of automated fiber placement for thermoset composites.For high quality production,this paper proposes a new prediction model of layup temperature by considering the structure of infrared heater of automatic fiber placement equipment.The model was first verified by comparing with the temperature results of layup experiments.Then a prediction on the effects of heater structure arrangement on layup temperature was conducted in the model.The research shows that the length of infrared tube and the radian of reflective-film have significant influences,rather than other parameters.According to this investigation,a heater structure-based heating strategy was presented in the paper to efficiently achieve constant temperature control in variable speed layup process.

关键词： Automated fiber placement Heating strategy optimization Infrared heater structure Thermal management Variable speed

Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems

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Science China Mathematics 2020年第1期63卷 183-204页

作者： haijin wang Qiang Zhang Shiping wang Chi-wang Shu School of Science Nanjing University of Posts and TelecommunicationsNanjing 210023China Department of Mathematics Nanjing UniversityNanjing 210093China College of Shipbuilding Engineering Harbin Engineering UniversityHarbin 150001China Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

In this paper,we discuss the local discontinuous Galerkin methods coupled with two specific explicitimplicit-null time discretizations for solving one-dimensional nonlinear diffusion problems Ut=(a(U)Ux)x.The basic idea is to add and subtract two equal terms a0 Uxx the right-hand side of the partial differential equation,then to treat the term a0 Uxx implicitly and the other terms(a(U)Ux)x-a0 Uxx explicitly.We give stability analysis for the method on a simplified model by the aid of energy analysis,which gives a guidance for the choice of a0,i.e.,a0≥max{a(u)}/2 to ensure the unconditional stability of the first order and second order schemes.The optimal error estimate is also derived for the simplified model,and numerical experiments are given to demonstrate the stability,accuracy and performance of the schemes for nonlinear diffusion equations.

关键词： local discontinuous Galerkin explicit-implicit-null time discretization nonlinear diffusion stability error estimates

循证依据下“一病一品”干预模式对静脉曲张术后患者疼痛、踝泵运动及不良反应的影响

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全科医学临床与教育 2024年第5期22卷 478-480页

作者：全海舟胡益鹏王海金詹颜颜方立舟山医院普外科浙江舟山316000 舟山医院风湿免疫科浙江舟山316000

静脉曲张常因静脉因壁松弛、扩张而形成的静脉血液回流障碍疾病[1],可引起疼痛、溃疡、出血等并发症,严重者甚至危及生命。目前,静脉曲张的治疗方法主要包括保守治疗和手术治疗。循证医学作为一种以临床实践为基础的医学决策模式,常依... 详细信息

静脉曲张常因静脉因壁松弛、扩张而形成的静脉血液回流障碍疾病[1],可引起疼痛、溃疡、出血等并发症,严重者甚至危及生命。目前,静脉曲张的治疗方法主要包括保守治疗和手术治疗。循证医学作为一种以临床实践为基础的医学决策模式,常依赖于最新的研究证据和临床经验来指导治疗决策[2]。而“一病一品”模式则通过将个体化医疗理念应用于临床实践中并基于患者的疾病特点和需求来提供个性化的治疗方案[3]。基于此,本次研究探究循证依据下“一病一品”干预模式对静脉曲张术后患者的影响。现报道如下。

关键词：血液回流障碍循证医学疾病特点静脉曲张治疗决策临床实践一病一品个体化医疗

ERROR ESTIMATE ON A FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD FOR LINEAR CONVECTION-DIFFUSION PROBLEM

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Journal of Computational Mathematics 2013年第3期31卷 283-307页

作者： haijin wang Qiang Zhang Department of Mathematics Nanjing University Nanjing 210093 China

In this paper we present the error estimate for the fully discrete local discontinuous Galerkin algorithm to solve the linear convection-diffusion equation with Dirichlet boundary condition in one dimension. The time is advanced by the third order explicit total variation diminishing Runge-Kutta method under the reasonable temporal-spatial condition as general. The optimal error estimate in both space and time is obtained by aid of the energy technique, if we set the numerical flux and the intermediate boundary condition properly.

关键词： Runge-Kutta Local discontinuous Galerkin method Convection-diffusion equation Error estimate.

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旋挖钻机桅杆截面优化设计

机械管理开发 2024年第3期39卷 29-32页

作者：钱文君张旭楠杜浩然刘超勤王海金吉林大学机械与航空航天工程学院吉林长春130000 徐工集团工程机械股份有限公司江苏徐州221000

旋挖钻机是一种用于施工和钻探的工程机械设备,由于其经常面对复杂工况,需要对旋挖钻机的桅杆截面进行优化设计,以提高桅杆的抗弯能力和抗扭能力。通过对常用的凹箱形截面和大圆角方形截面进行理论计算及有限元分析,确定最优截面形状,... 详细信息

旋挖钻机是一种用于施工和钻探的工程机械设备,由于其经常面对复杂工况,需要对旋挖钻机的桅杆截面进行优化设计,以提高桅杆的抗弯能力和抗扭能力。通过对常用的凹箱形截面和大圆角方形截面进行理论计算及有限元分析,确定最优截面形状,选取极端钻进工况和极端提钻工况,计算桅杆上最大的应力值和挠度值,得到含待优化未知数的表达式,并利用许用应力和许用变形对未知量进行约束,求得截面宽高比和板厚的最优解。

关键词：旋挖钻机截面形状宽高比优化设计

基于ArcGIS与多因子模型的光伏电站选址评估

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太阳能学报 2023年第11期44卷 120-130页

作者：王海金唐若笠周雨诗张彦武汉理工大学船海与能源动力工程学院武汉430063 武汉理工大学交通与物流工程学院武汉430063

该文基于中国光伏资源的时空分布,研究并提出一种基于ArcGIS与多因子评价的光伏电站选址及发电潜力预测模型。利用ArcGIS软件与层次分析法,综合考虑多种影响大型光伏电站建设的因素,对不同地势和土地类型赋予不同的光伏利用系数,得到大... 详细信息

该文基于中国光伏资源的时空分布,研究并提出一种基于ArcGIS与多因子评价的光伏电站选址及发电潜力预测模型。利用ArcGIS软件与层次分析法,综合考虑多种影响大型光伏电站建设的因素,对不同地势和土地类型赋予不同的光伏利用系数,得到大型光伏电站建设适宜度、光伏潜力与光伏电站选址的多因子评价模型。基于该模型得出中国光伏发电潜力并给出光伏电站选址建议。评估结果表明,全国年光伏总发电量约为570.07×10^(6)kWh,其中新疆为年光伏总发电量最高的省份。中国较为适宜建设光伏电站的地区主要为西北部地区,其中适宜区面积为1.08×10^(6)km^(2),最适宜区面积为2.10×10^(5)km^(2),研究可结果将为中国光伏产业长期的规划与建设提供可靠的理论依据。

关键词：光伏组件光伏电站选址层次分析法地理信息系统

基于ArcGIS与多因子模型的风力发电场选址评估

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太阳能学报 2023年第12期44卷 251-259页

作者：周雨诗张彦王海金唐若笠袁成清武汉理工大学交通与物流工程学院武汉430063 武汉理工大学船海与能源动力工程学院武汉430063

基于地理信息系统,研究并提出一种基于ArcGIS与多因子模型的风力发电场选址评估方法,以实现对不同地区风能资源空间分布情况、开发适宜性和理论发电量的有效评估,进而为风电场的选址提供理论依据。首先,基于不同地区的风资源气象数据,... 详细信息

基于地理信息系统,研究并提出一种基于ArcGIS与多因子模型的风力发电场选址评估方法,以实现对不同地区风能资源空间分布情况、开发适宜性和理论发电量的有效评估,进而为风电场的选址提供理论依据。首先,基于不同地区的风资源气象数据,通过引入地形、道路等地理限制因素,提出一种多因子模型,以实现对不同地区风能资源开发适宜性评估。然后,基于10 m高度处的风速分布,通过风速外推得到80 m高度处的风速分布,进而用于评估80 m高度处的风能理论发电量。最后,综合上述开发适宜性和理论发电量评估结果,可较为准确地给出计及风速、风功率密度、地形、道路等多因子模型的风电场选址建议。结果发现:风电场选址主要集中在西北部、东北部以及内蒙古等地。

关键词：风电场风力发电机地理信息系统选址 ArcGIS 多因子模型层次分析法