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Gradient Recovery Based Two-Grid Finite Element Method for Parabolic Integro-Differential Optimal Control Problems
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作者 Miao Yang 《Journal of Applied Mathematics and Physics》 2024年第8期2849-2865,共17页
In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and ... In this paper, the optimal control problem of parabolic integro-differential equations is solved by gradient recovery based two-grid finite element method. Piecewise linear functions are used to approximate state and co-state variables, and piecewise constant function is used to approximate control variables. Generally, the optimal conditions for the problem are solved iteratively until the control variable reaches error tolerance. In order to calculate all the variables individually and parallelly, we introduce a gradient recovery based two-grid method. First, we solve the small scaled optimal control problem on coarse grids. Next, we use the gradient recovery technique to recover the gradients of state and co-state variables. Finally, using the recovered variables, we solve the large scaled optimal control problem for all variables independently. Moreover, we estimate priori error for the proposed scheme, and use an example to validate the theoretical results. 展开更多
关键词 Optimal Control Problem Gradient Recovery two-Grid Finite element Method
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A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations
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作者 Yiming Wen Luoping Chen Jiajia Dai 《Journal of Applied Mathematics and Physics》 2023年第2期361-376,共16页
In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m... In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator. 展开更多
关键词 two-Grid Mixed Finite element Methods Posteriori Error Estimates Semilinear Elliptic Equations Averaging Technique
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Local and parallel finite element algorithms based on two-grid discretization for steady Navier-Stokes equations 被引量:3
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作者 马飞遥 马逸尘 沃维丰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第1期27-35,共9页
Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine fini... Local and parallel finite element algorithms based on two-grid discretization for Navier-Stokes equations in two dimension are presented. Its basis is a coarse finite element space on the global domain and a fine finite element space on the subdomain. The local algorithm consists of finding a solution for a given nonlinear problem in the coarse finite element space and a solution for a linear problem in the fine finite element space, then droping the coarse solution of the region near the boundary. By overlapping domain decomposition, the parallel algorithms are obtained. This paper analyzes the error of these algorithms and gets some error estimates which are better than those of the standard finite element method. The numerical experiments are given too. By analyzing and comparing these results, it is shown that these algorithms are correct and high efficient. 展开更多
关键词 Navier-Stokes equations finite element method two-grid LOCAL PARALLEL
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Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems 被引量:2
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作者 严承华 王赤忠 程尔升 《China Ocean Engineering》 SCIE EI 2001年第2期291-300,共10页
A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domain second order theory of water waves. Liquid sloshing in a rectangular container Subjected to a horizontal ... A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domain second order theory of water waves. Liquid sloshing in a rectangular container Subjected to a horizontal excitation is simulated by the finite element method. Comparisons between the two theories are made based on their numerical results. It is found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur for large amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features of nonlinear wave and can be used instead of the fully nonlinear theory. 展开更多
关键词 liquid sloshing finite element two-DIMENSIONAL nonlinear theory time domain second order theory
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TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM 被引量:2
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作者 文娟 何银年 +1 位作者 王学敏 霍米会 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期960-972,共13页
In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique ... In this article, on the basis of two-level discretizations and multiscale finite element method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element discretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme. 展开更多
关键词 Multiscale finite element method two-level method error analysis the Navier- Stokes problem
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Simple experimental scheme of teleporting a two-qubit state via linear optical elements 被引量:1
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作者 袁洪春 李恒梅 齐开国 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第8期1686-1689,共4页
We propose a simple experimental scheme in which an unknown two-qubit state is faithfully and deterministically teleported from Alice to Bob. The scheme is constructed with four photons from parametric down conversion... We propose a simple experimental scheme in which an unknown two-qubit state is faithfully and deterministically teleported from Alice to Bob. The scheme is constructed with four photons from parametric down conversion, linear optical elements, and conventional photon detectors, all of which are available in current technology. It is shown that the probability of successful teleportation ideally reaches 100% based on single-photon two-qubit-assisted Bell-state measurement, which can distinguish all four Bell-states simultaneously via conventional photon detectors. By generalizing the scheme, the teleportation of an unknown multi-qubit system can also be realized. 展开更多
关键词 TELEPORTATION two-qubit state single-photon two-qubit linear optical elements
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Two-grid methods for semi-linear elliptic interface problems by immersed finite element methods 被引量:2
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作者 Yang WANG Yanping CHEN +1 位作者 Yunqing HUANG Ying LIU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2019年第11期1657-1676,共20页
In this paper,two-grid immersed finite element (IFE) algorithms are proposed and analyzed for semi-linear interface problems with discontinuous diffusion coefficients in two dimension.Because of the advantages of fini... In this paper,two-grid immersed finite element (IFE) algorithms are proposed and analyzed for semi-linear interface problems with discontinuous diffusion coefficients in two dimension.Because of the advantages of finite element (FE) formulation and the simple structure of Cartesian grids,the IFE discretization is used in this paper.Two-grid schemes are formulated to linearize the FE equations.It is theoretically and numerically illustrated that the coarse space can be selected as coarse as H =O(h^1/4)(or H =O(h^1/8)),and the asymptotically optimal approximation can be achieved as the nonlinear schemes.As a result,we can settle a great majority of nonlinear equations as easy as linearized problems.In order to estimate the present two-grid algorithms,we derive the optimal error estimates of the IFE solution in the L^p norm.Numerical experiments are given to verify the theorems and indicate that the present two-grid algorithms can greatly improve the computing efficiency. 展开更多
关键词 two-grid METHOD INTERFACE PROBLEM FINITE element METHOD immersed INTERFACE
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A control volume based finite element method for simulating incompressible two-phase flow in heterogeneous porous media and its application to reservoir engineering 被引量:3
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作者 SADRNEJAD S A GHASEMZADEH H +1 位作者 GHOREISHIAN AMIRI S A MONTAZERI G H 《Petroleum Science》 SCIE CAS CSCD 2012年第4期485-497,共13页
Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on e... Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces.Discontinuity of velocity field leads this method not to conserve mass locally.Moreover,the accuracy and stability of a solution is highly affected by a non-conservative method.In this paper,a three dimensional control volume finite element method is developed for twophase fluid flow simulation which overcomes the deficiency of the standard finite element method,and attains high-orders of accuracy at a reasonable computational cost.Moreover,this method is capable of handling heterogeneity in a very rational way.A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution.The accuracy and efficiency of the method are verified by simulating some waterflooding experiments.Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media. 展开更多
关键词 Finite element method control volume two-phase flow HETEROGENEITY porous media WATERFLOODING
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TWO-GRID METHOD FOR CHARACTERISTICS FINITE-ELEMENT SOLUTION OF 2D NONLINEAR CONVECTION-DOMINATED DIFFUSION PROBLEM
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作者 秦新强School of Sciences Xi’an Jiaotong University +7 位作者 Xi’an 710049 P.R.China School of Sciences Xi’an University of Technology Xi’an 710048 P.R.China) 马逸尘 章胤 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第11期1506-1514,共9页
For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid an... For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical is more efficient than that of characteristics example confirms that the two-grid method finite-element method. 展开更多
关键词 convection-diffusion equation characteristics finite-element two-grid method CONVERGENCE
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A simplified two-dimensional boundary element method with arbitrary uniform mean flow 被引量:2
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作者 Bassem Barhoumi Safa Ben Hamouda Jamel Bessrour 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2017年第4期207-221,共15页
To reduce computational costs, an improved form of the frequency domain boundary element method(BEM) is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitr... To reduce computational costs, an improved form of the frequency domain boundary element method(BEM) is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation(BIE) representation solves the two-dimensional convected Helmholtz equation(CHE) and its fundamental solution, which must satisfy a new Sommerfeld radiation condition(SRC) in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green's kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation. 展开更多
关键词 two-dimensional convected Helmholtz equation two-dimensional convected Green’s function two-dimensional convected boundary element method Arbitrary uniform mean flow two-dimensional acoustic sources
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Two-scale finite element method for piezoelectric problem in periodic structure 被引量:2
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作者 邓明香 冯永平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第12期1525-1540,共16页
The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-sc... The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented. 展开更多
关键词 two-scale method PIEZOELECTRICITY periodic structure finite element method homogenization constant
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A parallel two-level finite element method for the Navier-Stokes equations
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作者 尚月强 罗振东 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第11期1429-1438,共10页
Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations... Based on domain decomposition, a parallel two-level finite element method for the stationary Navier-Stokes equations is proposed and analyzed. The basic idea of the method is first to solve the Navier-Stokes equations on a coarse grid, then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations, error bounds of the approximate solution are derived. Numerical results are also given to illustrate the high efficiency of the method. 展开更多
关键词 Navier-Stokes equations finite element two-level method overlapping domain decomposition parallel algorithm
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Finite element equations and numerical simulation of elastic wave propagation in two-phase anisotropic media
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作者 刘洋 魏修成 《Acta Seismologica Sinica(English Edition)》 CSCD 2003年第2期166-174,共9页
Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical sol... Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical solution of finite element equations is given.Finally,Properties of elastic wave propagation are observed and analyzed through FEM modeling. 展开更多
关键词 two-PHASE anisotropic media elastic wave propagation finite element equations numerical simulation
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HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS 被引量:4
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作者 Wang Tongke(王同科) 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2002年第2期213-225,共13页
In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference me... In this paper, a high accuracy finite volume element method is presented for two-point boundary value problem of second order ordinary differential equation, which differs from the high order generalized difference methods. It is proved that the method has optimal order error estimate O(h3) in H1 norm. Finally, two examples show that the method is effective. 展开更多
关键词 SECOND order ordinary differential equation two-POINT boundary value problem high accuracy finite volume element method error estimate.
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球阀开度及入口速度对固-液两相流场的影响
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作者 加万里 王勇 高勇 《化工科技》 CAS 2024年第1期1-4,30,共5页
球阀广泛应用于固-液两相流的运输和流量调节。利用有限元软件研究球阀不同开度和不同入口速度下流场的变化,对于设计、制造球阀及优化球阀结构具有一定的指导意义。结果表明,阀门开度越大,轴截面流线越平直,压力梯度、速度梯度和流阻... 球阀广泛应用于固-液两相流的运输和流量调节。利用有限元软件研究球阀不同开度和不同入口速度下流场的变化,对于设计、制造球阀及优化球阀结构具有一定的指导意义。结果表明,阀门开度越大,轴截面流线越平直,压力梯度、速度梯度和流阻系数越小,流动状态越稳定;入口速度越大,轴截面流线越弯曲,压力和速度变化越明显,流动状态越紊乱,但流阻系数与入口流速无关。 展开更多
关键词 球阀 两相流 有限元 流阻系数
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COMPACTLY SUPPORTED NON-TENSOR PRODUCT FORM TWO-DIMENSION WAVELET FINITE ELEMENT 被引量:2
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作者 金坚明 薛鹏翔 +1 位作者 徐应祥 朱亚莉 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第12期1673-1686,共14页
Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor... Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last. 展开更多
关键词 compactly supported non-tensor product two-dimension wavelet interpolation function elastic thin plate DEFLECTION finite element
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圆形利兹线绕组高频损耗三维快速计算模型
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作者 赵志刚 刘朝阳 +2 位作者 贾慧杰 陈天缘 郑宇萱 《中国电机工程学报》 EI CSCD 北大核心 2024年第19期7901-7910,I0035,共11页
绕组损耗作为高频变压器总体损耗的重要组成,是影响磁性元件体积、效率和温升的关键参数。利兹线复杂的三维绞合结构,可以有效降低高频集肤效应与邻近效应引起的附加绕组损耗,广泛应用于高频变压器。然而,利兹线绕组内部的涡流分布极为... 绕组损耗作为高频变压器总体损耗的重要组成,是影响磁性元件体积、效率和温升的关键参数。利兹线复杂的三维绞合结构,可以有效降低高频集肤效应与邻近效应引起的附加绕组损耗,广泛应用于高频变压器。然而,利兹线绕组内部的涡流分布极为复杂,现有解析计算方法需要对模型进行较多简化和近似处理,难以精确表征利兹线绕组高频涡流效应。数值计算方法需要对利兹线进行精细化建模,造成计算资源的严重耗费。因此,如何准确、快速计算利兹线绕组损耗对高频磁性元件的优化设计具有重要意义。该文通过分析利兹线绕组损耗机理,并基于解析法与有限元数值法,建立一种同时考虑绕组端部效应及圆形利兹线绞合结构的绕组损耗三维快速计算模型。最后,针对两种不同利兹线绕组的变压器模型,从计算精度和计算成本的角度分别进行详细的实验研究与对比分析。结果表明,所提模型实现了宽频范围内圆形利兹线绕组损耗的精确、高效计算。 展开更多
关键词 利兹线 Tourkhani模型 邻近效应 集肤效应 二维有限元模型
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径向井辅助前置液酸压裂缝扩展数值模拟
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作者 齐宁 甘俊冲 +3 位作者 章泽辉 刘毅龙 申玉洋 刘练 《中国石油大学学报(自然科学版)》 EI CAS CSCD 北大核心 2024年第3期101-110,共10页
基于扩展有限元及双尺度连续模型理论建立径向井辅助前置液酸压裂缝扩展模型,引入偏离系数作为量化评价指标,分析各因素对裂缝形态的影响,并利用灰色关联分析方法明确主控因素。结果表明:径向井对前置液酸压裂缝扩展具有显著引导作用,... 基于扩展有限元及双尺度连续模型理论建立径向井辅助前置液酸压裂缝扩展模型,引入偏离系数作为量化评价指标,分析各因素对裂缝形态的影响,并利用灰色关联分析方法明确主控因素。结果表明:径向井对前置液酸压裂缝扩展具有显著引导作用,裂缝优先沿径向井方向起裂并扩展一定距离,而后逐渐偏向最大水平主应力方向;径向井方位角、水平地应力差和地层弹性模量越小,径向井长度越长,偏离系数越小,径向井引导效果越好,其中水平地应力差为主控因素;当径向井方位角为15°时,前置液酸压裂缝沿着径向井方向扩展14.32 m后偏向最大水平主应力方向,径向井的引导效果最好,偏离系数为0.005。 展开更多
关键词 径向井 前置液酸压 裂缝扩展 扩展有限元 双尺度模型
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一种新型组合式弯曲型金属阻尼器性能研究 被引量:1
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作者 吴子英 李永越 +1 位作者 户哲 韩明雨 《机械设计》 CSCD 北大核心 2024年第1期51-56,共6页
为解决U形阻尼器承载能力低、耗能性差的问题,文中提出了由U形金属板与X形金属板组成的一种新型组合式弯曲型金属阻尼器,基于随动强化模型对阻尼器进行静力循环模拟加载,采用ABAQUS软件进行仿真研究,发现组合式金属阻尼器滞回性能和承... 为解决U形阻尼器承载能力低、耗能性差的问题,文中提出了由U形金属板与X形金属板组成的一种新型组合式弯曲型金属阻尼器,基于随动强化模型对阻尼器进行静力循环模拟加载,采用ABAQUS软件进行仿真研究,发现组合式金属阻尼器滞回性能和承载能力均有提高,比U形阻尼器承载能力提高了24%,根据材料屈服强度的理论分析,当X形金属板的材料屈服应力大于307.38 MPa时,组合式金属阻尼器可实现双级屈服效果,仿真中选用Q235B钢U形板和Q345B钢X形板,组合式金属阻尼器取得了较好的双阶段屈服效果。 展开更多
关键词 组合式金属阻尼器 有限元分析 滞回曲线 骨架曲线 双阶段屈服
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基于二次图像分解的红外图像与可见光图像融合
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作者 马鑫 喻春雨 +1 位作者 童亦新 张俊 《光学精密工程》 EI CAS CSCD 北大核心 2024年第10期1567-1581,共15页
针对红外图像与可见光图像融合中细节丢失严重,红外图像的特征信息未能突出显示以及源图像的语义信息被忽视的问题,提出一种基于二次图像分解的红外图像与可见光图像融合网络(Secondary Image Decomposition For Infrared And Visible I... 针对红外图像与可见光图像融合中细节丢失严重,红外图像的特征信息未能突出显示以及源图像的语义信息被忽视的问题,提出一种基于二次图像分解的红外图像与可见光图像融合网络(Secondary Image Decomposition For Infrared And Visible Image Fusion,SIDFuse)。利用编码器对源图像进行二次分解以提取不同尺度的特征信息,然后利用双元素注意力为不同尺度的特征信息分配权重、引入全局语义支路,再采用像素相加法作为融合策略,最后通过解码器重建融合图像。实验选择FLIR数据集用于训练,采用TNO和RoadScene两个数据集进行测试,并选取八种图像融合客观评价参数进行实验对比分析。由TNO数据集的图像融合实验表明,在信息熵、标准差、空间频率、视觉保真度、平均梯度、差异相关系数、多层级结构相似性、梯度融合性能评价指标上,SIDFuse比基于卷积网络中经典融合算法DenseFuse分别平均提高12.2%,9.0%,90.2%,13.9%,85.1%,16.8%,6.7%,30.7%,比最新的融合网络LRRNet分别平均提高2.5%,5.6%,31.5%,5.4%,25.2%,17.9%,7.5%,20.7%。可见本文所提算法融合的图像对比度较高,可以同时更有效保留可见光图像的细节纹理和红外图像的特征信息,在同类方法中占有明显优势。 展开更多
关键词 图像融合 图像二次分解 全局语义支路 双元素注意力 图像对比度
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