EXTRAPOLATION FOR FINITE ELEMENT METHODS OF THE FIRST KIND FREDHOLM INTEGRAL EQUATIONS

In this paper,a numerical analysis of finite element methods for Fredholm equationsof the first kind,which is based upon regularization,is made.It shows that extrapolationalgorithms can accelerate the convergence of approximate solutions.     

求解非均匀介质问题的双共轭梯度方法

分析非均匀介质条件下的电成像问题 ,在说明电成像仪的测量环境和测量原理之后 ,对这种复杂条件的电磁场问题 ,采用三维有限元方法进行分析。为了保证计算精度 ,在分析过程中 ,需要划分较多的空间网格 ,从而生成大型的有限元矩阵方程。对此大型矩阵方程 ,采用计算效率较高的双共轭梯度方法求解 ,给出了双共轭梯度方法的算法和利用该算法求解有限元矩阵方程时的收敛速度曲线 ,并对水平分层和倾斜分层两种典型情况下的非均匀介质成像问题进行分析 ,给出了模拟测量成像结果。     

Nonconforming finite element method for nonlinear parabolic equations

<正> A nonconforming finite element method for the nonlinear parabolic equations is studied inthis paper.The convergence analysis is presented and the optimal error estimate in L~2(‖·‖_h)norm isobtained through Ritz projection technique,where ‖·‖_h is a norm over the finite element space.     

ANISOTROPIC BIQUADRATIC ELEMENT WITH SUPERCLOSE RESULT

The main aim of this paper is to study the convergence of biquadratic finite element forthe second order problem on anisotropic meshes.By using some novel approaches and techniques,theoptimal error estimates are obtained.At the same time,the anisotropic superclose results are alsoachieved.Furthermore,the numerical results are given to demonstrate our theoretical analysis.     

AN EXTRAPOLATION METHODFOR FINITE ELEMENT APPROXIMATION OF INTEGRODIFFERENTIAL EQUATIONS WITH PARAMETERS

In this paper,we discuss the accelerating convergence method for finite elementapproximation of integro-differential equations with parameters.As applications,we give theerror estimates of finite element for the first kind of Fredholm integral equation,particularlyfor the Volterra integral equation with kernel condition k(x,x)=0.     

RESIDUAL A POSTERIORI ERROR ESTIMATE OF A NEW TWO-LEVEL METHOD FOR STEADY NAVIER-STOKES EQUATIONS

Residual-based a posteriori error estimate for conforming finite element solutions of incom-pressible Navier-Stokes equations,which is computed with a new two-level method that is differentfrom Volker John,is derived.A posteriori error estimate contains additional terms in comparison tothe estimate for the solution obtained by the standard finite element method.The importance of theadditional terms in the error estimates is investigated by studying their asymptotic behavior.For opti-mal scaled meshes,these bounds are not of higher order than the convergence of discrete solution.Thetwo-level method aims to solve the nonlinear problem on a coarse grid with less computational work,then to solve the linear problem on a fine grid,which is superior to the usual finite element methodsolving a similar nonlinear problem on the fine grid.     

基于HoloLens的有限元分析变形结果可视化研究

使用Unity3D软件开发基于Microsoft HoloLens的UWP(Universal Windows Platform)有限元分析结果虚拟评审应用。利用Matlab进行编程完成三维实体静力有限元分析。为实现变形效果的可视化,提取有限元分析结果,生成VTK(Visualization Toolkit)格式文件,利用自制的文件转换器转换成.dae文件。在Unity3D软件中编写顶点着色器脚本实现片面模型的颜色显示和变形效果的可视化,最终发布UWP应用。实验结果表明:Matlab和Ansys Workbench有限元分析结果相吻合,基于HoloLens的有限元分析变形结果虚拟评审应用沉浸感强,交互性高,并可以推广到其他有限元分析应用领域。     

Finite volume element method with Lagrangian cubic functions

This paper establishes a new finite volume element scheme for Poisson equation on triangular meshes. The trial function space is taken as Lagrangian cubic finite element space on triangular partition, and the test function space is defined as piecewise constant space on dual partition. Under some weak condition about the triangular meshes, the authors prove that the stiffness matrix is uniformly positive definite and convergence rate to be O(h ³) in H ¹-norm. Some numerical experiments confirm the theoretical considerations.     

Error reduction, convergence and optimality of an adaptive mixed finite element method

This paper proves the error reduction property(saturation property),convergence and optimality of an adaptive mixed finite element method(AMFEM) for the Poisson equation.In each step of AMFEM,the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations,depending only on the marking strategy,under some restriction of refinement.The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe(2006) and the quasi-orthogonality estimate proved by Chen,Hoist,and Xu (2009).Numerical experiments fully confirm the theoretical analysis.     

实数编码化学反应优化的全局收敛性研究

作为一种新的自然计算方法,化学反应优化性能优越,适应性强,但其理论研究缺乏.针对上述问题,以实数编码化学反应优化(RCCRO)为对象,研究其收敛性和收敛速度.首先,建立RCCRO在连续时间上有限吸收的Markov链模型,并证明其为有限可吸收Markov链;然后,基于有限吸收Markov链证明RCCRO的收敛性;进而,对于采用不同初等反应组合的RCCRO,研究初等反应的有效性和算法全局收敛的必要条件;最后分析了RCCRO的收敛速度和首达时间.     

DOMAIN DECOMPOSITION WITH NON-MATCHING GRIDS FOR COUPLING OF FEM AND NATURAL BEM

In this paper, we introduce a domain decomposition method with non-matching grids for solving Dirichlet exterior boundary problems by coupling of finite element method （FEM） and natural boundary element method（BEM）. We first derive the optimal energy error estimate of the nonconforming approximation generated by this method. Then we apply a Dirichlet-Neumann（D-N） alternating algorithm to solve the coupled discrete system. It will be shown that such iterative method possesses the optimal convergence. The numerical experiments testify our theoretical results.     

基于有限元法的永磁磁场内套管缺陷仿真研究

漏磁法是在役油气套管缺陷检测的重要方法之一,对于确定套管内缺损的位置和评价其损伤程度,以及后续的修复处理工作都具有非常重大的意义。提出一种基于二维轴对称永磁磁场有限元分析的漏磁检测和处理方法。使用泛函分析和内插值方法在理论上证明永磁磁场有限元分析的可行性;利用有限元法分析套管饱和临界条件,借此确定实际检测装置的结构参数;模拟实际的工作环境,并在不同缺损尺寸和多个缺损的条件下进行仿真。实验结果验证了永磁磁场内有限元法的正确性及可靠性,为后续的套管漏磁检测装置设计提供了理论依据。     

Least-squares Galerkin procedure for second-order hyperbolic equations

This paper proposes the least-squares Galerkin finite element scheme to solve second-order hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in (L ²(Ω))² × L ²(Ω) norms. Moreover, the method gets the approximate solutions with second-order accuracy in time increment. A numerical example testifies the efficiency of the novel scheme.     

INTERPOLATED FINITE ELEMENT METHODS FOR SECOND ORDER HYPERBOLIC EQUATIONS AND THEIR GLOBAL SUPERCONVERGENCE

We develop the interpolated finite element method to solve second-order hy-perbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation over adjacent elements. We prove that this interpo-lated finite element solution has superconvergence. This method can easily be applied togenerating more accurate gradient either locally or globally, depending on the applications.This method is also completely vectorizable and parallelizable to take the advantages ofmodern computer structures. Several numerical examples are presented to confirm ourtheoretical analysis.     

冶金专用车车架结构的优化设计

在某型冶金专用车车架概念化设计的基础上,以有限元结构分析和优化算法相结合为手段,对横梁和纵梁的截面尺寸进行优化,建立了车架的有限元模型,优化数学模型,通过电测试验验证了有限元模型的正确性,采用ANSYS参数化设计语言编制了优化设计程序,用ANSYS软件中的一阶优化方法获得最优设计。实际应用表明该优化设计方法比原有的设计方法更为有效和快捷,该方法可广泛应用于车架优化设计工程中。     

基于刚柔混合建模的柴油机曲轴系动态仿真

在分析PA6V12柴油机曲轴系运动及受力的基础上,利用Pro/E对曲轴系进行了整体造型,同时利用PATRAN对曲轴进行了有限元建模,通过ADAMS/View构建了曲轴系的刚柔多体动态仿真模型.模型主要考虑了柴油机在额定工况下的边界条件.结果分析表明,该模型能够准确的反映曲轴系的运动和受力情况,其结果也为曲轴动态有限元的疲劳寿命计算提供了依据.     

考虑发动机推力受限和动特性的有限时间收敛制导律

针对发动机推力受限和动态延迟的制导问题,设计了一种具有鲁棒性的非奇异滑模制导律,并证明了有限时间收敛条件。首先,基于平面弹-目相对运动学关系,建立了考虑发动机一阶动态延迟的弹-目相对运动数学模型。其次,基于有限时间理论,证明了推力受限下制导律有限时间收敛条件及其性质;并推广到动态延迟情况下,设计了非奇异滑模制导律;最后,用边界层函数代替符号函数去除抖振。仿真结果表明了制导律具有更高的制导精度并对高速目标机动具有鲁棒性,验证了有限时间收敛条件和性质。     

空间望远镜分块式主镜面形控制系统建模

新一代空间望远镜采用分块式主镜方案,以多个旁瓣子镜背后布置的若干致动器为控制手段,对主镜面形进行高精度控制,是一个复杂的控制系统。应用BP神经网络的方法建立了以致动器作用力为输入、镜面形变的Zernike多项式拟合系数为输出的镜面形变模型,并利用镜面形变的有限元分析的大量数据,对BP模型进行离线训练和模型预测效果的检验。仿真结果表明所建BP模型接近有限元分析的精度,并可以满足空间望远镜在线控制的实时性要求。     

外积取等联想记忆神经网络部分同步收敛性

在生物视觉系统中发现的部分同步振荡现象被认为是视觉信息处理的重要机制 ,并对认识脑信息处理机制有重要意义。以联想记忆神经网络为例 ,针对外积取等学习准则定义了两种部分同步运行规则 ,通过引入样本向量割、割等价及割互补的概念 ,对外积取等联想记忆神经网络部分同步运行的收敛性作了直接的数学分析 ,证明了实现收敛所需的迭代数是有限的。     

新型横向磁通永磁电机电磁场有限元分析

为了验证新型四相横向磁场永磁电机(TFPM)的可行性,为其建立了模型并进行电磁场有限元分析。采用Solidworks软件,为其新型拓扑结构建立了三维模型;在Maxwell 3D仿真环境下进行网格划分,材料赋值,定义边界条件等操作,对其磁通密度、自定位力、电磁力、转矩等参数进行了三维电磁场有限元分析。实验证明,样机运行平稳,四相结构设计减小了电机自定位力,有效抑制了转矩脉动,有限元仿真结果与实验结果一致,验证了该拓扑结构的可行性。