HIGH-ACCURACY FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEM

1 IntroductionOptimal design or control is playing an increasingly importal role in engineering designwork. Efficient numerical methods are among the keys to successful application of optimalcontrol in practical work. With its wide range of application in scielltific and engineeringnumerical simulation, finite element approximation of optimal control problems plays a veryimportant role in numerical method of these problems. There have been eXtensive studies inthis respect, see, for example, […     

A MULTI－PARAMETER SPLITTING EXTRAPOLATION AND A PARALLEL ALGORITHM FOR PARABOLIC PROBLEM

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IMPLICIT—EXPLICIT MULTISTEP FINITE ELEMENT METHODS FOR THE SEMICONDUCTOR DEVICE PROBLEM

The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by the finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The optimal L^2-norm error estimates are derived.     

FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED SYMMETRIC REGULARIZED LONG WAVE EQUATIONS

This paper deals with the asymptotic behaviour of solutions for the generalized symmetric regularized long wave equations with dissipation term. We first show the existence of global weak attractors for the periodic initial value problem of this equations in H2 x H1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the global weak attractor is actually the global strong attractor for S(t) in H2(2) x H1(M).The finite dimensionality of the global attractor is also established.     

GLOBAL SUPERCONVERGENCE FOR A MIXED FINITE ELEMENT METHOD FOR THE WAVE EQUATION

1.IntroductionWeconsiderthesecondorderhyperbolicequationwithinitialconditionswhereaCRZisaboundeddomainwithboundariesparalleltotheaxes.Forconvenience,weassumehomogeneousDirichletboundaryconditions'Weassumethatthefunctionsailandfareuniformlyboundedandmeasurable,andthespatialoperatorisuniformlyellipticinthesensethatthereexistpositiveconstantsorandPsuchthatInamixedfiniteelementformulationbothdisplacementsandstressesareapproximatedsimultaneously.ThispropertyisimportantincomputingDarcyvelocitieso…     

高次有限元方程的一种并行预条件子

偏微分方程(PDEs)是大规模科学工程计算与数值仿真中的基本数学模型,有限元方法是数值求解偏微分方程的一类重要的离散化方法,高次有限元又是其中的一类常用有限元。针对一类基本的PDE模型(Poission方程)的高次有限元方程,设计了一种基于辅助变分问题的并行预条件子,并从理论上严格证明了该预条件子的条件数的一致有界性,数值实验验证了理论结果的正确性及相应预条件共轭梯度(PCG)法的高效性和鲁棒性。     

有限元边界积分结合撕裂对接法分析电磁散射

有限元边界积分方法采用有限元法分析物体内部复杂材料,采用矩量法分析物体开域表面,充分结合了两种方法的优点。然而单机求解电大尺寸问题面临着运算速度不高和内存容量不足的问题,因此发展有效的并行技术亟不可待。利用区域分解法固有的并行性,将有限元撕裂对接法引入到有限元边界积分方法中,解决了硬件资源不足的问题,提高了求解问题的效率。该方法在处理内部未知量大和内部材料复杂的电大尺寸问题方面具有较大优势。给出的数值算例充分证明了该方法的可行性和有效性。     

曲面微带天线电磁散射特性分析

使用矩量法分析研究了有限曲面微带天线的结构散射特性。运用等效原理,建立了一般曲面微带天线的体面耦合电场积分方程,在积分方程中由于采用的是自由空间格林函数,从而避免涉及微带天线分层介质格林函数的解析表示和精确计算。在伽略金法中,介质部分采用SWG基函数,金属表面部分采用RWG基函数,通过金属表面与介质基片交界面处施加电流连续性方程,有效地减少了待求未知量数目,明显改善了阻抗矩阵条件数。     

A discontinuous Galerkin method combined with mixed finite element for seawater intrusion problem

<正> Seawater intrusion problem is considered in this paper.Its mathematical model is anonlinear coupled system of partial differential equations with initial boundary problem.It consistsof the water head equation and the salt concentration equation.A combined method is developedto approximate the water head equation by mixed finite element method and concentration equationby discontinuous Galerkin method.The scheme is continuous in time and optimal order estimates inH~1-norm and L~2-norm are derived for the errors.     

雷达目标远区角闪烁线偏差与观察距离无关的一般性证明

和利用高频区散射中心模型计算目标角闪烁不同,直接从Stratton-Chu积分公式出发给出了目标散射场分量随观察距离的变化关系,并证明在远区近似条件下任意目标的远区角闪烁线偏差与目标观察距离无关,只跟目标本身电尺寸、形状及观察目标方向有关。利用驻相法说明所提方法和散射中心建模方法在高频区的结果是一致的,而所提方法适合在全频带上分析目标角闪烁,更具一般性。最后利用电场积分方程结合矩量法计算了有限大导体平板和有限长导体圆柱的角闪烁线偏差,验证了目标远区角闪烁线偏差与观察距离无关。     

Fast computation of scattering from 3D complex structures by MLFMA

This paper introduces the research work on the extension of multilevel fast multipole algorithm （MLFMA） to 3D complex structures including coating object, thin dielectric sheet, composite dielectric and conductor, cavity. The impedance boundary condition is used for scattering from the object coated by thin lossy material. Instead of volume integral equation, surface integral equation is applied in case of thin dielectric sheet through resistive sheet boundary condition. To realize the fast computation of scattering from composite homogeneous dielectric and conductor, the surface integral equation based on equivalence principle is used. Compared with the traditional volume integral equation, the surface integral equation reduces greatly the number of unknowns. To computc conducting cavity with electrically large aperture, an electric field integral equation is applied. Some numerical results are given to demonstrate the validity and accuracy of the present methods.     

用有限元法分析管道在空间内的固液耦合振动

本文用有限元方法研究有液体流动管道在空间内振动,液体流速与压强对其固有频率的影响。给出运动微分方程及其解法,并通过实例加以验证。     

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.     

对数正态分布均值的Bayes及Fiducial精确限

本文提出了对数正态分布均值在取共轭型及无信息先验分布时的Ｂａｙｅｓ精确限及Ｆｉｄｕｃｉａｌ精确限，它们能用有限区间上的一重积分迭代地求出。这种新算法非常方便，且有很高的精度，能极好地满足工程需要。而原来的算法是相当麻烦的，本文同时还推导出精度很高、算法简单的近似限。这种近似限既能直接用于工程，又能在迭代求解精确限时作为其搜索区间。     

Exact Bayesian and Fiducial Limits for the Mean of Lognormal Distribution

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基于有限单元的贝叶斯滤波估计算法

现代工程系统具有较强的非线性特性,针对这类非线性系统的状态估计问题,提出基于有限单元的贝叶斯原理估计的非线性滤波方法。采用有限单元法逼近系统状态的先验概率解,即前向Kolmogorov方程的解,通过贝叶斯估计得到状态的后验信息。将其方法应用到惯性/地形组合导航系统中,仿真结果表明该方法的可行性。     

An impact angle constraint integral sliding mode guidance law for maneuvering targets interception

An integral sliding mode guidance law(ISMGL)combined with the advantages of the integral sliding mode control(SMC)method is designed to address maneuvering target interception problems with impact angle constraints.The relative motion equation of the missile and the target considering the impact angle constraint is established in the longitudinal plane,and an integral sliding mode surface is constructed.The proposed guidance law resolves the existence of a steady-state error problem in the traditional SMC.Such a guidance law ensures that the missile hits the target with an ideal impact angle in finite time and the missile is kept highly robust throughout the interception process.By adopting the dynamic surface control method,the ISMGL is designed considering the impact angle constraints and the autopilot dynamic characteristics.According to the Lyapunov stability theorem,all states of the closed-loop system are finally proven to be uniformly bounded.Simulation results are compared with the general sliding mode guidance law and the trajectory shaping guidance law,and the findings verify the effectiveness and superiority of the ISMGL.     

ON THE NONEXISTENCE OF PERIODIC SOLUTIONS FOR LIENARD-TYPE EQUATIONS

1.IntroductionConsiderthefollowinggeneralizedLi6nardtypeequationwhereshallowing[1],thisequationwillbecalledasaLi6nard-typeequationofordern.Whenn=1,theequation(1.1)canbewrittenasthefollowingformClearly)whenfi(x)=j(x),f200=0,theequation(1.3)isreducedtothewellknownLi6nardequationx j(x)x g(x)=0.(1.4)Recently,theequation(1.3)hasalreadybeenstudiedwithparticularemphasisontheex-istenceanduniquenessofperiodicsolutionsbyseveralauthors.Forexample,needmanandKuangll],GuidorizzilZ],ZhouJinI3],andJiangJ…     

CONTINUATION METHOD OF NONLINEAR INTEGRAL EQUATIONS

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