HIGHLY NONCONFORMING FINITE ELEMENT APPROXIMATIONS FOR A FOURTH ORDERVARIATIONAL INEQUALITY WITH CURVATURE OBSTACLE

The purpose of this paper is to obtain the optimal error estimates of O(h) for the highly nonconforming elements to a fourth order variational inequality with curvature obstacle in a convex domain with simply supported boundary by using the novel function splitting method and the orthogonal properties of the nonconforming finite element spaces.Morley‘s element approximation is our special case.     

A HIGH ACCURACY ANALYSIS OF THE MIXED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATIONS

In this paper,the linear mixed finite element method is considered forthe biharmonic Dirichlet boundary value problem.Almost optimal error estimates,superconvergence estimates and the derivative error expansion are obtained.     

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.     

"无分红美式看涨期权不宜提前执行"的新的证明

利用自由边界方法对美氏看涨期权进行分解，对无分红的美式看涨期权提前执行不是最优的策略这一结论给出另一种证明。     

注塑模三维温度场的边界元计算及其仿真

注塑模具的冷却系统对塑料件的质量有至关重要的影响。本文针对注塑模具温度场的特点,建立了基于传热学和边界元法的数学模型,对三维边界元网格剖分和边界条件作了特殊的处理。在此基础上开发了三维稳态温度场分析(CAE)软件。在实际应用中表明分析结果合理。     

SUPERCONVERGENCE ANALYSIS OF A NONCONFORMING TRIANGULAR ELEMENT ON ANISOTROPIC MESHES

The class of anisotropic meshes we conceived abandons the regular assumption. Some distinct properties of Carey＇s element are used to deal with the superconvergence for a class of two- dimensional second-order elliptic boundary value problems on anisotropic meshes. The optimal results are obtained and numerical examples are given to confirm our theoretical analysis.     

结构声辐射的虚边界元最小二乘法及仿真研究

提出用虚边界元最小二乘法研究结构体声辐射,推导了该方法计算振动结构辐射声场的计算公式,与常规边界元法相比,虚边界元最小二乘法避免了奇异积分的数值处理,且系数矩阵是对称的,通过仿真计算与解析解验证。结果表明,本文方法思想简单,程序处理容易,能够有效克服特征频率处解的非唯一问题,在边界附近解的精度较高等优点,便于工程应用。     

基于CAD模型的边界离散元法仿真算法研究

为实现由边界的二维CAD模型(二维CAD软件设计图)建立边界的二维离散元法分析模型,提出一种基于图元的二维边界离散元法仿真算法。该算法采用Bresenham方法设置边界图元信息以进行邻居搜索,采用几何和数值方法进行颗粒与边界图元的接触检测、接触点求解和接触叠合量的计算。实例验证证明了该算法的正确性和有效性,为实现由机械部件的CAD模型进行机械部件工作过程的离散元法仿真分析奠定了基础。     

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。     

基于神经网络的时变参数系统仿真优化方法

时变参数系统的仿真优化问题是一个新兴的研究课题,相比传统仿真优化,时变参数系统对实时性的要求高,而对解的精度要求不高。本文提出将该问题转换为一类神经网络预测问题,并从理论上证明了该方法的可行性。首先,线下构建神经网络模型描述输入参数到最优解的映射关系;然后,利用训练好的神经网络模型线上实时预测最优解。考虑到边界样本对最优解拟合曲面的影响,提出构建中心样本和边界样本,分别训练两个神经网络模型。仿真和实例表明,该方法能够随时变参数的变化实时给出满意解,从而为求解时变参数仿真优化问题提供一种新的解决思路。     

基于背景值和边值修正的GM(1,1)模型优化

针对灰色GM(1,1)预测模型提高精度的问题, 提出了新的背景值优化公式代替传统的背景值优化公式, 再进行边值修正的方法. 该方法采用新的背景值优化公式求出紧邻均值生成序列, 并使用均方误差和最小准则, 针对原始序列和生成序列进行边值的修正. 通过对优化后的模型实证测算, 验证了修正后的模型在提高预测精度上的可行性和有效性.     

违约回收率密度函数模拟的非参数估计方法研究

本文研究违约回收率密度函数的模拟估计问题. 本文的工作由两个方面组成. 首先,我们解决了在应用非参数方法估计违约回收率密度函数时如何选取窗宽,以及在使用对称核时如何处理在有界区间上产 生的边界问题. 针对如何选取合理窗宽提高估计效果的问题,我们通过将最优窗宽选取通过渐近积分误差最小作为 标准,然后将满足渐近积分误差最小的问题转换为一个非线性方程,进而应用插入法与迭代算法,求出最优窗 宽的收敛解. 第二,针对应用普通对称核拟合分布于[0,1] 区间内的回收率会产生的估计量偏差在边界有增大趋势问题,我们通过引入边界核来改善这一现象：首先对两种核的统计性质进行理论推导,随后使用蒙特卡罗模拟（Monte Carlo Simulation）方法对其拟合绩效进行数值分析. 本文的数值结果表明我们引入边界核方法,这较之普通对称核可以有效改善边界问题,同时边界核方法在各个指标上效果更优. 最后,基于穆迪公司官方网站公布的2006年到2011年全球每年违约公司债券和贷款的违约回收率统计数据共653个数据,我们的实证案例分析表明,本文引入的边界核方法与现有普遍使用的以Beta分布刻画回收率的方法相比较,通过拟合优度检验和Bootstrap检验,我们的违约回收率密度函数模拟的非参数边界核方法比对应的Beta分布刻画方法更可靠,同时我们的结果也明显优于Beta分布刻画的回收率模型.     

拥堵交通网络能耗节约边界信号优化方法

为了缓解宏观交通网络拥堵区的拥堵状况并降低机动车燃油消耗,首先依据路网状态划分的宏观基本图控制子区,建立了拥堵区边界车流平衡方程.其次将路网分为交叉口和路段两类,根据宏观基本图参数建立了网络能耗估计模型.再次以宏观路网出行车辆完成率最高同时能耗最低建立了能耗节约拥堵区边界双目标优化控制模型.最后以实际城市道路网络为测试对象,通过比较无区域边界控制、拥堵区入口Bang-Bang边界控制和本文提出的双目标优化控制方案,仿真结果表明:1)在高峰时段,双目标优化控制方法路网疏散能力比无区域边界控制、Bang-Bang控制分别提高20.14%、2.1%,同时机动车燃油消耗分别降低43.14%、24.48%;2)本文提出的双目标优化控制方法可有效改善拥堵区内外交通密度的均衡性;3)宏观路网拥堵区的边界控制可有效降低高峰期间拥堵区的拥塞程度,提高整个路网的疏散能力.     

On Minimum Norm Control for an Elastic Robot System

In this paper, we discuss a robot system formulated as a vibrating elastic system. By regarding the damping coefficient of structure as the control variable and adjudging its optimality by norm minimum, we have proved the existence, the uniqueness and the approximation of the optimal control element by utilizing space L2(0,L) 's the reflexivity, the smoothness and the strict convexity.     

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE STOKES AND NAVIER-STOKES EQUATIONS PART II. THE NONLINEAR CASE

1 IntroductionIt is necessary to make some conuneots on some of the re1ated methodologies lately emp1oyedto stabilize the Ga1erkin finite e1ement method for the incompressible NavierStokes equations,including the Stokes equation and the advectiondiffusion problem. Owing to the fact that thehigh Reynold number amounts to a small diffusive term in the advection--diffusion problem,here we will repeatedly mention the diffosion, not the Reynold number or the viscosity in the.. Jincompressible Na…     

Optimal control using microscopic models for a pollutant elimination problem

Optimal control problem with partial derivative equation (PDE) constraint is a numerical-wise difficult problem because the optimality conditions lead to PDEs with mixed types of boundary values. The authors provide a new approach to solve this type of problem by space discretization and transform it into a standard optimal control for a multi-agent system. This resulting problem is formulated from a microscopic perspective while the solution only needs limited the macroscopic measurement due to the approach of Hamilton-Jacobi-Bellman (HJB) equation approximation. For solving the problem, only an HJB equation (a PDE with only terminal boundary condition) needs to be solved, although the dimension of that PDE is increased as a drawback. A pollutant elimination problem is considered as an example and solved by this approach. A numerical method for solving the HJB equation is proposed and a simulation is carried out.     

基于状态转移随机模型的SSADT可靠性评估方法

为评估步进应力加速退化试验 (step stress accelerated degradation test, SSADT)中具有非线性退化趋势的产品的可靠性,提出一种基于状态转移的随机退化建模与可靠性评估方法。首先将状态转移关系与高斯随机过程相结合建立步进应力随机退化模型,以表征微观缺陷的产生和发展对宏观性能的影响;然后应用最佳线性逼近和随机过程曲线边界首达理论建立可靠性模型;最后将其应用在介质振荡器(dielectric resonator oscillator, DRO)贮存可靠性评估中。以修正高斯牛顿算法和Powell共轭梯度算法相结合的方法对退化模型参数进行识别,其结果表明,状态转移随机退化模型能够有效地刻画产品SSADT中性能退化的非线性趋势特性和随机特性,得到较为准确的评估结果。     

Approximate Solutions to the Hamilton-Jacobi Equations for Generating Functions

For a nonlinear finite time optimal control problem, a systematic numerical algorithm to solve the Hamilton-Jacobi equation for a generating function is proposed in this paper. This algorithm allows one to obtain the Taylor series expansion of the generating function up to any prescribed order by solving a sequence of first order ordinary differential equations recursively. Furthermore, the coefficients of the Taylor series expansion of the generating function can be computed exactly under a certain technical condition. Once a generating function is found, it can be used to generate a family of optimal control for different boundary conditions. Since the generating function is computed off-line,the on-demand computational effort for different boundary conditions decreases a lot compared with the conventional method. It is useful to online optimal trajectory generation problems. Numerical examples illustrate the effectiveness of the proposed algorithm.     

基于量子进化算法的空区激光探测点布局设计

针对地下空区边界不规则并且可能包含多个遗留矿柱,如何布局合适的探测点以便三维激光探头能扫描空区内部全貌的工程难题,提出了在基于空区初步资料获得的水平特征截面图上预先布置待选探测点,设计探测点布局方案评价函数,采用量子进化算法进行探测点布局优化的方案.优化设计中,考虑了采空区边界的凸凹不规则性及内部包含多个边界不规则遗留矿柱,以及激光探测范围等因素,建立了通用优化模型,寻求探测点最少的技术及经济上的最优布局方案.实例运算及统计分析结果表明,和遗传算法相比,本文提出的量子进化算法优化模型可快速得出优化的探测点布局方案,保证三维激光探测法成功实施,为复杂空区三维激光探测提供科学决策依据.