D-N交替法与Schwartz交替法的收敛关系分析

This paper has demonstrated that the Schwartz alternating process must converge if D-N alternating process has converged. Its technique is that the overlapping regions in Schwartz alternating process are considered as independent domains, then Schwartz alternating process could be transformed into D-N alter-nating process. Finally the convergence estimation of Schwartz alternating process could be obtained. The results show that its convergence rate is same as that of D-N alternating process.     

One-Dimensional Poisson Growth Models With Random and Asymmetric Growth

Suppose there is a Poisson process of points X _i on the line. Starting at time zero, a grain begins to grow from each point X _i , growing at rate A _i to the left and rate B _i to the right, with the pairs (A _i , B _i ) being i.i.d. A grain stops growing as soon as it touches another grain. When all growth stops, the line consists of covered intervals (made up of contiguous grains) separated by gaps. We show (i) a fraction 1/e of the line remains uncovered, (ii) the fraction of covered intervals which contain exactly k grains is (k–1)/k!, (iii) the length of a covered interval containing k grains has a gamma(k–1) distribution, (iv) the distribution of the grain sizes depends only on the distribution of the total growth rate A _i +B _i , and other results. Similar theorems are obtained for growth processes on a circle; in this case we need only assume the pairs (A _i , B _i ) are exchangeable. These results extend those of Daley, et al. (2000) who studied the case where A _i =B _i =1. Simulation results are given to illustrate the various theorems.     

解单障碍问题的Lagrangian乘子非匹配网格区域分解法

针对二阶椭圆型单障碍问题提出了一类基于非匹配网格的Lagrang ian乘子非重叠型区域分解方法.并在适当条件下给出了该方法的收敛性分析和收敛速度估计.     

A non-overlapping domain decomposition dual reciprocity method for solving the forward–backward heat equation in two-dimension

We apply a boundary element dual reciprocity method (DRBEM) to the numerical solution of the forward–backward heat equation in a two-dimensional case. The method is employed for the spatial variable via the fundamental solution of the Laplace equation and the Crank–Nicolson finite difference scheme is utilized to treat the time variable. The physical domain is divided into two non-overlapping subdomains resulting in two standard forward and backward parabolic equations. The subproblems are then treated by the underlying method assuming a virtual boundary in the interface and starting with an initial approximate solution on this boundary followed by updating the solution by an iterative procedure. In addition, we show that the time discrete scheme is unconditionally stable and convergent using the energy method. Furthermore, some computational aspects will be suggested to efficiently deal with the formulation of the proposed method. Finally, two forward–backward problems, for which the exact solution is available, will be numerically solved for two different domains to demonstrate the efficiency of the proposed approach.     

求解界面方程的Chebyshev加速算法

非重叠区域分解算法在于建立和求解相关的界面方程．建立界面方程在理论上虽。然容易推导，例如某些问题可用Gauss块消去法，但在实际计算时并不可行，所以界面方程在一些算法中是陷式的．而求解界面方程一般要进行预处理，本提出一种区域分解算法，可得出界面方程的显式表达．算法是完全并行的，所得出的界面方程的系数矩阵的条件数已与网参数无关，事实上就是(Sh^（1）)^-1Sh，进而可直接用收敛速度较快的Chebyshev加速算法求解该界面方程，在充分应用并行计算方法的条件下，本算法与[4]中的算法相比计算效率提高．     

Three-dimensional finite element simulation of closed delaminations in composite materials

Early stage delaminations in composite materials tend to be closed at rest. Inspection with traditional linear ultrasonic techniques generally fails to diagnose and locate such imperfections. However, if undetected and left untreated, incipient defects may gradually grow within the material and eventually lead to failure of the component. Kissing bonds or clapping contacts inherently demand a non-linear diagnostic method, applying a finite excitation amplitude that is able to overcome an activation threshold to open and close the contact. In order to obtain a better understanding and analysis of the macroscopic non-linear behavior that can be observed at the component level, we developed and investigated the results of a finite element model for a composite material containing a single circular delamination. The model makes use of local node splitting and the non-linear constitutive behavior is implemented by means of spring-damper elements at the delamination interface. The results of this parametric study allow a better insight in the behavior of the excited delamination in experimental conditions, including the appearance of localized subharmonics and harmonics of the excitation frequency. Based on the developed model, two different detection and localization techniques (using either a single frequency or a sweep excitation) were demonstrated to determine position, shape, depth and orientation of one or multiple delaminations.     

Sooner and later waiting time problems in a two-state Markov chain

LetX ₁,X ₂,... be a time-homogeneous {0, 1}-valued Markov chain. LetF ₀ be the event thatl runs of 0 of lengthr occur and letF ₁ be the event thatm runs of 1 of lengthk occur in the sequenceX ₁,X ₂, ... We obtained the recurrence relations of the probability generating functions of the distributions of the waiting time for the sooner and later occurring events betweenF ₀ andF ₁ by the non-overlapping way of counting and overlapping way of counting. We also obtained the recurrence relations of the probability generating functions of the distributions of the sooner and later waiting time by the non-overlapping way of counting of 0-runs of lengthr or more and 1-runs of lengthk or more.     

Mechanics of Delaminations in Laminate Composite Structures

A survey of the literature and state of the art of the mechanical aspects of delaminations in laminate composite structures is presented. Surface and internal delaminations of various origin, shape, and location are discussed. The origination, stability, and postcritical behavior of delaminations under quasi-static, cyclic, and dynamic loads are analyzed. Some problems for further investigations are discussed.     

基于非重叠区域分解算法的大地电磁法二维正演模拟

区域分解算法采用分而治之的思想,将大规模问题转化为若干个小问题进行求解,已成为大规模数值计算领域的常用算法之一。将非重叠区域分解算法引入到大地电磁法二维正演模拟中。首先将整个求解区域分解为多个互不重叠的子域,子域之间共享边界元素;然后对每个子域采用有限差分进行离散,采用Schur补偿算法解耦得到共享边界节点上的未知数,并作为子域问题的边界条件得到关于子域内部节点的线性方程组;最后,利用直接求解算法对上述方程组进行求解,实现了大地电磁法二维正演。该算法的准确性和可行性通过多个地电模型的对比试算得到了验证。此外,还统计分析了采用不同子域分区方式和分解个数时的计算耗时,结果表明子域分区的方式对计算效率影响不大,但子域分解个数的影响则较大,进行区域分解时需要选择合适的子域个数。     

金刚石砂轮表面二维形貌全场测量和分析

为了实现金刚石砂轮表面二维形貌的全场测量,有效评价砂轮形貌对磨削力、磨削深度、功率消耗、磨削温度、加工精度的影响,提出基于机器视觉的测量方法;结合CCD感光元件和自动砂轮驱动回转技术实现砂轮形貌的非接触全场测量.根据测量对象尺寸和测量特征量优化选取单次采样面积,通过不重叠拼接实现全场成像;对图像进行处理,提取特征磨粒,分析金刚石砂轮表面形貌的二维关键指标.采用搭建的系统对钎焊金刚石砂轮进行测量实验研究,提取磨粒总数为1 518颗,磨粒分布密度为0.5 颗·mm^-2,磨粒平均面积为0.404 mm²,磨粒平均粒径为0.359 mm.实验结果表明:文中方法可实现对钎焊金刚石砂轮表面形貌的非接触全场测量,并提供砂轮表面磨粒数、粒径及位置等关键参数.