边界

The main objective of this dissertation was to develop methodologies with capability of engineering application for simulating flow in fractured rock using discontinuum models. The study work includes three parts. In the first part, numerical methodology of three-dimensional discrete fracture network model casing on hybrid BEM-channel was presented, and the technique for improve the model's computing efficiency was also studied. Firstly in this part, computer simulation methodology based on the Baechermodel for generating network of discrete fractures was presented, which includes the follow details: probability distributions of fracture density,orientation, trace length, size, and aperture and estimation of their statistical parameters; stochastic models of fracture network; Monte-Carlo's simulation method; numerical simulation procedure and technicality.

给出了离散裂隙网络模型所依据的基本假定；发展了基于Baecher模型的离散裂隙网络计算机随机生成技术：详细地推导了单裂隙渗流和多裂隙相交网络渗流的边界单元法公式，发展了离散裂隙网络中稳态渗流的边界元数值技术，并且讨论了相关的具体数值技术细节，如角点的处理方法，单元的自动剖分等：描述了混合边界元—管流模拟方法及其数值实现；研究了裂隙网络的简化方法，并针对裂隙网络边界元法的特点提出了一种改进的分块三角分解法。

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

For this method, integeral was proceed by triangular Gaussian quadrature method in polygon domain, which can reduce computational time greatly. Neighbor nodes database was create which can reduce neighbor nodes searching time. Rock and soil cutting problem are two complicated problems, so a robust method is needed to treat essential boundary condition.

岩土掘削数值分析要求无网格法拥有高效而适应性强(来源：ABC论文f1网www.abclunwen.com)的本质边界条件处理方法，本文提出一种新的处理方法，该方法通过改变边界节点权函数使试函数通过边界节点，并采用对角元素改1法满足本质边界条件，该方法灵活性强，适用于各种岩土掘削问题。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

In order to develop this local property,this paper presents a method,which uses Fourier Series to approximate the boundary shapes of the shafts with periodic boundary of cross section,and uses the conformal mapping in Theory of Function of a Complex Variable to make the complicated boundary shapes of the shafts map a unit circle.Thus elastic theory can analyze...

本文提出一种方法，其实质是：采用富里埃级数来逼近横截面呈周期性变化边界的轴类零件的边界形状；并应用复变函数论中保角映射原理，将零件复杂的边界形状映像成单位圆，从而使弹性理论可以分析和计算复杂边界轴类零件的应力场；再通过留数的求解实现保角映射的反变换。

Boundary features are the boundary lines of a group of points distributed on a fitting feature.

边界特徵之萃取理论是利用拟合特徵所给予之资讯，找出属於边界之点云资料，再由这些边界点云资料计算出边界特徵。

However the lower order traditional absorbing boundary conditions are only effective for the incident waves with smaller incident angles. A fourth-order absorbing boundary condition equation based on Higden's ABC is deduced in this thesis, and a new algorithm is presented to automatically select the Higden's parameters.

本文基于Higdon提出的吸收边界条件方法，推导出四阶吸收边界条件方程，并提出了一种新的吸收边界条件角度参数的自动选择方法，使该吸收边界条件能够吸收全角度(0～90度)入射波。

The establishment principles of traditional and improved PML absorbing boundary condition were described. Through numerical simulation, the absorbing effect of improved and traditional PML absorbing boundary and low-order Higdon absorbing boundary on boundary reflection was discussed.

阐述了传统和改进的PML吸收边界条件的构建原理，通过数值模拟讨论了改进和传统的PML吸收边界以及低阶Higdon吸收边界对边界反射的吸收效果。

There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome.

边界方程有多种选择，在选定一种边界方程的基础上，可以通过建立一个新的边界方程来表示问题的边界，以克服积分核的奇异性。

Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcame. Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations.

边界方程有多种选择，在选定一种边界方程的基础上，可以通过建立一个新的边界方程来表示问题的边界，以克服积分核的奇异性；最后由积分方程的离散化方程组有非平凡解的条件，求得固有频率。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。