边界单元法

In this thesis, the virtual boundary integral equation is based on double layer potential with the virtual density to be determined on virtual boundary. Since this integral equation related to double layer potential only involves the computation of the normal derivative and second normal derivative of fundamental solution, the exponential integral function is not involved in it, so numerical computation for the exponential integral function is avoid.

本文则基于双层位势，引入虚拟矩密度函数来建立虚边界积分方程，并首先对时间变量进行解析积分，在虚、实边界上采用常单元和等额配点离散，该方程只涉及含基本解的法向导数及其二阶法向导数项的计算，对时间变量进行解析积分后，不会出现对指数积分函数的空间变量的积分计算。

It is the first important step in video analysis and will directly affects the effectiveness of indexing Shot boundary detection is one of our major research interests and we will tackle the following existing problems the ambiguity between gradual change and camera motion, the discontinuity during gradual change, false detection caused by illumination variation and flashlight, automatic threshold selection Firstly, we discuss shot boundary detection in non-compressed domain In chapter 2, we compare some of the commonly used detection methods which are based on frame difference and point out that single feature will not generate good results As a conclusion, we use fuzzy logic to combine multiple features Presently, most frame difference based shot boundary detection algorithms rely on threshold and hence the selection of such thresholds will greatly affect the performance of boundary detection We propose a membership function to define frame difference and calculate the membership with self adaptation according to the statistic distribution of frame differences to satisfy different type of video clips Experiments show that the proposed fuzzy shot boundary detection algorithm can be used with different video types and has a high detection precision and recall In chapter 3, we discuss model-based shot boundary detection algorithms regarding chromatic and spatial editing effects such as fade-in, fade-out, dissolve and wipe Various parameters are proposed to better describe the characteristics of each editing type.

镜头边界的检测是把视频自动地分割为一个个镜头，作为基本的索引单元，因此它是视频分析重要的第一步，直接影响到视频检索的成败。镜头边界的检测是本文研究的重点之一。目前镜头边界检测算法主要存在以下问题：渐变与镜头运动难以区别；渐变过程中的不连续与停顿、光照条件的变化及闪光灯等特殊情况会引起误检测；自动选择阈值比较困难等。本文首先针对非压缩域视频进行了镜头边界检测的研究。在第二章中我们采用了比较流行的基于帧间差的方法。在比较各种帧间差计算方法的基础上，指出使用单一的特征难以取得很好的检测效果，提出用模糊逻辑综合使用各种特征。目前大多数基于帧间差的镜头边界检测算法都采用阈值法进行镜头转换的判别。阈值选择的误差对检测性能有较大的影响，本文提出用隶属度函数定义帧间差较大、中等较大和较小等概念，并根据帧间差的统计分布自适应地确定隶属度，以适应不同类型的视频片断。实验结果表明这种基于糊逻辑的镜头边界检测算法可以适应不同的视频，并具有较高的检测精度和检出率。在第三章中采用基于模型的方法进行镜头渐变的检测，研究了淡入／淡出、慢转换和扫换的模型。

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用"去行去列法"和"置大数法"进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

Relative hydraulic conductivity is first evaluated cell boundaries by using full upstream weighting, the arithmetric mean, or the geometic mean of values from adjacent cells. Saturated hydraulic conductivites are evaluated at cell boundaries by using distance—weighted harmonic mean.

首次采用分散平均方法估算水力传导率，即运用上风权重法来估算单元边界的相对水力传导率，运用距离权重调和平均法来估算单元边界的饱和水力传导率。

Boundary polynomial point interpolation mesh-free method and boundary radial point interpolation mesh-free method were presented, based on polynomial basis and radial basis respectively for transient eddy current analysis, and their interpolation shape functions satisfy the Kronecker delta function and the essential boundary conditions can be directly imposed on the boundary nodes. An example on analyzing transient eddy current of a square metal column was set to prove the validity of the proposed methods, and a comparison on accuracy between BPPIM and BRPIM was analyzed as well.

运用多项式点插值法和径向基点插值法构造形函数，推导了适合于工程电磁场瞬态涡流问题的多项式基点插值边界无单元方法和径向基点播值边界无单元方法，这两种方法的空间插值形函数满足Kronecker delta条件，从而强加边界条件可以直接施加在边界点上，以金属长方柱的瞬态涡流分析作为数值算例，证实了两种方法的正确性和有效性，并对两种基类的点插值法进行了精度分析和比较。

Zhu Jialin[23]used a simple layer distribution expression based on velocity-pressure formula for the Dirichlet problem of Stokes equation with a Galerkin boundary element method and presented some numerical examples calculated by constant boundary element.

祝家麟从速度-压力公式出发，利用单层位势表示定常Stokes 方程Dirichlet 问题的解，用Galerkin 边界元法求解，并用常单元给出数值算例。

In this paper, the authors try, in light of the principle of the finite strip method, to give their ALGOL60 Programme for use on the D...

程序中运用了自动划分板条及处理边界约束的技巧。计算结果表明，其精度明显地优于有限单元法。

Then the element equation and unit tangent rigid matrix are deducted on the basis of description of UL coordiate and principle of imaginary, the balance equation and overall tangent rigid matrix are integrated via introduction of terminal condition, and the nonlinear equation group is finally parsed on the basis of combination method of Newton-Raphson and increment.

接着基于U.L 坐标描述，从虚功原理出发推导出单元的平衡方程和单元切线刚度矩阵，引入边界处理条件集成了整体结构的平衡方程和总切线刚度矩阵，并采用Newton—Raphson 法和增量法相结合的方法求解非线性方程组。

Remove row and column' and 'put a big number' have been used for the first boundary;a continuous Regional Identification Function is used on the basis of non-variant nodal virtual flux method for the free surface boundary;Gauss formula is used to make the curved surface integral of the free surface boundary transformed as the difference between volumn integral and other curved surface integral to calculate the integral item on boundaries, which avoiding finding the position of free surface, while the continuous Regional Identification Function is applied to calculate volumn integral and surface integral;Crout and PCG method is used for solusion.

对于已知水头边界，采用&去行去列法&和&置大数法&进行处理；对于自由面穿过的单元，在固定网格节点虚流量法的基础上，引入连续的区域识别函数；对于非稳定渗流中自由面边界积分项，采用高斯公式将求自由面的面积分转化为求体积分与其他面积分之差，避免了求自由面的具体位置，同时在计算体积分和面积分时采用连续的区域识别函数；在解法上，采用直接解法和PCG法。

Flow-field simulation shows that radial pressure gradient goes down fast and air flowrate is nearly directly proportional to the well vacuum and the soil permeability coefficient. It also indicates that stop-off coating will play an important role in SVE.

采用Galerkin三角形有限单元法对复合地表边界的竖井土壤气相抽提稳态流动问题进行了数值模拟分析，模拟结果显示：气相压力沿径向梯度迅速下降，抽提流量与土壤通透系数及真空度呈现高度相关的正比例关系，且地表隔绝覆盖层对流场影响很大。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。