边界点

In the numerical simulation, the Blasius equation of boundary layer based on the Chebyshev interpolation points was solved by using of the Runge-Kutta method with variable step.

在数值模拟中，采用变步长的Runge-Kutta方法，求解基于Chebyshev插值点的边界层Blasius方程，然后对边界条件进行坐标变换，使Chebyshev谱方法适用于边界层稳定性方程的求解。

In the numerical simulation, the Blasius equation of boundary layer based on the Chebyshev interpolation points was solved by using of the Runge utta method with variable step. On the basis of the coordinate transformation of the boundary condition, the Chebyshev spectral method was applied to solve the hydrodynamic stability equation of boundary layer.

在数值模拟中，采用变步长的Runge Kutta方法，求解基于Chebyshev插值点的边界层Blasius方程，然后对边界条件进行坐标变换，使Chebyshev谱方法适用于边界层稳定性方程的求解。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented.

对结构声辐射的边界积分方程的内部形式与外部形式进行了详细的推导，给出了角点系数的计算方法与边界积分方程的形式，在此基础上，分析了奇异积分产生的原理及其对数值计算的重要性，提出了一种计算奇异积分的非等参(来源：Ae8a8BC论文网www.abclunwen.com)单元的变换方法，该方法给Helmholtz 声学边界积分方程中的弱奇异积分与Cauchy 奇异积分的计算以及编程提供了极大便利。

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。

Thus LES is proved to be suitable to simulate the flow and temperature fields of large scale vortices with complex geometric boundaries. LES cooperated with the second order full extension ETG finite element method is applied to simulate the forced convection heat transfer around two square cylinders arranged side by side. While the boundary conditions are symmetrical, the time history and power spectrums of drag coefficient, lift coefficient, averaged Nusselt number at the wall, and the streamwise velocity and temperature on the symmetrical points are calculated. The results show that the power spectrums are all almost symmetrical.

应用大涡模拟与二阶全展开ETG有限元离散格式相结合的方法对间距比为1.5的条件下横掠并列双方柱强制对流换热问题进行了数值模拟，通过边界条件对称时，对并列双方柱对称点上的速度和温度以及方柱的阻力系数、升力系数和壁面平均Nu数进行的时域分析和频域分析，得到了在对称边界条件下并列双方柱对称点上的速度和温度以及方柱的阻力系数、升力系数和壁面平均Nu数的功率谱均基本对称的结论。

In this thesis,the voltage stability boundary is the combined boundary which correspond to Saddle-node bifurcations and Hopf bifurcations.The closest Hopf bifurcation point is found through the proposed iterative method under the assumption that the Hopf hypersurface is continuous and convex.

因此在本论文中，在多维参数空间下，将稳定边界推广到鞍点和Hopf分岔点构成的混合稳定边界，探索性寻求Hopf分岔超平面的法向量，采用迭代算法求取系统发生最近振荡型电压失稳的负荷增长方式。

Given a mesh, we first solve a Poisson equation to construct a scalar field and use it to generate some critical points. The cutting paths between the critical points and the boundaries are solved in the Poisson scalar field using the deepest descent method. For meshes with nonzero-genus, we construct a Harmonic scalar field, and connect the saddle points with the boundaries based on the Morse theory.

对于给定的任意网格，通过求解泊松方程构造标量场来选取临界点，并采用最速下降法给出临界点到边界或者初始点的切割路径；对于亏格不为零的网格，基于Morse理论，通过构造一个调和标量场来得到鞍点，并将它们连接到边界。

The advantages and limitations of every kind of methods for calculating the failure probability is reviewed. The frist order reliability method, the second order reliability method and many kinds of boundary method have achieved remarkable success and formed nature fields of reliability. However, the precision of these methods decrease as the increase of complexity of problem. The numrical methods are versatile, except numerical intergration is only adaptable to special problems which have small number variables and regular intergral domain. Particularly, the advanced variance reduction techniques own the following character: high precision and a small amount computation. But some questions remain to study in the future because only an initial work about these techniqes is developed.

全面评述了计算失效概率各种方法的优点和局限性，其中经典的解析法包括一次可靠性方法、二次可靠性方法、一阶边界法、Vanmarcke上边界、PENT上边界和Ditlevsen二阶窄边界法，这些方法对于多设计点、变量较多且相关、密度函数不是正态以及极限状态方程较复杂的情况，其计算精度较差；而已有的数值方法却是具有较好的通用性，其中除数值积分法只对变量较少、积分域较规则的特殊问题适用外，各种数值模拟方法均具有较广的适应性，特别是各种改进的方差减小技术，精度高、计算量小，但由于其处在研究的初级阶段，还有许多问题有待于解决。

Based on the tooth profile plane model's boundary scope and the geometry dimension of the transmission gear, the paper calculates every point's Cartesian coordinate in all parts of tooth profile, such as addendum arc, involute, dedendum easement curve, axle hole arc and other boundary line section.

最后根据齿廓的几何尺寸和五类齿廓平面模型的边界范围，计算齿廓各部分，即齿顶圆圆弧段、渐开线段、齿根过渡曲线段、轴孔圆圆弧段和齿廓平面模型上其他边界线段上点的坐标，并连接这些点生成各部分线段，从而生成齿廓平面模型。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新