边界元法

The most-used numerical method for solving direct boundary integral equation is collocation method, which is simple and faster. Seldom have been used the Galerkin scheme in this case.

一般来说，直接边界积分方程可以很方便的用配点法求解，还未见有实际用Galerkin边界元来解的报道。

The non_singular fictitious boundary integral equations are derived by using the fundamental solutions and the singular points exterior to domain techniques.

利用基本解和域外奇点技术导出了弹性力学平面问题的非奇异虚边界积分方程，然后利用虚边界元－边界子段法对导出的积分方程进行数值求解。

Second order incident boundary condition on fixed incident boundary is derived for numerical simulations, based on the cnoidal or sinusoidal motions of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. 2 The analytical solution for higher-order Boussinesq equations is derived and its applicable range is discussed. 3 A 2-D fully non-linear numerical model using boundary element method is developed to obtain wave forces acting on rectangular obstacle. 4 The three-dimensional fully non-linear waves are studied in a numerical wave tank using finite element method.The studies on the coupled numerical model combined Boussinesq equations with Laplace equation are following.

非耦合非线性波浪计算模型：1 根据造波板做椭圆余弦运动或正弦运动速度，推导出数值模拟波浪水槽时固定入射边界上的二阶波浪入射边界条件，数值计算结果和实验结果的对比表明采用二阶入射边界条件对波面升高的预报比采用一阶入射边界条件对波面升高的预报更为精确；2 推导了波浪水槽造波板做正弦运动所产生波浪的高阶Boussinesq方程摄动展开解析解，讨论了该解析解的适用范围；3 对整个波浪水槽应用边界元方法数值模拟了波浪对物体的非线性作用；4 用有限元法求解三维Laplace方程模拟了三维完全非线性波浪水槽。

Boundary element method is a kind of numerical algorithm on boundary; it is based on the boundary integral equation and employs the element discretization technique.

边界元属于边界型的数值方法，它是以边界积分方程为数学基础，同时采用了有限元法的单元离散技术。

The Neumann boundary value prob-lem is firstly reduced into the equivalent natural boundary integral equation withthe kernel possessing 2nd-order singularity,and then the corresponding variationalproblem on the boundary is obtained.By applying Quak trigonometric wavelet basisBjsee(1.2.3as boundary elements and the method of expanding kernel functionto its Galerkin discretization,we obtain simple computational formulae of the en-tries in the stiffness matrix.

首先，我们将Neumann边值问题归化为等价的带有2阶强奇性核的自然边界积分方程，然后化为边界上相应的变分形式，以Hermite插值Quak三角小波基Bj见(1.2.3作为边界元并利用积分核函数展开法将其离散，得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵具有十分简单的形式，它是分块循环对角阵。

In the second chapter the theory of weighted residual technique is illustrated and the boundary integral function of the potential problem is deduced by it. Method of obtaining Greens function fundamental solution is presented. It also illustrates how to deal with inhomogeneous regions and the third boundary condition. At last the numerical solution of boundary integral function is presented.

第二章首先说明了加权余量法的原理，并由此推出了势问题的边界元积分方程，还介绍了无限域中格林函数的基本解的求法，以及多介质域和第三类边界条件的处理方法，最后说明了边界积分方程的数值解法。

To avoid the trouble to construct the basis functions, we introduce a Lagrange multiplier into the variational formulation to replace the constraint condition for the basis.

本文采用同样的思路用Galerkin 边界元方法求解带有约束条件的与第一类Fredholm 间接边界积分方程等价的变分方程，为避免构造基函数时约束条件的限制，我们采用Lagrange 乘子法，把约束条件放入变分方程中去，形成扩展的变分方程，用线形单元离散后求解。

An optimum design for the complex body formed together with the volute casing, base ring and cement foundation of a hydraulic turbine is made by the gradient method and a program is developed on the basis of finite element analysis with the plane and shell element, body element, boundary element and pseudo element.

本文对由水轮机蜗壳、座环和水泥基础所构成的复杂组合体，在采用板壳元、块体元、边界元和伪单元等四类单元进行有限元分析的基础上，选用最速下降法研究了优化设计过程，并编制成程序系统。

The gap element method is proposed in the paper for two kinds of problems, which include contact problem and gap joint problem. Elasticity contact problem falls into the category of unknown boundary value problems. It follows that the contact area and contact conditions or states can never be determined without special mathematical analysis, which is a very difficult work. The boundary conditions of the contact surfaces are deduced.

文中给出了间隙元法在空间可动部件接触问题中的应用，推导了其几何边界条件和力学边界条件，利用虚功原理推导了含间隙元弹性接触问题的有限元方程式，给出了其数值解法的迭代步骤，并指出了利用间隙单元进行分析的特点。

That is, the constant element for velocity potential, called 0 type element, and linear element for its nor

即对势函数采用线性元(或称之&1&型单元)，而对势函数法向导数采用常数元(或称之&0&型单元)，以这样的0-1混合型边界元剖分计算域的

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。