位势问题边界元法中几乎奇异积分的正则化

将一种通用算法应用于平面位势问题边界元法中近边界点几乎奇异积分的正则化。对线性单元,位势问题近边界点的几乎强和超奇异积分可归纳为两种形式。通过分部积分,将引起奇异的积分元素变换到积分号之外,从而对这两种积分分别给出了无奇异的正则化计算公式。除了线性元,二次元也应用于该算法。与近边界点临近的二次单元划分为两段线性单元,该算法仍然适用。算例证明了方法的有效性和精确性。对曲线边界问题,联合二次元和线性元可提高计算结果精确度。     

正交各向异性弹性力学平面问题的样条虚边界元法

采用域外奇点技术并根据问题的边界条件,建立了正交各向异性弹性力学平面问题的非奇异虚边界积分方程,然后采用性态优越的B样条函数去逼近未知虚荷载函数,并采用性能稳定的最小二乘边界子段法去消除边界余量,据此获得积分方程的数值解.数值算例表明:该方法具有相当高的精度和良好的数值稳定性,且计算工作量少.文中引言部分还对域外奇点法的发展作了系统的评述.     

奇异边界法分析含水下障碍物水域中的水波传播问题

研究奇异边界法模拟水波在含水下障碍物水域的传播过程.奇异边界法是一种最近提出的新型边界配点方法,具有无网格和无数值积分、数学简单、编程容易等优点.首先研究了奇异边界法分析典型水波算例的精度及效率,并与边界元法的计算结果进行比较,然后通过数值模拟讨论分析了水下障碍物位置、尺寸及形状等因素对水波传播的影响.发现奇异边界法的计算精度较高,且与边界元法的计算结果吻合较好;数值结果显示水下障碍物的不同高宽比对水波的传播影响明显:障碍物无量纲高度越大对水波的屏障作用越明显;障碍物无量纲宽度增加对水波的屏障作用先增强后变弱.在高宽比一定时,斜率变化对水波的屏障作用不明显;含吸收边界水下障碍物可以得到较低的传递系数和较高的反射系数, 对水波的屏障作用更为明显.     

薄体结构温度场的高阶边界元分析

分析了二维问题边界元法3节点二次单元的几何特征,区分和定义了源点相对高阶单元的Ⅰ型和Ⅱ型接近度.针对二维位势问题高阶边界元中奇异积分核,构造出具有相同Ⅱ型几乎奇异性的近似核函数,在几乎奇异积分单元上分离出积分核中主导的奇异函数部分.原积分核扣除其近似核函数后消除几乎奇异性,成为正则积分核函数,并采用常规Gauss数值方法计算该正则积分;对奇异核函数的积分推导出解析公式,从而建立了一种新的边界元法高阶单元几乎奇异积分半解析算法.应用该算法计算了二维薄体结构温度场算例,计算结果表明高阶单元半解析算法能充分发挥边界元法优势,显著提高计算精度.     

边界元法中的改进等参变换

首先考察三维边界元法中八结点等参单元边中结点的敏感性,指出对于常规等参变换计算,边中结点同有限元计算情形一样,仍必须遵守位于相邻角点间距离的三分之一内的建议,且限制应更严格,才能保证计算的有效性.其次,将改进等参变换引入到边界元法,并解决了相应的奇异积分处理等问题,提出了一个比常规等参变换时更加一般的坐标变换关系式.最后,对于立方块受单向拉伸和纯弯曲两种情况作了计算,结果表明,在边界元法中,改进等参变换的引入,使得计算具有更大的适应性.     

三维无限接合体双材料多界面裂纹的超奇异微积分方程法

利用有限部积分的概念,导出了三维无限接合体中多个界面裂纹,在任意载荷作用下的超奇异微积分方程组.数值分析中,未知的位移间断采用基本分布函数和多项式乘积的形式来近似,其中基本分布函数是根据界而裂纹应力的振荡奇异性来选取的.作为典型算例,研究了存在两个矩形界面裂纹时,裂纹之间距离、裂纹形状及双材料弹性常数对应力强度因子的影响.计算表明,应力强度因子随裂纹间的距离的增大而减小.     

弹性力学问题解唯一的边界积分方程

从积分方程式出发,应用基本解的特性分析,说明在力边值问题中,位移边界积分方程和面力边界积分方程的位移解不唯一.提出了位移解唯一的条件,建立了唯一解的位移边界积分方程和面力边界积分方程.实例计算结果表明唯一解的边界积分方程是有效的.     

粘弹性薄板动力响应的边界元方法（Ⅰ）

本文中我们给出了粘弹性薄板动力响应的边界元方法．在Laplace变换区域中，给出了基本解的两种近似方法，运用这些近似基本解建立了边界元方法，再利用改进的Bellman反交换技术，求得问题的解，计算表明该方法具有较高精度和较快收敛性．     

粘弹性薄板动力响应的边界元方法（Ⅱ）——理论分析

本文中，对（１）中提出的粘弹性结构动力响应的近似边界元方法给出了必要的理论分析，得到了近似解的存在唯一性定理和误差估计。基于这些结论给出了网格宽度与基本解中截断项数的选取原则。本文中得到的理论结果和（１）中数值实验结果是一致的。     

泊松类型方程边界元解法

本文采用高阶拉普拉斯算子基本解将泊松类型方程的区域积分全部变换成边界积分，使计算问题的维数减少一维．通过斯托克斯方程的算例，表明本文所用的方法是有效的方法。     

A BOUNDARY ELEMENT METHOD FOR A NONLINEAR BOUNDARY VALUE PROBLEM IN STEADY-STATE HEAT TRANSFER IN DIMENSION THREE

In this paper, a new method of boundary reduction is proposed, which reduces thesteady-state heat transfer equation with radiation. Moreover, a boundary element method is pre-sented for its solution and the error estimates of the numerical approximations are given.     

一种改进边界元法在弹性扭转问题中的应用

本文用一种改进边界元法分析与计算了椭圆截面等直杆的扭转问题.并与边界元法的解进行比较,其结果极为符合.然而,改进边界元法较边界元法所需要的数据量少得多,计算时间也将大大减少了.因此,本文方法对求解Poisson方程问题是一种经济而行之有效的数值计算方法.     

Modelling groundwater changes due to fluctuating dam discharge

In this contribution, two numerical methods are used to predict the free surface changes in a sand bar due to fluctuations in river stage. One is a fixed-mesh, finite-element seepage formulation including Biot's consolidation theory, and the other is a boundary element method solution of the Laplace equation. Both models give overall predictions that are in good agreement with field data recorded at an instrumented sand bar in the Colorado River subjected to stage fluctuations from operation of the Glen Canyon Dam. The boundary element method appears to offer significant advantage in data preparation and computational times over the finite-element method for the problem studied in this paper.     

A BOUNDARY ELEMENT PROCEDURE FOR THE SIGNORINI PROBLEM IN THREE-DIMENSIONAL ELASTICITY

In this paper, a new numerical method for the Signorini problem in three-dimensional elasticity is presented. The problem is reduced to a boundary variational inequality based on a new representation of the derivative of the doublelayer potential. Furthermore, a boundary element procedure is described for the numerical approximation of its solution and an abstract error estimate is given.     

边界伸缩原理

文[5]提出边界伸缩原理及边界伸缩法.本文补充叙述了边界伸缩原理,并根据已有研究成果给予了较严格地证明,进一步完善了边界伸缩法理论基础.     

A boundary element method for homogenization of periodic structures

Homogenized coefficients of periodic structures are calculated via an auxiliary partial differential equation in the periodic cell. Typically, a volume finite element discretization is employed for the numerical solution. In this paper, we reformulate the problem as a boundary integral equation using Steklov–Poincaré operators. The resulting boundary element method only discretizes the boundary of the periodic cell and the interface between the materials within the cell. We prove that the homogenized coefficients converge super-linearly with the mesh size, and we support the theory with examples in two and three dimensions.     

The method of fundamental solutions for problems in potential flow

The method of fundamental solutions is a form of indirect boundary integral equation method. Its distinctive feature is adaptivity, gained through the use of an auxiliary boundary that is chosen automatically by a least squares procedure. The paper demonstrates the application of the method to problems in potential flow. A further advantage of the method is that the velocity field can be computed easily and accurately by a direct evaluation procedure.     

A boundary only procedure for time-dependent diffusion equations

In the recent literature, the boundary element method (BEM) is extensively used to solve time-dependent partial differential equations. However, most of these formulations yield algorithms where one has to include all interior points in the computation process if finite difference procedures are used to approximate the temporal derivative. This obviously restricts the advantages of the BEM, which is mainly considered to be a boundary only algorithm for time-independent problems. A new algorithm is demonstrated here, which extends the boundary only nature of the method to time-dependent partial differential equations. Using this procedure, one can reduce the finite difference time integration algorithm, generated in a standard manner, to a boundary only process. The proposed method is demonstrated with considerable success for diffusion problems. Results obtained in these applications are presented comparatively with analytical and other boundary element time integration procedures. The algorithm proposed may utilize several coordinate functions in the secondary reduction phase of the formulation. A summary of such functions is described here and performances of these functions are tested and compared in three applications. It is shown that some coordinate functions perform better than others under certain conditions. Using these results, we propose a general coordinate function, which may be used with satisfactory results in all parabolic partial differential equation applications.     

一种有效的分析弹塑性问题的边界元法

本文提出了一组有效的边界元公式.该公式通过利用一个新的变量,使核函数仅具有lnr(r为源点和场点的距离)的较低阶奇异性,从而,在积分点的传统位移和应力公式的奇异性得到降低,且原公式中影响应力计算精度的边界层效应得到消除.同时,也避免了难于计算的参数C.将该方法应用到弹塑性分析中,数值分析结果表明该公式具有明显的优势.     

椭圆外区域上Helmholtz问题的耦合法

以椭圆外区域上Helmholtz方程为例,研究一种带有椭圆人工边界的自然边界元与有限元耦合法,给出了耦合变分问题的适定性及误差分析并给出数值例子.理论分析及数值结果表明,用方法求解椭圆外问题是十分有效的.为求解具有长条型内边界外Helmholtz问题提供了一种很好的数值方法.