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1.
边界元法(BEM)和多重互易法(MRM)相结合求解一类重调和方程.通过重调和基本解序列给出的MRM-方法和BEM, 推导出该类问题的MRM-边界变分方程, 用边界元法求解该变分方程, 从而得到重调和方程的近似解, 并给出了解的存在唯一性证明.通过数值算例说明了MRM-方法具有收敛速度快、计算精度高, 易编程等优点, 为使用边界元法数值求解重调和方程提供了方法和理论依据.适合于工程中的实际运算.  相似文献   

2.
椭圆外区域上Helmholtz问题的自然边界元法   总被引:1,自引:1,他引:0  
张敏  杜其奎 《计算数学》2008,30(1):75-88
本文研究椭圆外区域上Helmholtz方程边值问题的自然边界元法.利用自然边界归化原理,获得该问题的Poisson积分公式及自然积分方程,给出了自然积分方程的数值方法.由于计算的需要,我们详细地讨论了Mathieu函数的计算方法(当0相似文献   

3.
三维调和问题的自然积分方程及其数值解   总被引:13,自引:0,他引:13  
邬吉明  余德浩 《计算数学》1998,20(4):419-430
1.引言许多椭圆型偏微分方程边值问题可以通过不同途径归化为边界积分方程,由此发展出各种边界元方法.由我国学者冯康和余德浩首创并发展的自然边界元方法便是其中之一山.这一方法与经典边界元法相比有其独特的优点,它有着较高的数值稳定性,能与传统的有限元方法基于同一变分原理自然而直接地耦合[2].近年来,无界区域问题倍受关注[2-71,其中,基于自然边界归化的耦合算法及区域分解算法是处理无界区域问题的一种有效手段.但是,迄今为止关于自然边界归化的研究仅仅局限于二维问题.而三维问题显然更需要发展相应方法且其结果…  相似文献   

4.
有势场逆问题的边界元法   总被引:5,自引:0,他引:5  
本文给出了位势方程逆问题的一种最小二乘边界元解法。控制方程为Laplace方程,但一部分边界上未给出任何边值,而只在某些内点上给出了势函值。这一问题在数学上属不适定问题,但在一定条件下存在唯一解。本文同时给出了一种估计解的可靠性的方法。数值试验表明,这类逆问题采用边界元法是非常有效的。  相似文献   

5.
外边值问题的边界元法与有限元法组合及奇性处理   总被引:2,自引:0,他引:2  
本文讨论了以一条直线为边界的Helmholts方程外边值问题的边界元法与有限元法的组合过程,推导变分公式,并分别用奇性函数扩大有限元空间和用奇性单元处理尖点附近解的奇性,同边界元法的结果相比较,边界元法与有限元法的组合优越于边界元法。  相似文献   

6.
多裂纹问题计算分析的本征COD边界积分方程方法   总被引:3,自引:3,他引:0       下载免费PDF全文
针对多裂纹问题,若采用常规的数值求解技术,计算效率较低.为实现多裂纹问题的大规模数值模拟,建立了本征裂纹张开位移(crack opening displacement, COD)边界积分方程及其迭代算法,并引入Eshelby矩阵的定义,将多裂纹分为近场裂纹和远场裂纹来处理裂纹间的相互影响.以采用常单元作为离散单元的快速多极边界元法为参照,对提出的计算模型和迭代算法进行了数值验证.结果表明,本征COD边界积分方程方法在处理多裂纹问题时取得较大的改进,其计算效率显著高于传统的边界元法和快速多极边界元法.  相似文献   

7.
构造了一种正则化的积分方程方法来由Cauchy数据确定一维热传导方程的移动边界.在将区域延拓至规则区域后,通过Fourier方法将问题转化为一个第一类Volterra积分方程.然后分别用Lavrentiev正则化方法以及Tikhonov正则化方法将不稳定的第一类Volterra积分方程转化为适定的第二类积分方程,并分别将积分方程转化为常微分方程组,并用Runge—Kutta方法数值求解,以及直接离散来求解.最后通过自由边界上的条件得到数值的移动边界.通过一些数值试验表明此方法是有效可行的,并且给出的方法无需迭代,数值计算较简单.  相似文献   

8.
该文讨论半平面上有局部扰动情况下的散射问题.通过位势理论,应用边界积分方程的方法研究了该问题解的存在与唯一性.主要方法是运用对称反射,使该无界区域上的散射问题变成一个有界区域上的散射问题,只是这一有界区域的边界不光滑.通过仔细分析相应的边界积分算子,作者得到了其解的存在与唯一性.  相似文献   

9.
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.  相似文献   

10.
声波方程吸收边界条件的稳定性分析   总被引:3,自引:0,他引:3  
张关泉  魏素花 《计算数学》1998,20(1):103-112
引言对于无界区域中波动现象的数值模拟,必需引进人工边界将计算限制在一个有界区域上.为了确定解,需要在人工边界上加适当的边界条件.对于声波和弹性波方程,这样的一组人工边界条件,也叫吸收边界条件,在[1,2]中被系统地构造出来.对于声波方程,这些吸收边界条件恰好是单程波方程的近似.如山中所指出,减少边界反射,便于在计算中应用和稳定性是构造吸收边界条件的三点关键.Ellgqllist和Maid。用模态分析方法15]证明,带有[IJ中构造的吸收边界条件的波动方程初边值问题是适定的,并且估计了人工边界所产生的误差.对于更广…  相似文献   

11.
In this paper, we represent a new numerical method for solving the steady-state Stokes equations in an unbounded plane domain. The technique consists in coupling the boundary integral and the finite element methods. An artificial smooth boundary is introduced separating an interior inhomogeneous region from an exterior one. The solution in the exterior domain is represented by an integral equation over the artificial boundary. This integral equation is incorporated into a velocitypressure formulation for the interior region, and a finite element method is used to approximate the resulting variational problem. This is studied by means of an abstract framework, well adapted to the model problem, in which convergence results and optimal error estimates are derived. Computer results will be discussed in a forthcoming paper.  相似文献   

12.
Under consideration are the questions of the numerical solution by the finite element method (FEM) of the first boundary value problem for an elliptic equation with degeneration on a part of the boundary. The weak and strong variational statements are posed in the function spaces with the coordinated weights that correspond to the problem. Using the method of the multiplicative extraction of singularities for the finite element method that utilizes piecewise linear elements, we prove that the convergence of the approximate solutions to the exact solution in the weighted norm is not worse than in the case of an elliptic equation without degeneration.  相似文献   

13.
本文将Laplace算子的Steklov特征值问题归化为一个边界变分问题,从而使原问题的空间维数降低了一维,基于此变分问题给出了Steklov特征值问题的边界元近似解,计算实例表明此方法是十分有效的。  相似文献   

14.
本文研究无穷凹角区域上一类各向异性问题的自然边界元与有限元耦合法.利用自然边界归化原理,获得圆弧或椭圆弧人工边界上的自然积分方程,给出了耦合的变分形式及其数值方法,以及逼近解的收敛性和误差估计,最后给出了数值例子,以示方法的可行性和有效性.  相似文献   

15.
In this paper, we study natural boundary reduction for Laplace equation with Dirichletor Neumann boundary condition in a three-dimensional unbounded domain, which is theoutside domain of a prolate spheroid. We express the Poisson integral formula and naturalintegral operator in a series form explicitly. Thus the original problem is reduced to aboundary integral equation on a prolate spheroid. The variational formula for the reducedproblem and its well-posedness are discussed. Boundary element approximation for thevariational problem and its error estimates, which have relation to the mesh size andthe terms after the series is truncated, are also presented. Two numerical examples arepresented to demonstrate the effectiveness and error estimates of this method.  相似文献   

16.
本文对服从OldroydB型微分模型的粘弹性流体问题给出了一种数值逼近算法.该算法对压力方程采用标准混合有限元方法,对速度方程采用并行非重叠区域分解方法和特征线法.这种并行算法在子区域上用Galerkin方法,通过积分平均方法显式地给出内边界的数值流.在本文最后还给出了该算法的最优L^2。一误差估计.  相似文献   

17.
Free boundary problems with nonlinear source terms   总被引:6,自引:0,他引:6  
Summary The method of lines is used to semi-discretize the non-linear Poisson equation over a domain with a free boundary. The resulting multipoint free boundary problem is solved with a line Gauss-Seidel method which is shown to converge monotonically. The method of lines solution is then shown to converge to the continuous solution of the variational inequality form of the obstacle problem. Some numerical results for the diffusion-reaction equation indicate that the method is applicable to more general free boundary problems for nonlinear elliptic equations.This research was supported by the U.S. Army Research Office under Contract DAAG-79-0145  相似文献   

18.
In this article a numerical method for solving a two‐dimensional transport equation in the stationary case is presented. Using the techniques of the variational calculus, we find the approximate solution for a homogeneous boundary‐value problem that corresponds to a square domain D2. Then, using the method of the fictitious domain, we extend our algorithm to a boundary value problem for a set D that has an arbitrary shape. In this approach, the initial computation domain D (called physical domain) is immersed in a square domain D2. We prove that the solution obtained by this method is a good approximation of the exact solution. The theoretical results are verified with the help of a numerical example. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010  相似文献   

19.
This paper deals with the coupled procedure of the boundary element method (BEM) and the finite element method (FEM) for the exterior boundary value problems for the Helmholtz equation. A circle is selected as the common boundary on which the integral equation is set up with Fourier expansion. As a result, the exterior problems are transformed into nonlocal boundary value problems in a bounded domain which is treated with FEM, and the normal derivative of the unknown function at the common boundary does not appear. The solvability of the variational equation and the error estimate are also discussed.

  相似文献   


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