二维Laplace方程Neumann问题直接边界积分方程的Galerkin解法  

Galerkin Boundary Element Method in Direct Boundary Integral Equation of 2-D Laplace Equation with Neumann Problem

作　　者：张守贵[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《重庆师范大学学报（自然科学版）》2009年第4期67-69,共3页Journal of Chongqing Normal University:Natural Science

基　　金：重庆师范大学青年基金资助项目(No.08xlq05)

摘　　要：对任意形状区域的二维Laplace方程Δu(x)=0的Neumann问题,用Green公式和基本解-21πlnx-y推导得出与之等价的直接边界积分方程,采用直接边界积分方程的Galerkin解法来解该第二类Fredholm积分方程,在进行边界离散化处理时采用常单元。为了提高数值计算的误差精度,在形成线性代数方程组的刚度矩阵元素时,对二重积分的内层积分采用精确积分表达式,外层积分使用Gauss数值积分,数值实验表明该方法的有效性和实用性。The direct boundary integral equation in Neumann problem of two-dimension Laplace equation △u （x） = 0 is discussed. It is deduced from Green＇ s formula and fundamental solution -1/2ln｜x-y｜. The Galerkin method with constant boundary elements is applied to solve the variational equation of second kind Fredholm integral equation. In computation of stiffness matrix, the exactly inte- gral formula are used in the first order integral expression, the numerical integral formula are used in the second order integral expression. Thus the precision of the scheme is improved. The numerical results of example illustrate that the scheme presented is effective and practical.

关 键 词：直接边界积分方程 Galerkin边界元法 LAPLACE方程 NEUMANN问题 

分 类 号：O241.82[理学—计算数学]