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

Galerkin Boundary Element Method for Direct Boundary Integral Eqution for Dirichlet Problem of 2-D Laplace Eqation

作　　者：董海云[1] 祝家麟[1] 张守贵[1] 

机构地区：[1]重庆大学数理学院,重庆400030

出　　处：《重庆大学学报（自然科学版）》2006年第4期122-125,共4页Journal of Chongqing University

摘　　要：用Green公式和基本解推导得出的直接边界积分方程来求解二维Laplace方程的D irichlet问题.对直接边界积分方程大都采用配点法求解,还未见有实际用Galerkin边界元来解的报道.对La-place方程的直接边界积分方程进行变分后,利用Galerkin方法,同时采用线性单元变分对方程进行了求解.该方法需要在边界上计算重积分,推出了第一重积分的解析计算公式,对无奇异性的外层积分则采用高斯数值积分.数值实验表明该方法是可行有效的.The direct boundary integral equation of two-dimensional Laplace equation for Dirichlet problem is con - sidered. It is deduced by Green＇ s formula and the fundamental solution. The most-used numerical method for solving direct boundary integral equation is collocation method, and seldom have been used the Galerkin scheme in this case. The direct boundary integral eqution is changed into the variational eqution. Using linear dement, it is solved by Galerkln boundary method. In the variational eqution double integrations shall be carried out. The paper presents the analytical formula to calculate the inner integration and the Gaussian quadrature is used for the outer integration. The numerical experimentation proved thefaesibility and the efficiency.

关 键 词：LAPLACE方程 直接边界积分方程 Galerkin边界元法 线性元 

分 类 号：O241.82[理学—计算数学]