用双层位势求解Neumann外问题的Galerkin边界元解法  

Galerkin Boundary Element Method for Two-dimension Laplace Equation of Neumman Condition

作　　者：张守贵[1] 祝家麟[2] 董海云[2] 

机构地区：[1]重庆师范大学数计学院,重庆400047 [2]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3期103-106,共4页Journal of Chongqing University

摘　　要：对二维Laplace方程的Neumann问题采用双层位势来求解时,要出现超强奇异积分.对得出的与之等价的边界边分方程,通过引入边界旋度,经过一系列推导,得到二维情况边界旋度的具体表达式,使超强奇异性转化为弱奇异的积分.计算时采用线性单元,利用Galerkin边界元方法求解.在计算单元刚度矩阵时,对二重积分的第一重使用精确积分,第二重使用数值积分.数值算例验证了这种方法的有效性和实用性.The authors apply the Galenkin variational equation to solve the integral equation with hyper singularity, which can be deduced from the double layer solution for Neumann problem of Laplace equation. The scheme of partial integration in the sense of distributions is introduced to reduce the hyper singularity integral into a weak one with the boundary rotation of unknown function. The numerical implementation with linear boundary elements is presented. The numerical examples illustrate the feasibility and efficiency of the method.

关 键 词：边界元 双层位势 GALERKIN方法 LAPLACE方程 Neumann外问题 

分 类 号：O241.82[理学—计算数学]