带超强奇异积分的Galerkin边界元法  

Garlerkin Boundary Element Method with Hyper Singular integral kernel

作　　者：张玲玲[1] 祝家麟[1] 林鑫[1] 张守贵[2] 王贵学[3] 

机构地区：[1]重庆大学数理学院,重庆400030 [2]重庆师范大学,重庆400000 [3]重庆大学生物工程学院,重庆400030

出　　处：《重庆大学学报（自然科学版）》2008年第1期115-118,共4页Journal of Chongqing University

基　　金：国家科技部国际科技合作重点项目(2004DFA06400)

摘　　要：当采用Calderon投影的第二个表达式的直接边界公式解Laplace方程的Neumann问题时,需求解含超强奇异性的第一类Fredholm积分方程。为了克服积分方程的奇异性,采用Galerkin边界元方法,利用广义函数的分部积分公式,把对积分核的两阶导数转移为未知边界量的旋度。对二维问题,采用线性单元时,边界旋度可离散为常向量,从而得到简单的计算公式,避免了超强奇异积分数值计算的困难。数值算例验证了这种方法的有效性和实用性。A Galerkin Boundary Elements was applied to solve the first kind of integral equation with hyper-singularity, which can be deduced from the direct boundary integral formula for the Neumann problem of Laplace equation. The concept of integration by parts in the sense of distributions was used. When boundary rotation is introduced, the two order derivatives of singular kernel are shifted to the boundary rotation of unknown function in the Galerkin variational formulation. While linear boundary elements are used for 2-dimensional problems, the boundary rotation on each element can be discretized into a constant vector, so that the integration can be performed in a simple way and the difficulty of numerical calculation for hyper-singularity is overcome. The results of numerical examples demonstrate that the scheme presented is practical and effective.

关 键 词：Galerkin边界元 超强奇异积分 LAPLACE方程 NEUMANN问题 

分 类 号：O242[理学—计算数学]