Laplace方程Robin问题的虚边界配点求解法  

Virtual Boundary Collocation Method for Laplace Robin Problem

作　　者：马健军[1] 林鑫[1] 李茂军[1] 

机构地区：[1]重庆大学数理学院,重庆400030

出　　处：《重庆工学院学报（自然科学版）》2009年第2期70-74,共5页Journal of Chongqing Institute of Technology

基　　金：国家杰出青年科学基金资助项目(50625824)

摘　　要：针对Laplace方程Robin边值问题,采用虚边界元方法进行求解.首先基于双层位势的延拓,推导出虚边界积分方程,然后用配点法求解,计算时对虚边界上的虚拟密度函数分别采用常单元和线性元离散.该方法避免了传统边界元中的奇异积分,采用较少边界节点即可达到较高精度.数值算例验证了此方法的有效性.The Robin boundary value problems of Laplace equation is solved by using the Virtual boundary element method. Based on the extension of double layer potential function, Virtual boundary integral equation is deduced. Then the collocation method is used to solve the boundary integral equation, and the unknowable virtual density distribute is discretized into constant elements and linear elements respectively. The proposed method can avoid the singular integral, and it can reach a good accuracy with less boundary nodes. Some numerical examples show its efficiency.

关 键 词：LAPLACE方程 双层位势 虚边界元 ROBIN问题 

分 类 号：O241.82[理学—计算数学]