泊松方程的边界节点解法  

Solution to the Poisson Equation by the Boundary Node Method

作　　者：汪学海[1] 祝家麟[1] 林鑫[1] 张永兴[2] 

机构地区：[1]重庆大学数理学院,重庆400030 [2]重庆大学土木工程学院,重庆400030

出　　处：《重庆大学学报（自然科学版）》2007年第12期84-88,共5页Journal of Chongqing University

基　　金：国家自然科学基金资助项目(50679097);国家杰出青年科学基金资助项目(50625824)

摘　　要：边界节点法是一种将边界积分方程和移动最小二乘近似方案相结合的边界型无网格法.对于求解泊松方程的边界元方程中的区域积分,采用多重互换法把区域积分转化为边界积分,然后用边界节点法求解边界积分方程.给出了用多重互换法把区域积分转化为边界积分的收敛性证明.数值算例验证了这种方法的实用性和有效性.A meshless method was presented, which couples Boundary Node Method （BNM） with Multiple Reciprocity Method （MRM） to solve Poisson＇ s problems. The BNM is a boundary-only meshless method that combines the moving least-squares interpolation scheme with the standard boundary integral equations. In this proposed method, MRM was used to translate the domain integral which involves in Poisson＇ s boundary element equation into boundary integral. BNM was employed to solve the boundary integral equation. Meanwhile, the convergence analysis of MRM was presented. Tnumerical examples illustrate the feasibility and the efficiency of the proposed meshless method.

关 键 词：泊松方程 边界节点法 多重互换法 

分 类 号：O241.82[理学—计算数学]