二维Helmholtz方程的边界点解法  

Boundary Node Method for the 2-D Helmholtz Equation

作　　者：陈林冲[1] 

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆理工大学学报（自然科学）》2017年第7期188-194,共7页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11471063);重庆市基础科学与前沿技术研究重点项目(cstc2015jcyj BX0083)

摘　　要：针对二维Helmholtz方程的混合边值求解问题,采用边界点方法(boundary node method),在直接边界积分方程的基础上,建立了求解Helmholtz方程边值问题的正则化形式,有效地避免了强奇异积分的计算,并且推导了弱奇异积分的计算公式。两个数值算例表明本方法可取得较高的可行性和有效性。Aiming at 2D Helmhohz equation mixed boundary problem, based on the boundary node method, the regularized form to 2D Helmhohz equation boundary value problem is given on the foundation of direct boundary integral equation. The method can effectively avoid strongly singular integral, and it also deduces a calculating formula to weakly singular integral in detail. Two numerical examples demonstrate that this method has the high feasibility and efficiency.

关 键 词：二维Helmholtz方程 混合边值问题 边界点法 强奇异积分 弱奇异积分 

分 类 号：O242.2[理学—计算数学]