角形域上Hermite三次样条多小波自然边界元法  

Natural boundary element method with cubic Hermite spline multi-wavelet in angle domain

作　　者：陈一鸣[1] 李裕莲[1] 周志全[1] 耿万海[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《辽宁工程技术大学学报（自然科学版）》2012年第1期127-130,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：河北省自然科学基金资助项目(E2009000365);河北省高等学校科学技术研究重点基金资助项目(ZD2010116)

摘　　要：为了解决应用自然边界元方法解角形区域上的调和方程Neumann边值问题中存在的奇异积分问题,采用保角映射,利用自然边界元Hermite三次样条多小波法.由于Hermite三次样条多小波基函数具备紧支集较短、稳定性良好和显式表达式简单,所以与自然边界元法相耦合,利用Galerkin-wavelet法去离散自然边界积分方程,使自然边界积分方程中的强奇异性减弱,从而将原问题的复杂性得以降低.算例表明:该方法切实可行.The Neumann boundary value problem of the Laplace equation in angle domain can be solved using natural boundary element method.In order to solve its singular integral,this study introduces the conformal mapping and proposes a natural boundary element method with cubic Hermite spline multi-wavelet.The cubic Hermite spline multi-wavelet has a shorter tight collection,better stability and good explicit expression.Thus it is coupled with the natural boundary element method.Accordingly,Galerkin-wavelet method is used to discretize the natural boundary integral equation and to make the strong singular integral of the natural boundary equations become a weak singular integral.Therefore,the problem is simplified.A numerical example shows that the method is feasible.

关 键 词：保角变换 角形区域 自然边界归化 Hermite三次样条多小波 Galerkin-wavelet方法 NEUMANN边值 奇异积分 自然边界方程 

分 类 号：O175.2[理学—数学]