双互易杂交边界点方法求解Helmholtz方程  

Title Dual Reciprocity Hybrid Boundary Node Method for Helmholtz Equation

作　　者：杨庆年[1,2] 郑俊杰[1] 苗雨[1] 

机构地区：[1]华中科技大学土木工程与力学学院,湖北武汉430074 [2]南阳理工学院土木工程系,河南南阳473004

出　　处：《湖南大学学报（自然科学版）》2010年第11期31-35,共5页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(50978112;50808090);河南省基础与前沿技术研究计划项目(102300410148)

摘　　要：提出了一种新的边界类型无网格法——双互易杂交边界点方法,它将杂交边界点法和双互易法结合,来求解Helmholtz方程.该方法将Helmholtz方程的解分为通解和特解两部分,通解使用杂交边界点方法求解,特解则利用径向基函数近似.该方法只需要边界上离散的点,域内少数的点仅仅是为了径向基函数插值.通过数值算例对影响该方法性能的参数进行了研究.数值算例表明,该方法在求解Helmholtz方程时有较高的精度和数值稳定性.This paper presented a new boundary-type meshless method,Dual Hybrid Boundary Node Method（DHBNM）,which combines the Hybrid BNM with the Dual Reciprocity Method（DRM）,to solve Helmholtz equation.In this method,the solution of Helmholtz problem was divided into two parts,namely,the general solution and the particular solution.The general solution was solved by means of Hybrid BNM and the particular one was obtained with DRM.The proposed method retains the characteristics of the meshless method and BEM,which only requires discrete nodes constructed on the boundary of a domain,and several nodes in the domain are needed just for the RBF interpolation.The parameters that influence the performance of this method were studied with numerical examples.Numerical results for the solution of Helmholtz equation have shown that high convergence rates and high accuracy can be achieved.

关 键 词：无网格法 双互易杂交边界点法 HELMHOLTZ方程 移动最小二乘近似 径向基函数 

分 类 号：O242.21[理学—计算数学]