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类Helmholtz方程的无网格局部Petrov-Galerkin法
引用本文:李茂军,马健军. 类Helmholtz方程的无网格局部Petrov-Galerkin法[J]. 贵州师范大学学报(自然科学版), 2008, 26(3)
作者姓名:李茂军  马健军
作者单位:重庆大学,数理学院,重庆,400044;重庆大学,数理学院,重庆,400044
摘    要:将无网格局部Petrov-Galerk in方法和改进的移动最小二乘近似相结合,求解了二维类Helmholtz方程。改进的移动最小二乘近似采用加权正交函数系作为基函数,与传统的移动最小二乘近似相比,改进的移动最小二乘近似中的系数矩阵变成了非奇异的对角矩阵,因而无需计算系数矩阵的逆。数值结果表明该方法数值精度高,收敛速度快。

关 键 词:类Helmholtz方程  无网格局部Petrov-Galerkin方法  改进的移动最小二乘近似

The meshless local Petrov-Galerkin method for solving the analogic Helmholtz equation
LI Mao-jun,MA Jian-jun. The meshless local Petrov-Galerkin method for solving the analogic Helmholtz equation[J]. Journal of Guizhou Normal University(Natural Sciences), 2008, 26(3)
Authors:LI Mao-jun  MA Jian-jun
Abstract:In this paper,the meshless local Petrov-Galerkin method with improved moving least-squares approximation for two-dimensional analogic Helmholtz equation is discussed.In the improved moving least-squares approximation,an orthogonal function system with a weight function is used as the basis function.In comparison with the existing moving least-squares approximation,the system matrix in the improved moving least-squares approximation is a nonsingular diagonal matrix and can be solved without obtaining the inverse matrix.In numerical examples,the convergence and stability of the presented method are studied and accurate results are obtained.
Keywords:analogic Helmholtz equation  meshless local Petrov-Galerkin method  improved moving least-squares approximation
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