类Helmholtz方程的无网格局部Petrov-Galerkin法  

The meshless local Petrov-Galerkin method for solving the analogic Helmholtz equation

作　　者：李茂军[1] 马健军[1] 

机构地区：[1]重庆大学数理学院,重庆400044

出　　处：《贵州师范大学学报（自然科学版）》2008年第3期68-71,共4页Journal of Guizhou Normal University：Natural Sciences

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。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.

关 键 词：类Helmhohz方程 无网格局部PETROV-GALERKIN方法 改进的移动最小二乘近似 

分 类 号：O241.82[理学—计算数学]