局部Petrov-Galerkin无网格方法

Meshless Local Petrov-Galerkin(MLPG) Method

简要地阐述了无网格方法,概括了几种典型的无网格插值方案。论述了建立在各种无网格方法一般基础之上的局部彼得洛夫-迦辽金无网格方法,此方法是一种真正的无网格方法,这种方法采用移动最小二乘近似函数作为试函数。此方法的最大特点是在所考虑点处的规则局部区域上以及局部边界上积分,同时给出了建立在无网格局部Petrov-G alerk in方法基础之上的几种M LPG方法,以及M LPG方法的进展和应用。

This paper reviewed all kinds of meshless methods and simply summaried several typical interporlation schemes of meshless methods. The Meshless Local Petrov Galerkin （MLPG） method was dealt with on the general basis for several variations of meshless methods presented in this literature. MLPG method is a truly new meshless method which uses the moving least square approximation as a trial function and uses the weighted function of the moving least square approximation as a test function. The most typical characteristic of MLPG is that it involves only integration on a local subboundary centered and over a regular local subdomain at the node. Moreover, it was stated that recent developments and applications of MLPG methods were presented.