波前法在无网格伽辽金法中的应用

THE APPLICATION OF WAVE FRONT METHOD IN THE GALERKIN ELEMENT-FREE METHOD

有别于有限元法,无网格法采用基于点的近似,可彻底或部分地去除网格(只保留积分所需的背景网格),在保证计算精度同时降低计算难度.无网格伽辽金法(Element Free Galerkin Method,EFG)是一种基于移动最小二乘近似(Moving Least-Squares,MLS)的全局弱式无网格法,广泛应用于计算力学等领域,该方法的一个缺点是:计算过程中产生的系数矩阵含有的非零元数量比有限元法多,即使处理中等规模模型时,也要求计算机有很大的存储空间,并且计算时间长.波前法在有限元法中已有很成熟的应用,但至今没有应用于无网格方法.论文介绍了波前法在无网格伽辽金法中的应用方法,编写了相应的计算程序,并以弹性力学为例做了验算.

Different from grid-based algorithm,meshless （or meshfree） method is a node-based algorithm that merely needs nodes information. Without the need of connecting nodes into mesh cell, this method is convenient with a good accuracy. The Galerkin element-free method （EFG） is a method based on the global weak form and moving least square （MLS） approximation, which is widely used in computational mechanics. One disadvantage of this method is that, the number of nonzero elements in coefficient matrix produced in EFG is much more than in finite element method, requiring bigger memory space. The wave front method is applied in finite element method for a long time,however,it has not used in meshless method yet. In this article,applying the wave front method to EFG method is discussed, and some numerical experiments are presented to validate the present method.