Shape Function for Mesh Free Methods Using Moving Least-Squares Approximation

Abstract

Computational numerical simulation has increasingly become a very important approach for solving complex practical problems in engineering and science. Many of these approximate solution techniques are well-developed and possess much versatility in analyzing complicated phenomena whose behaviours is governed by increasingly complex partial differential equations. Among these approximate methods, the finite element method (FEM) is one of the most popular. Mesh free (MF) methods are among the breed of numerical analysis technique that are being vigorously developed to avoid the drawbacks that traditional methods like Finite Element method (FEM) possess. The main differentiating point between the meshfree and finite element methods is the shape function. The paper is intended to elaborate the construction of the moving least square (MLS) approximation shape function and their derivatives in one-dimension, by presenting the related plots of shape function and its derivatives; with different parameters. Element Free Galerkin (EFG) method is applied and results are obtained using MATLAB.