Studies on the effects of parameters on the convergence of local radial point interpolation method (LRPIM)

Abstract

Numerical solutions in physical engineering problems need appropriate numerical approximation methods. Meshless methods have attracted increasing attention in recent years for seeking of approximate solutions of initial boundary value problem governed by partial differential equations. In this paper, we will present a study of a 2D problem of an elastic homogenous rectangular plate by using the local radial point interpolation method (LRPIM). We investigate the convergence and accuracy of method LRPIM and numerical values are presented to specifying the convergence domain by precising maximum and minimum values as a function of distribution nodes number and by using the radial basis function: Gaussian (EXP). It also presents a comparison with numerical results for different materials and the radial basis functions (RBF). Finally, a comparative study of numerical results with analytical solutions is presented.