Convergence of MLPG method for various materials of a 2D problem

Abstract

Atluri and Zhu (1998) have advocated the meshless local Petrov-Galerkin methods (MLPG). It is derived from the local weak form (WF) of the equilibrium equations and by inducting the moving last square approach for trial and test functions in (WF). Finally is discussed over local sub-domains. However, the convergence of the method presents dependency to number of parameters deriving from local weak form and different subdomains. This paper deals with the effect of sizing parameter of subdomains on the convergence and accuracy of the methods and numerical values are presented to specifying the convergence domain by precising maximum and minimum values as a function of distribution nodes number. It also presents a comparison with numerical results for different materials. Numerical results agree with the analytical solution of the deflection.

A Comparative Study of Size Parameters Effects in Meshless Method Local Petrov-Galerkin (Mlpg) and Local Radial Point Interpolation Method (Lrpim)

“…. The results obtained [11] for the studied spline functions are consistent with those found by the MLPG method. The results found by MLPG are very good.…”

“…We note that all the curves of each of the different materials studied have the same shape for a fixed value of S  . The obtained results are compared with the results found by method MLPG [11] for different materials. .…”