Accuracy and performance of Meshless Local Petrov-Galerkin methods in 2-D elastostatic problems.

A widespread solution approach to compute stresses and displacements in structural mechanics is the standard Finite Element Method (FEM). Recently, meshless methods, such as the Meshless Local Petrov-Galerkin (MLPG) method, have received an increasing attention due to their flexibility in solving several engineering problems, especially with reference to discontinuities, moving boundaries, or complex non-standard geometries. The present paper addresses the issue of the computational performance and numerical accuracy of MLPG with the aim at solving elastostatic problems. Numerical accuracy is investigated versus the analytical solution for the Laplace equation, while both performance and accuracy versus FEM are considered in a 2D structural sample test. The numerical solution to the linear system resulting with the MLPG approach is obtained with the aid of efficient projective solvers preconditioned with the incomplete LU factorization with partial fill-in. The results show that MLPG can provide accurate solutions with a limited number of nodes, distributed over the integration domain with a generally irregular pattern. However MLPG may be computationally more expensive than FEM depending on the values of some user-defined parameters.