Evaluation of Localization Strategies with the Meshless Method of Approximate Particular Solutions

Abstract

In the present work, several localization schemes developed by the Method of Approximated Particular Solutions are evaluated. This meshless method uses solutions of a non-homogeneous Poisson auxiliary equation to approximate the dependent variable. Diusion problems with Dirichlet and Neumann boundary conditions are selected to evaluate the performance of the localization strategy by using cross-shaped, cross- elongated shaped and circular neighborhoods. The results obtained with the cross-shaped neighborhoods show greater stability with respect to the shape parameter. Local formulations perform better on problems
with Dirichlet boundary conditions while the global formulation obtains better results on diffusion problems with Neumann boundary conditions.