An enriched meshless numerical approach for potential theory problems

Abstract

[Abstract] One of the meshless thechniques that have been recently proposed for solving Boundary Value Problems is the so-called Weighted Least Square (WLS) Method with a Point Collocation approach. Meshless methods were initially intended for problems in which mesh egenration becomes a critical point in the overall process, and/or the subsequent computing effort in extremely hard, due to the geometrical complexity of the domain. Obiously, if mesh generation is discarded, the regular element by element kind of interpolation procedures can not be used anymore. Therefore, the essential concepts of meshless methods rely on the avalibility of simple, efficient and robust interpolation procedures for non-structured distribution of points. In substation grounding analysis we can find a paradigmatic example of the extreme difficulties that mesh generation may involve and/or may procedure. The authors have developed a BEM formulation in order to incorporate more realistic soil models. For this reason we have turner our attention to meshless methods. In this paper we present a WLS point collocation approach with extrinsic enrichment. In order to point out the perfomance of the proposed technique we present several 2D application examples. On the other hand, we present two numerical tests that have been designed to explore the possible stabilizing properties of this method when it is applied to the transport equation.