Shape Function Object Modeling for Meshfree Methods

Abstract

This article presents a computational object modeling for shape functions used in Meshfree Methods, especially those derived from the of Moving Least Square Method, such as Generalized Finite Differences, Element-Free Galerkin, Hp-Clouds and Finite Point Method, for example. The class model includes abstractions for the basis of functions, the weighting functions and the strategy of building the sparse point cloud. These abstractions allow the definition of classes of shape functions considering specific problems and methods. It should be noted that the Finite Element Method fits this class structure; the points that define the element are the cloud points in Meshfree Method. As ultimate goal, this work aims to build a framework of classes, which allows the construction of agile applications for numerical experiments of Meshfree Methods. In this work the Java language was adopted to implement the proposed design.