ABSTRACT
The natural neighbor meshfree method, or natural element method (NEM) provides equivalent quality compared to quadrangular or hexahedral finite elements but is based on the automatic technology of Delaunay triangulation arithmetic. Since the NEM shape functions possess the Kronecker delta property as well as strict linearity over the boundaries of the domain, the essential boundary conditions can be directly implemented with ease as in the conventional finite element method (FEM). Nevertheless, the extension of the method in 3D is complex and costly, involving many geometric constructions in the Vornoi diagram of the set of nodes. In this paper a new method combining the methodology of element-free Galerkin and natural neighbors is proposed to simplify the implementation and reduce the costs of 3D NEM, as well as to provide automatic connectivity in the element-free Galerkin. A 3D Poisson problem is proposed to evaluate the numerical solution as well as the computational costs.