Topological aspects of meshless methods and nodal ordering for meshless discretizations

The meshless element-free Galerkin method (EFGM) is considered and compared to the finite-element method (FEM). In particular, topological aspects of meshless methods as the nodal connectivity and invertibility of matrices ar e studied and compared to those of the FE method. We define four associated graphs for meshless discretizations of EFGM and investigate their connecti vity. The ways that the associated graphs for coupled FE-EFG models might b e defined are recommended. The associated graphs are used for nodal orderin g of meshless models in order to reduce the bandwidth, profile, maximum fro ntwidth, and root-mean-square wavefront of the corresponding matrices. Fina lly, the associated graphs are numerically compared. Copyright (C) 2001 Joh n Wiley & Sons, Ltd.