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 are studied and compared to those of the FE method. We define four associated graphs for meshless discretizations of EFGM and investigate their connectivity. The ways that the associated graphs for coupled FE‐EFG models might be defined are recommended. The associated graphs are used for nodal ordering of meshless models in order to reduce the bandwidth, profile, maximum frontwidth, and root‐mean‐square wavefront of the corresponding matrices. Finally, the associated graphs are numerically compared. Copyright © 2001 John Wiley & Sons, Ltd.