Graph‐based data structures for skeleton‐based refinement algorithms
José Pablo Suárez, Graham F. Carey, Ángel Plaza · Communications in Numerical Methods in Engineering · 2001
Abstract In this paper, we discuss a class of adaptive refinement algorithms for generating unstructured meshes in two and three dimensions. We focus on skeleton‐based refinement (SBR) algorithms as proposed by Plaza and Carey (Appl. Numer. Math. 2000; 32:195) and provide an extension that involves the introduction of the graph of the skeleton for meshes consisting of simplex cells. By the use of data structures derived from the graph of the skeleton, we reformulate the SBR scheme and devise a more natural and consistent approach for this class of adaptive refinement algorithms. As an illustrative case, we discuss in detail the graphs for 2D refinement of triangulations and for 3D we propose a corresponding new face‐based data structure for tetrahedra. Experiments using the 2D algorithm and exploring the properties of the associated graph are provided. Copyright © 2001 John Wiley & Sons, Ltd.