Graph-based data structures for skeleton-based refinement algorithms

Abstract

In this paper, we discuss a class of adaptive re0nement algorithms for generating unstructured meshesin two and three dimensions. We focus on skeleton-based re0nement (SBR )algorithms as proposedby Plaza and Carey (Appl. Numer. Math.2000;32:195 )and provide an extension that involves theintroduction of the graph of the skeleton for meshes consisting of simplex cells. By the use of datastructures derived from the graph of the skeleton, we reformulate the SBR scheme and devise a morenatural and consistent approach for this class of adaptive re0nement algorithms. As an illustrativecase, we discuss in detail the graphs for 2D re0nement of triangulations and for 3D we propose acorresponding new face-based data structure for tetrahedra. Experiments using the 2D algorithm andexploring the properties of the associated graph are provided.