On refinement of constrained delaunay tetrahedralizations

Abstract

This paper discusses the problem of refining constrained Delaunay tetrahedralizations (CDTs) into good quality meshes suitable for adaptive numerical simulations. A practical algorithm which extends the basic Delaunay refinement scheme is proposed. It generates an isotropic mesh corresponding to a sizing function which can be either user-specified or automatically derived from the geometric data. Analysis shows that the algorithm is able to produce provable-good meshes, i.e., most output tetrahedra have their circumradius-to-shortest edge ratios bounded, except those in the neighborhood of small input angles. Good mesh conformity can be obtained for smoothly changing sizing information. The algorithm has been implemented. Various examples are provided to illustrate the theoretical aspects and practical performance of the algorithm. © 2006 Springer.