Guaranteed-Quality Simplical Mesh Generation with Cell Size and Grading Control

Abstract.

Unstructured mesh quality, as measured geo-metrically, has long been known to influence solution accuracy and efficiency for finite-element and finite-volume simulations. Recent guaranteed-quality unstructured meshing algorithms are therefore welcome tools. However, these algorithms allow no explicit control over mesh resolution or grading. We define a geometric length scale, similar in principle to the local feature size, which allows automatic global control of mesh resolution and grading. We describe how to compute this length scale efficiently and modify Ruppert’s two-dimensional and Shewchuk’s three-dimensional meshing algorithms to produce meshes matching our length scale. We provide proofs of mesh quality, good grading, and size optimality for both two- and three-dimensions, and present examples, including comparison with existing schemes known to generate good-quality meshes.