Aggressive tetrahedral mesh improvement

Abstract

We present a tetrahedral mesh improvement schedule that usually creates meshes whose worst tetrahedra have a level of quality substantially better than those produced by any previous method for tetrahedral mesh generation or "mesh clean-up." Our goal is to aggressively optimize the worst tetrahedra, with speed a secondary consideration. Mesh optimization methods often get stuck in bad local optima (poor-quality meshes) because their repertoire of mesh transformations is weak. We employ a broader palette of operations than any previous mesh improvement software. Alongside the best traditional topological and smoothing operations, we introduce a topological transformation that inserts a new vertex (sometimes deleting others at the same time). We describe a schedule for applying and composing these operations that rarely gets stuck in a bad optimum. We demonstrate that all three techniques - smoothing, vertex insertion, and traditional transformations - are substantially more effective than any two alone. Our implementation usually improves meshes so that all dihedral angles are between 31° and 149°, or (with a different objective function) between 23° and 136°.