Reviving the Search for Optimal Tetrahedralizations

This paper revisits a local mesh modification method known as the Small Polyhedron Reconnection (SPR) [1]. The core of the SPR operation is a branch and bound algorithm which computes the best 3D triangulation (tetrahedralization) of a polyhedron through an efficient exploration of the set of all its triangulations. The search can accomodate for additional geometric constraints and will inevitably find the highest quality triangulation of the polyhedron if a triangulation exists. This paper focuses on the design of an optimized SPR operator and its application to improving the quality of finite element meshes. Compared to the original algorithm, a speed-up of 10 million is obtained by changing the heuristics determining the search space exploration order. This enables the integration of the SPR operator into standard mesh generation procedures. We show quality improvements obtained by applying this operation to meshes that have already been optimized using smoothing and edge removal techniques.