One machine, one minute, three billion tetrahedra

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A simple dedicated data structure, an efficient sorting of the points and the optimization of the insertion algorithm have permitted to accelerate reference implementations by a factor three. Our second contribution is a multi-threaded version of the Delaunay kernel that is able to concurrently insert vertices. Moore curve coordinates are used to partition the point set, avoiding heavy synchronization overheads. Conflicts are managed by modifying the partitions with a simple rescaling of the space-filling curve. The performances of our implementation have been measured on three different processors, an Intel core-i7, an Intel Xeon Phi and an AMD EPYC, on which we have been able to compute 3 billion tetrahedra in 53 seconds. This corresponds to a generation rate of over 55 million tetrahedra per second. We finally show how this very efficient parallel Delaunay triangulation can be integrated in a Delaunay refinement mesh generator which takes as input the triangulated surface boundary of the volume to mesh

Parallel tetrahedral mesh generation

Complex industrial applications, e.g. in fluid mechanics, require finer and finer discretizations with meshes made of hundreds of millions of tetrahedra. Today's mesh generators are essentially sequential and are not able to produce more than ten millions of tetrahedra per minute, which makes mesh generation the main bottleneck of engineering analysis. This thesis primarily addresses the efficiency of tetrahedral mesh generation. It presents a new parallelization strategy based on the Hilbert curve, with unprecedented performance results. Finite element solvers are also very sensitive to the quality of meshes: even a few badly shaped tetrahedra can make a simulation unreliable. Finding better solutions for generating high quality meshes is the second challenge that this thesis tackles.(FSA - Sciences de l'ingénieur) -- UCL, 202

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 accommodate 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