Célestin Marot | Searcharxiv

arXiv2020

Quality tetrahedral mesh generation with HXT

We proposed, in a recent paper (10.1002/nme.5987), a fast 3D parallel Delaunay kernel for tetrahedral mesh generation. This kernel was however incomplete in the sense that it lacked the necessary mesh improvement tools. The present paper builds on that previous work and proposes a fast parallel mesh improvement stage that delivers high-quality tetrahedral meshes compared to alternative open-source mesh generators. Our mesh improvement toolkit includes edge removal and improved Laplacian smoothing as well as a brand new operator called the Growing SPR Cavity, which can be regarded as the mother of all flips. The paper describes the workflow of the new mesh improvement schedule, as well as the details of the implementation. The result of this research is a series of open-source scalable software components, called HXT, whose overall efficiency is demonstrated on practical examples by means of a detailed comparative benchmark with two open-source mesh generators: Gmsh and TetGen.

cs.CG↗

arXiv2018

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.

cs.CG↗