Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations

The centroidal Voronoi tessellation based Delaunay triangulation (CVDT) provides an optimal distribution of generating points with respect to a given density function and accordingly generates a high-quality mesh. In this paper, we discuss algorithms for the construction of the constrained CVDT from an initial Delaunay tetrahedral mesh of a three-dimensional domain. By establishing an appropriate relationship between the density function and the speci ed sizing eld and applying the Lloyd’s iteration, the constrained CVDT mesh is obtained as a natural global optimization of the initial mesh. Simple local operations such as edges=faces ippings are also used to further improve the CVDT mesh. Several complex meshing examples and their element quality statistics are presented to demonstrate the e ectiveness and e ciency of the proposed mesh generation and optimization method