BOUNDARY CONFORMING DELAUNAY MESH GENERATION

摘要

plices such that all boundary simplices satisfy the generalized Gabriel property. It's dual is a Voronoipartition of the same domain which is preferable for Voronoi-box based finite volume schemes. For ar-bitrary 2D polygonal regions, such meshes can be generated in optimal time and size. For arbitrary3D polyhedral domains, however, this problem remains a challenge. The main contribution of this pa-per is to show that boundary conforming Delaunay meshes for 3D polyhedral domains can be gener-ated efficiently when the smallest input angle of the domain is bounded by arccos 1/3 70.53. In ad-dition, well-shaped tetrahedra and appropriate mesh size can be obtained. Our new results areachieved by reanalyzing a classical Delaunay refinement algorithm. Note that our theoretical guaran-tee on the input angle (70.53°) is still too strong for many practical situations. We further discuss vari-ants of the algorithm to relax the input angle restriction and to improve the mesh quality.