Boundary conforming Delaunay mesh generation

• Published in: Computational mathematics and mathematical physics Vol. 50; no. 1; pp. 38 - 53
• Main Authors: Si, H., Gärtner, K., Fuhrmann, J.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01.01.2010; Springer Nature B.V
• Subjects: Algorithms; Boundary conditions; Computational mathematics; Computational Mathematics and Numerical Analysis; Finite volume method; Mathematical analysis; Mathematical problems; Mathematics; Mathematics and Statistics; Physics; Studies; partitions of polyhedres; Voronoi partitions; Delaunay mesh
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542510010069

A boundary conforming Delaunay mesh is a partitioning of a polyhedral domain into Delaunay simplices such that all boundary simplices satisfy the generalized Gabriel property . It’s dual is a Voronoi partition of the same domain which is preferable for Voronoi-box based finite volume schemes . For arbitrary 2D polygonal regions, such meshes can be generated in optimal time and size. For arbitrary 3D polyhedral domains, however, this problem remains a challenge. The main contribution of this paper is to show that boundary conforming Delaunay meshes for 3D polyhedral domains can be generated efficiently when the smallest input angle of the domain is bounded by arccos 1/3 ≈ 70.53°. In addition, well-shaped tetrahedra and an appropriate mesh size can be obtained. Our new results are achieved by reanalyzing a classical Delaunay refinement algorithm. Note that our theoretical guarantee on the input angle (70.53°) is still too strong for many practical situations. We further discuss variants of the algorithm to relax the input angle restriction and to improve the mesh quality.