Boundary conforming Delaunay mesh generation |
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Authors: | H Si K Gärtner J Fuhrmann |
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Institution: | 1.Weierstrass Istitute for Applied Analysis and Stochastics,Berlin,Germany |
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Abstract: | 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. |
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