Graded conforming Delaunay tetrahedralization with bounded radius-edge ratio
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On the sizes of Delaunay meshes
Computational Geometry: Theory and Applications
Sparse parallel Delaunay mesh refinement
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
On the sizes of Delaunay meshes
Computational Geometry: Theory and Applications
Beating the spread: time-optimal point meshing
Proceedings of the twenty-seventh annual symposium on Computational geometry
Efficient and good Delaunay meshes from random points
Computer-Aided Design
A new approach to output-sensitive voronoi diagrams and delaunay triangulations
Proceedings of the twenty-ninth annual symposium on Computational geometry
A fast algorithm for well-spaced points and approximate delaunay graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
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In this paper we show that the control volume algorithm for the solution of Poisson's equation in three dimensions will converge even if the mesh contains a class of very flat tetrahedra (slivers). These tetrahedra are characterized by the fact that they have modest ratios of diameter to shortest edge, but large circumscribing to inscribed sphere radius ratios, and therefore may have poor interpolation properties. Elimination of slivers is a notoriously difficult problem for automatic mesh generation algorithms. We also show that a discrete Poincaré inequality will continue to hold in the presence of slivers.