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Voronoi-based point-placement for three-dimensional Delaunay-refinement

Engwirda, Darren

24th International Meshing Roundtable, Elsevier Ltd., October 12-14 2015

IMR
PROCEEDINGS

24th International Meshing Roundtable
Austin, TX
October 12-14,2014

Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia
Email: engwirda@mit.edu

Abstract
An extension of the restricted Delaunay-refinement algorithm for three-dimensional tetrahedral mesh generation is described, in which an off-centre type point-placement scheme is utilised. It is shown that the use of generalised Steiner points, positioned along edges in the associated Voronoi complex, typically leads to improvements in the overall size, quality and grading of the resulting tetrahedral meshes. The new algorithm can be viewed as a Frontal-Delaunay approach - a hybridisation of conventional Delaunay-refinement and advancing-front techniques, in which new vertices are positioned to satisfy both element size- and shape-constraints. The new method is shown to inherit many of the best features of classical Delaunay-refinement and advancing-front type algorithms, combining good practical performance with theoretical robustness. Experimental comparisons show that the new method outperforms classical Delaunay-refinement techniques for a number of three-dimensional benchmark problems.

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