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Tetrahedral mesh generation using Delaunay refinement with non‐standard quality measures
Author(s) -
Gosselin S.,
OllivierGooch C.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3138
Subject(s) - delaunay triangulation , polygon mesh , dihedral angle , tetrahedron , bowyer–watson algorithm , measure (data warehouse) , chew's second algorithm , ruppert's algorithm , mesh generation , computer science , constrained delaunay triangulation , algorithm , mathematics , topology (electrical circuits) , geometry , combinatorics , finite element method , data mining , physics , hydrogen bond , quantum mechanics , molecule , thermodynamics
This paper studies the practical performance of Delaunay refinement tetrahedral mesh generation algorithms. By using non‐standard quality measures to drive refinement, we show that sliver tetrahedra can be eliminated from constrained Delaunay tetrahedralizations solely by refinement. Despite the fact that quality guarantees cannot be proven, the algorithm can consistently generate meshes with dihedral angles between 18 circ and 154 ∘ . Using a fairer quality measure targeting every type of bad tetrahedron, dihedral angles between 14 ∘ and 154 ∘ can be obtained. The number of vertices inserted to achieve quality meshes is comparable to that needed when driving refinement with the standard circumradius‐to‐shortest‐edge ratio. We also study the use of mesh improvement techniques on Delaunay refined meshes and observe that the minimum dihedral angle can generally be pushed above 20 ∘ , regardless of the quality measure used to drive refinement. The algorithm presented in this paper can accept geometric domains whose boundaries are piecewise smooth. Copyright © 2011 John Wiley & Sons, Ltd.