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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Quality Local Refinement of Tetrahedral Meshes Based on 8-Subtetrahedron Subdivision


Authors: Anwei Liu and Barry Joe
Journal: Math. Comp. 65 (1996), 1183-1200
MSC (1991): Primary 65N50; Secondary 51M20, 52B10, 65M50
MathSciNet review: 1348045
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Abstract: Let $\mathcal {T}$ be a tetrahedral mesh. We present a 3-D local refinement algorithm for $\mathcal {T}$ which is mainly based on an 8-subtetrahedron subdivision procedure, and discuss the quality of refined meshes generated by the algorithm. It is proved that any tetrahedron ${\mathbf T} \in \mathcal {T}$ produces a finite number of classes of similar tetrahedra, independent of the number of refinement levels. Furthermore, $\eta ({\mathbf T}_i^{n}) \geq c \eta ({\mathbf T})$, where ${\mathbf T} \in \mathcal {T}$, $c$ is a positive constant independent of $\mathcal {T}$ and the number of refinement levels, ${\mathbf T}_i^{n}$ is any refined tetrahedron of ${\mathbf T}$, and $\eta $ is a tetrahedron shape measure. It is also proved that local refinements on tetrahedra can be smoothly extended to their neighbors to maintain a conforming mesh. Experimental results show that the ratio of the number of tetrahedra actually refined to the number of tetrahedra chosen for refinement is bounded above by a small constant.


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Additional Information

Anwei Liu
Affiliation: Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2H1
Email: anwei@cs.ualberta.ca

Barry Joe
Affiliation: Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2H1
Email: barry@cs.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00748-X
PII: S 0025-5718(96)00748-X
Received by editor(s): May 28, 1994
Received by editor(s) in revised form: July 5, 1995
Additional Notes: This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 1996 American Mathematical Society