Mesh refinement based on the 8-tetrahedra longest-edge partition

Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.67-78, Sept. 2003

MESHING
RESEARCH
CORNER

12th International Meshing Roundtable
September 14-17, 2003
Santa Fe, New Mexico, U.S.A.

University of Las Palmas de Gran Canaria, Spain
aplaza@dmat.ulpgc.es

DCC, University of Chile, Santiago de Chile, Chile
mcrivara@dcc.uchile.cl

Abstract
The 8-tetrahedra longest-edge (8T-LE) partition of any tetrahedron is defined in terms of three consecutive edge bisections, the first one performed by the longest-edge. The associated local re?nement algorithm can be described in terms of the polyhedron skeleton concept using either a set of precomputed partition patterns or by a simple edgemidpoint tetrahedron bisection procedure. An e?ective 3D derefinement algorithm can be also simply stated. In this paper we discuss the 8-tetrahedra partition, the re?nement algorithm and its properties, including a non-degeneracy fractal property. Empirical experiments show that the 3D partition has analogous behavior to the 2D case in the sense that after the first refinement level, a clear monotonic improvement behavior holds. For some tetrahedra a limited decreasing of the tetrahedron quality can be observed in the first partition due to the introduction of a new face which re?ects a local feature size related with the tetrahedron thickness.

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