Mesh Refinement Based on the 8-Tetrahedra Longest- Edge Partition

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 refinement 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 effective 3D derefinement algorithm can be also simply stated. In this paper we discuss the 8-tetrahedra partition, the refinement 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

• Type: Conference
• Year: 2003
• Where: IMR
• Authors: Angel Plaza, Maria-Cecilia Rivara
• Keywords: Computational Geometry, IMR 2003, Precomputed Partition Patterns, Refinement Algorithm, Tetrahedron Bisection Procedure