Non-degeneracy study of the 8-tetrahedra longest-edge partition

In this paper we show empirical evidence on the non-degeneracy property of the tetrahedral meshes obtained by iterative application of the 8-tetrahedra longest-edge (8T-LE) partition. The 8T-LE partition of an initial tetrahedron t yields an infinite sequence of tetrahedral meshes tau(1) = {t}, tau(2) = {t(i)(2)}, tau(3) = {t(i)(3)},.... We give numerical experiments showing that for a standard shape measure introduced by Liu and Joe (eta), the non-degeneracy convergence to a fixed positive value is guaranteed, that is, for any tetrahedron t(i)(n) in tau(n), n >= 1, eta(t(i)(n)) >= c eta(t) where c is a positive constant independent of i and n. Based on our experiments, estimates of c are provided. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.