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

Abstract

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 τ1={t},τ2={ti2},τ3={ti3},… . We give numerical experiments showing that for a standard shape measure introduced by Liu and Joe (η), the non-degeneracy convergence to a fixed positive value is guaranteed, that is, for any tetrahedron tin in τn, n⩾1, η(tin)⩾cη(t) where c is a positive constant independent of i and n. Based on our experiments, estimates of c are provided.