The 8-tetrahedra longest-edge partition of right-type tetrahedra

Abstract

A tetrahedron t is said to be a right-type tetrahedron, if its four faces are right triangles. For any right-type initial tetrahedron t, the iterative 8-tetrahedra longest-edge partition of t yields into a sequence of right-type tetrahedra. At most only three dissimilar tetrahedra are generated and hence the non-degeneracy of the meshes is simply proved. These meshes are of acute type and then satisfy trivially the maximum angle condition. All these properties are highly favorable in finite element analysis. Furthermore, since a right prism can be subdivided into six right-type tetrahedra, the combination of hexahedral meshes and right tetrahedral meshes is straightforward.