Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision

Let I be a tetrahedral mesh. We present a 3-D local refinement algorithm for I which is mainly based on an 8-subtetrahedron subdivision procedure, and discuss the quality of refined meshes generated by the algorithm. It is proved that any tetrahedron T is an element of T produces a finite number of classes of similar tetrahedra, independent of the number of refinement levels. Furthermore, eta(T-i(n)) greater than or equal to c eta(T), where T is an element of T, c is a positive constant independent of T and the number of refinement levels, T-i(n) is any refined tetrahedron of T, and eta is a tetrahedron shape measure. It is also proved that local refinements on tetrahedra can be smoothly extended to their neighbors to maintain a conforming mesh. Experimental results show that the ratio of the number of tetrahedra actually refined to the number of tetrahedra chosen for refinement is bounded above by a small constant.