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

Let T T be a tetrahedral mesh. We present a 3-D local refinement algorithm for T T 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 ∈ T T ∈ T produces a finite number of classes of similar tetrahedra, independent of the number of refinement levels. Furthermore, η ( T i n ) ≥ c η ( T ) η (T_iⁿ) ≥ c η (T) , where T ∈ T T ∈ T , c c is a positive constant independent of T T and the number of refinement levels, T i n T_iⁿ is any refined tetrahedron of T T , and η η 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.