On the use of Delaunay triangulation as 3D finite element modeler

Delaunay triangulation, a geometric subdivision of any convex domain, is often used as a finite element modeling method, but there are still several problems, which originally come from the characteristics of Delaunay triangulation. One problem appears when we remove some nodes which are already introduced for the triangulation. In this case we aim to obtain the triangulation without nodes by partial modification of the Delaunay triangulation with the node. Another problem occurs when tetrahedra with zero volume are generated by Delaunay triangulation. In this case they must be removed for the numerical analysis in order to guarantee the numerical stability and good numerical solutions. In this paper these two problems occuring at the use of Delaunay triangulation are theoretically discussed.