Combinatorics Helps for Hexahedral Mesh Generation in CAD

In many applications, however, quadrilateral and hexahedral meshes have numerical advantages. Recent years showed many research efforts and brought up several approaches, but up to now, hexahedral mesh generation for an arbitrary 3D solid Technische Universitat Berlin, Fachbereich Mathematik, Sekr. MA 6-1, Straße des 17. Juni 136, D 10623 Berlin, Germany, e-mail: [email protected]; URL: http://www.math.tu-berlin.de/~mhannema. The author was partially supported by grant Mo 446/2-3 of the Deutsche Forschungsgemeinschaft (DFG). is still a challenge. Previous work. We briefly review approaches to hexahedral mesh generation which start the meshing from a quadrilateral surface mesh. Meshing from the bounding surface inward is preferred for three reasons. First, for many analysis purposes, it is essential to have the same surface mesh on the common boundary of adjacent solids. Second, good mesh quality is often more important near the bounda