Hexahedral mesh generation by successive dual cycle elimination

We propose a new method for constructing all hexahedral finite element mesh es. The core of our method is to build up a compatible combinatorial cell c omplex of hexahedra for a solid body which is topologically a ball, and for which a quadrilateral surface mesh of a certain structure is prescribed Th e step-wise creation of the hex complex is guided by the cycle structure of the combinatorial dual of the surface mesh. Our method transforms the grap h of the surface mesh iteratively by changing the dual cycle structure unti l we get the surface mesh of a single hexahedron. Starting with a single he xahedron and reversing the order of the graph transformations, each transfo rmation step can be interpreted as adding one or more hexahedra to the so f ar created hex complex. Given an arbitrary solid body, we first decompose i t into simpler subdomains equivalent to topological balls by adding virtual 2-manifolds. Secondly, we determine a compatible quadrilateral surface mes h for all subdomains created. Then, in the main part lye can use the core r outine to build up a hex complex for each subdomain independently. The embe dding and smoothing of the combinatorial mesh(es) finishes the mesh generat ion process. First results obtained for complex geometries are encouraging.