Volume subdivision based hexahedral finite element meshing of domains with interior 2-manifold boundaries

Abstract

We present a subdivision based algorithm for multi-resolution Hexahedral meshing. The input is a bounding rectilinear domain with a set of embedded 2-manifold boundaries of arbitrary genus and topology. The algorithm first constructs a simplified Voronoi structure to partition the object into individual components that can be then meshed separately. We create a coarse hexahedral mesh for each Voronoi cell giving us an initial hexahedral scaffold. Recursive hexahedral subdivision of this hexahedral scaffold yields adaptive meshes. Splitting and Smoothing the boundary cells makes the mesh conform to the input 2-manifolds. Our choice of smoothing rules makes the resulting boundary surface of the hexahedral mesh as C2 continuous in the limit (C1 at extra-ordinary points), while also keeping a definite bound on the condition number of the Jacobian of the hexahedral mesh elements. By modifying the crease smoothing rules, we can also guarantee that the sharp features in the data are captured. Subdivision guarantees that we achieve a very good approximation for a given tolerance, with optimal mesh elements for each Level of Detail (LoD).