Octree-based generation of hexahedral element meshes

The aim of this project is to develope an algorithm for the generation of hexahedral element meshes. Hexahedral element meshes are preferred in the fem-simulation of many engineering problems because of their good numerical qualities (e.g. the simulation of metal forming processes).

We have chosen an octree-based technique that allows the generation of solution- and geometry-adapted meshes. The algorithm ist based on a grid-based algorithm that was developed by Robert Schneiders in the last years.

Actually, the presented algorithm is Roland Schindler's master's thesis. His advisors were Frank Weiler and Robert Schneiders; the contribution of Joerg Dettmann is also acknowledged.

The following picture shows an object that has to be meshed for the simulation of an extrusion process. In this example it is clear that, in order to get a mesh with an acceptable number of elements, we should have large elements in the block and small elements in the thin part.

The algorithm starts with an octree-discretization of the object. The bounding box - the smallest box the object fits in - is split up into 27 smaller boxes (octants) which are then recursively split up until the edge lengths of the boxes fall below a predefined threshold. The octants that are outside the object or that intersect the object boundary are removed.

The resulting initial mesh is not conforming and thus not useful for fem calculations. The problem of finding a transition from the coarse to the fine part of the mesh is essentially a mesh refinement problem and solve by using a template technique (the 1-27-octree approach was chosen because of this problem). Finally the elements too closed to the object boudary are removed from the mesh.

The boundary region is then meshed with the isomorphism technique. This technique was developed for the grid-based mesh generator and was adapted for octree-based initial meshes. This (Robert's) part has not yet been completed (a problem that remains to be solved is the smoothing of the surface mesh).

You can download the mesh in patran-format here

References:

R. Schneiders, R. Schindler and F. Weiler: Octree-based Generation of Hexahedral Element Meshes. Proceedings 5th International Meshing Roundtable, Pittsburgh, USA (1996)