# An Algorithm for the Generation of Hexahedral Element Meshes based on an Octree Technique

## Schneiders, Robert

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.183-194, October 1997

MAGMA Gie"sereitechnologie GmbH, Kackertstr. 11, 52OT2 Aachen, F.R. Germany
Email: rjs@magmasoft.de

Abstract
This paper deals with the generation of unstructured hexahedral element meshes for arbitrary geometries. Octree-based methods have found acceptance in mesh generation, since the generated meshes have an underlying structure which allows to control the element size locally. The octree section of the meshing research corner [11 gives a good overview on octree-based algorithms.

Octree-based mesh generation is done in three steps. First an initial octree structure is setup whose resolution is chosen according to the geometry. This is a non-triyial task for complex geometries (see for example [2]).

The second problem to be solved is to derive a finite element mesh from the octree structure (removal of the hanging nodes). Most algorithms generate tetrahedral element meshes in this step. The first attempt to octree-ba-sed hexahedral element mesh generation was presented in [3]; the approach used a special 1-27-octree structure, and conversion was possible for a limited but practically useful number of cases. This talk will present a general procedure for the generation of hexahedral element meshes from arbitrary octree structures.

In the last step the mesh is fitted to the boundary of the geometry. This is done using a generalization of the technique presented in [4]. Fig. 1 shows the octree-based mesh before and after adaptation to the boundary.

References
[1] S. Owen (1997): Meshing Research Corner. Literature database, available at URL http://www.andrew.cmu.edu/user/sowen/mesh.html

[2] S.A. Mitchell and S.A. Vavasis (1992): Quality Mesh Generation in Three Dimensions. Proc. 8th ACM Symposium on Computational Geometry 212-221.

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

[4] R. Schneiders (1996): A Grid Based Algorithm for the Generation of Hexahedral Element Meshes. Engineering With Computers 12. pp. 168-177