H-Morph: An Indirect Approach to Advancing Front Hex Meshing

International Journal for Numerical Methods in Engineering, Wiley, Vol 1, Num 49, pp.289-312, 2000

MESHING
RESEARCH
CORNER

Special Edition on Unstructured Mesh Generation
International Journal for Numerical Methods in Engineering, Vol 49 Number 1-2, 10-20 September 2000

Steve Owen
Sandia National Laboratories
Email: sjowen@sandia.gov

Sunil Saigal
Department of Civil and Environmental Engineering, Carnegie Mellon University
Email: saigal+@cmu.edu

Abstract
H-Morph is a new automatic algorithm for the generation of a hexahedral-dominant finite element mesh for arbitrary volumes. The H-Morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedra into hexahedra. It uses an advancing front technique where the initial front consists of a set of prescribed quadrilateral surface facets. Fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh. Recovery techniques similar to those used in boundary constrained Delaunay mesh generation are used. Tetrahedra internal to the six hexahedral faces are then removed and a hexahedron is formed. At any time during the H-Morph procedure a valid mixed hexahedral-tetrahedral mesh is in existence within the volume. The procedure continues until no tetrahedra remain within the volume, or tetrahedra remain which cannot be transformed or combined into valid hexahedral elements. Any remaining tetrahedra are typically towards the interior of the volume, generally a less critical region for analysis. Transition from tetrahedra to hexahedra in the final mesh is accomplished through pyramid shaped elements. Advantages of the proposed method include its ability to conform to an existing quadrilateral surface mesh, its ability to mesh without the need to decompose or recognize special classes of geometry, and its characteristic well-aligned layers of elements parallel to the boundary. Example test cases are presented on a variety of models.