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Hexagon-Based All-Quadrilateral MeshGeneration with Guaranteed Angle Bounds

Xinghua Liang and Yongjie Zhang

Proceedings, 19th International Meshing Roundtable, Springer-Verlag, pp.1-22, October 3-6 2010

IMR
PROCEEDINGS

19th International Meshing Roundtable
Chattanooga, Tennessee, USA.
October 3-6, 2010

Department of Mechanical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213, U.S.A

Summary
In this paper, we present a novel hexagon-based mesh generation method which creates all-quadrilateral (all-quad) meshes with guaranteed angle bounds and feature preservation for arbitrary planar domains. Given any planar curves, an adaptive hexagon-tree structure is constructed by using the curvature of the boundaries and narrow regions. Then a bu er zone and a hexagonal core mesh are created by removing elements outside or around the boundary. To guarantee the mesh quality, boundary edges of the core mesh are adjusted to improve their formed angles facing the boundary, and two layers of quad elements are inserted in the bu er zone. For any curve with sharp features, a corresponding smooth curve is rstly con- structed and meshed, and then another layer of elements is inserted to match the smooth curve with the original one. It is proved that for any planar smooth curve all the element angles are within [60-", 120+"] ("  5). We also prove that the scaled Jacobians defined by two edge vectors are in the range of [sin(60-"), sin90], or [0.82, 1.0]. Furthermore, the same angle range can be guaranteed for curves with sharp features, with the exception of small angles in the input curve. In addition, all the elements in the nal mesh are grouped into ve types, and most elements only need a few ops to construct the sti ness matrix for nite element analysis. This will significantly reduce the computational time and the required memory during the sti ness matrix construction. We have applied our algorithm to a set of complicated geometries, including the Lake Superior map, and a three-component air foil with sharp features.

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