Automatic Scheme Selection for Toolkit Hex Meshing Page: 4 of 33
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The finite element method is used to simulate a wide variety of physical phenomena, for example heat transfer, structural
mechanics, and computational fluid dynamics. In recent years, mesh generation has emerged as one of the major bottlenecks in
the simulation process. Although a high degree of automation is available in tetrahedral mesh generators, hexahedral mesh
generators still require a great deal of user intervention. Since it is widely believed that hexahedral meshes are more accurate and
more robust for some types of finite element analysis, especially in the non-linear regime, these types of meshes are more
There has been a great deal of research into automated, all-hexahedral meshing algorithms, but as yet no algorithm has
been found with the key characteristics of high robustness, high mesh quality and low element count. Therefore, current
hexahedral mesh generation techniques rely on a set of simpler tools, which when combined with geometry decomposition leads
to an adequate mesh generation process. The meshing algorithms in these tools include mapping/submapping, primitive
templates, and sweeping or extrusion. Of these, sweeping tends to be the workhorse algorithm, usually accounting for at
least 50% of most meshing applications.
The sweeping algorithm involves extruding a set of quadrilaterals into a third dimension, producing a hexahedral mesh. The
cross-section of the geometry being meshed can vary along the sweep direction, and the number of quadrilaterals in the set being
swept can vary as well. Figure 1 shows several sweepable geometries. Many of the commercial mesh generation software
packages currently include some form of sweeping algorithmt8], and varieties of this algorithm are reported elsewhere in the
While sweeping is a widely used algorithm, it is not very automated. Before a volume can be "swept", the algorithm must be
provided with input about which surface meshes are being swept along which side surfaces, and for how far. In practice, the
process of determining and specifying these source/target surfaces is user-intensive and error prone. In order to increase the level
of automation in all-hexahedral meshing, an automatic method for determining sweep directions and source/target surfaces is
The detection of swept features has been studied in the feature recognition community for some time. However, the
resulting algorithms are usually geometry-based, relying on arrangements such as parallel surfaces for detecting the features.
These arrangements represent geometric constraints placed on extruded volumes that that are determined by the application, for
example solids to be manufactured by machining.
This paper describes a new algorithm for detecting extruded or sweepable geometries. This algorithm is based on topological and
local geometric criteria, and is more robust than feature recognition-based algorithms. This algorithm has been implemented in
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TAUTGES,TIMOTHY J. & WHITE,DAVID R. Automatic Scheme Selection for Toolkit Hex Meshing, article, September 27, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc620086/m1/4/: accessed March 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.