Automated Hexahedral Mesh Generation by Generalized Multiple Source to Multiple Target Sweeping

2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999

MESHING
RESEARCH
CORNER

Mingwu Lai, Steven Benzley
Civil and Environmental Engineering Department, Brigham Young University, Provo UT 84602
seb@byu.edu

David White
Parallel Computing Sciences Department, Sandia National Laboratories, Albuquerque, NM 87185
drwhite@sandia.gov

Abstract
Traditional sweeping techniques create all hexahedral finite element meshes by projecting an existing single surface mesh along a specified trajectory to a specified single target surface. This technique has proven to be one of the most efficient and robust methods for generating all hexahedral meshes on the subset of volumes that are defined by a source and target surfaces linked by a continuous sidewall. This paper presents an extension to this traditional sweeping technique by accommodating multiple unconnected source and target surfaces.

The new algorithm is based on the extensive use of Boolean operations to define segments of target surfaces that must be imprinted on related source surfaces. Within the algorithm the source, target, and linking surfaces are first identified. Next the linking surfaces are all meshed with either a mapping or submapping procedure. This linking surface mesh is then used to classify all source and target surfaces with an identifying layer. The source surfaces are then imprinted with segments of their related target surfaces. This imprinting process is the crucial component of the algorithm. Our complete paper specifies the four basic conditions that lead to proper imprint operations. After the imprinting operations are completed, some or all of the source surfaces may have been redefined with additional internal (i.e. imprinted) edges. These source surfaces are now easily meshed with a paving technique.

With the source surfaces meshed, the sweeping process can commence. This process begins at the uppermost source surface(s). When target surfaces are encountered, the nodes are divided into two groups, one group being the nodes that will lie on the target surface and the other group consisting of the remaining nodes that will continue in the sweep direction until another target in encountered. When all targets have been reached, the process is complete.

The major features of this process include 1) the generation of all hexahedral finite elements on solids that consist of multiple source and target surfaces that allow single axis sweeping, 2) the use of Boolean operations to accommodate a virtual decomposition of the body, and 3) the maintenance of the original mathematical representation of the solid. Numerous examples of meshed objects are provided in the complete paper to show the versatility of technique.