17th GAMM-Seminar Leipzig on
Construction of Grid Generation Algorithms

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  17th GAMM-Seminar
February, 1st-3rd, 2001
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  Abstract Mark S. Shephard, Thu, 10.00-10.50 Previous Contents Next  
  Automatic Mesh Generation for Geometry-Based Simulation
Mark S. Shephard (Rensselaer Polytechnic Institute, Troy, USA)

This presentation will discuss aspects of a toolkit for the automatic generation and modification of meshes over general three-dimensional domains given domain definitions in the form of toleranced non-manifold geometric models. Key components of a reliable automatic mesh generator for such curved solid models are (i) topological structures to define the geometric and mesh models, (ii) an operator driven interface to interact with the solid modeler, and (iii) a proper definition of what constitutes a valid finite element mesh for curved domains. The methods to be described underlie the meshing toolkit and have supported its reliable integration with the geometric modeling kernels of SDRC's I-DEAS, PTC's Pro/Engineer and Dasault Systems CATIA CAD systems, and Spatial's ACIS and Unigraphics' Parasolid modeling kernels.

Recent development efforts have been focused on boundary layer mesh generation for general domains, dealing with curved mesh entities as needed for p-version analysis and ensuring adaptively refined meshes on curved domains improve their geometric approximation during refinement. The boundary layer mesh generation procedure is a generalized advancing layers method where key generalizations added include procedures to properly blend layers at the boundaries of faces for non-manifold models and to account for situations where faces with boundary layers overlap or come into close proximity.

The procedure for curving p-version meshes to the domain boundary, and the procedure to ensure the mesh geometric approximation of the domain improves as refinement is performed, treat the process as one of mesh correction. In most cases the correction is simply an up-date to mesh entity geometry (i.e., moving a vertex to the boundary, curving an edge or face to the boundary). However, in a number of cases this process invalidates the mesh locally. In such cases more extensive mesh corrections involving local mesh modifications or remeshing are required. An outline of the procedures used to address these mesh corrections will be given. In addition, a local cavity creation and triangulation procedure used for the most complex of mesh correction situations will be described.

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[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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