of Three-Dimensional Domains

** Daniel Rypl and Zdenek Bittnar
Department of Structural Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic**

The present paper deals with the discretization of 3D domains into
tetrahedral boundary conforming meshes using a hybrid approach based on the
combination of the Delaunay triangulation (DT) with the advancing front
technique (AFT). The conformity of the
resulting mesh with the initial triangulation of the domain boundary
is ensured a priori thus the boundary recovery postprocessing step is eliminated.
The constrained DT of the boundary points is obtained using modified
Watson's point insertion algorithm. However, the actual
appearance of boundary faces in the final triangulation is
achieved by proper ordering of point insertion. This is driven by the
dependency, represented in the form of oriented graph, of the
violation of the empty-sphere property of all boundary faces. The
cyclic dependencies (closed loops in the graph) are eliminated via the nodal
perturbations, classification of some of the violations as safe and (as
the last resort) by forming a new tetrahedron using the AFT. Once all the
cyclic dependencies are eliminated, the point insertion process
controlled by the dependency graph is started and the constrained DT of
the boundary points is built. In the next phase, additional points
are inserted in the interior of the domain, while preserving the boundary
constraints, to make the elements of appropriate size with aspect ratio
close to one. The resulting mesh is then subjected to optimization in
terms of the combination of Laplacian smoothing and topological
transformations, in order to remove the potential slivers and to
improve the overall mesh quality.

- Introduction
- Constrained Delaunay Triangulation
- A Priori Boundary Recovery
- Domain Discretization
- Discussion
- Conclusions
- Acknowledgments
- Bibliography
- Figures

*Daniel Rypl
2005-11-06*