An Approach to Refining Three-Dimensional Tetrahedral Meshes Based on Delaunay Transformations
Golias, N.A. and Tsiboukis, T.D.
International Journal for Numerical Methods in Engineering, John Wiley, Num 37, pp.793-812, 1994
A technique for refining three-dimensional tetrahedral meshes is proposed inthis paper. The proposed technique is capable of treating arbitrary unstructured tetrahedral meshes, convex or non-convex with multiple regionsresulting in high-quality constrained Delaunay triangulations. The tetrahedragenerated are of high quality (nearly equalateral). Sliver tetrahedra, whichpresent a real problem to many algorithms are not produced with the new method.The key to the generation of high quality tetrahedra is the iterative application of a set of topological transformations based on the Voronoi-Delaunay theory and a reposition of nodes technique. The computationalrequirements of the proposed technique are in linear relationship with thenumber of nodes and tetrahedra, making it ideal for direct employment in afully automatic finite element analysis system for 3-D adaptive mesh refinement.Application to some test problems is presented to show the effectiveness and applicability of the new method.
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