WIAS Preprint No. 1176, (2006)

Adaptive tetrahedral mesh generation by constrained Delaunay refinement


  • Si, Hang

2010 Mathematics Subject Classification

  • 65M50 65N50


  • tetrahedral mesh generation, adaptive mesh generation, constrained Delaunay, mesh refinement, mesh quality




This paper discusses the problem of refining a constrained Delaunay tetrahedralization (CDT) for adaptive numerical simulation. A simple and efficient algorithm which makes use of the classical Delaunay refinement scheme is proposed. It generates an isotropic tetrahedral mesh corresponding to a sizing function which can be either user-specified or automatically derived from the input CDT. The quality of the produced meshes is guaranteed, i.e., most output tetrahedra have their circumradius-to-shortest-edge ratios bounded except those in the neighborhood of small input angles. Good mesh conformity can be obtained for smoothly changing sizing information. The algorithm has been implemented. Various examples are provided to illustrate its theoretical aspects as well as practical performance.

Appeared in

  • Internat. J. Numer. Methods Engrg., 75 (2008) pp. 856--880.

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