Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation
A method of unstructured technical mesh generation for general three-dimensional domains is presented. A conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology. The geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation. A preliminary surface mesh is generated by an advancing-front method, with the nodes inserted by hard-sphere packing in physical space in accordance with a prescribed mesh density. Interior nodes are inserted in a face-centered-cubic (FCC) crystal lattice arrangements coupled to octree spatial subdivision, with the local lattice parameter determined by a prespecified nodal density function. Prior to triangulation of the volume, the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume Delaunay triangulation. A joint Delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing-front approach. The resulting mesh is finally improved upon by the application of local transformations. The overall time complexity of the mesher is O(N log N). The robustness and versatility of the approach, as well as the good quality of the resulting meshes, is demostrated with the aid of selected examples.
© 2000 Elsevier. Available online 17 July 2000. The support of the Army Research Office through contract DAAH04-96-1-0056, and of the Sandia National Laboratories through contract DE-AC04-76DP00789, is gratefully acknowledged. We are grateful to Joe Jung, of the Sandia National Laboratories for helpful discussions and for providing the surface triangulations of the examples shown in Figs. 22 and 23.