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Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation. (English) Zbl 0980.74080
Summary: A method of unstructured tetrahedral 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 polynomial 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 crystal lattice arrangement 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 subdivision 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, are demonstrated with the aid of selected examples.

##### MSC:
 74S99 Numerical and other methods in solid mechanics 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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