Small polyhedron reconnection for mesh improvement and its implementation based on advancing front technique.

*(English)*Zbl 1171.74472Summary: Local transformation, or topological reconnection, is one of the effective procedures for mesh improvement method, especially for three-dimensional tetrahedral mesh. The most frequently used local transformations for tetrahedral mesh are so-called elementary flips, such as 2-3 flip, 3-2 flip, 2-2 flip, and 4-4 flip. Owing to the reason that these basic transformations simply make a selection from several possible configurations within a relatively small region, the improvement of mesh quality is confined. In order to further improve the quality of mesh, the authors recently suggested a new local transformation operation, small polyhedron reconnection \((SPR)\) operation, which seeks for the optimal tetrahedralization of a polyhedron with a certain number of nodes and faces (typically composed of 20-40 tetrahedral elements).This paper is an implementation of the suggested method. The whole process to improve the mesh quality by SPR operation is presented; in addition, some strategies, similar to those used in advancing front technique, are introduced to speed up the operation. The numerical experiment shows that SPR operation is quite effective in mesh improvement and more suitable than elementary flips when combined with smoothing approach. The operation can be applied to practical problems, gaining high mesh quality with acceptable cost for computational time.

##### MSC:

74S99 | Numerical and other methods in solid mechanics |

74S05 | Finite element methods applied to problems 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 |

##### Keywords:

mesh improvement; local transformation; tetrahedral mesh; optimal tetrahedralization; small polyhedron reconnection (SPR); advancing front technique
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\textit{J. Liu} et al., Int. J. Numer. Methods Eng. 79, No. 8, 1004--1018 (2009; Zbl 1171.74472)

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