zbMATH — the first resource for mathematics

Small polyhedron reconnection for mesh improvement and its implementation based on advancing front technique. (English) Zbl 1171.74472
Summary: 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.

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
Full Text: DOI
[1] Zavattieri, Optimization strategies in unstructured mesh generation, International Journal for Numerical Methods in Engineering 39 (12) pp 2055– (1996) · Zbl 0881.76079
[2] Lo, Optimization of tetrahedral meshes based on element shape measures, Computers and Structures 63 (5) pp 951– (1997) · Zbl 0899.73525
[3] Freitag, Tetrahedral mesh improvement using swapping and smoothing, International Journal for Numerical Methods in Engineering 40 (21) pp 3979– (1997) · Zbl 0897.65075
[4] Freitag, A cost/benefit analysis of simplicial mesh improvement techniques as measured by solution efficiency, International Journal of Computational Geometry and Applications 10 (4) pp 361– (2000) · Zbl 1074.68639
[5] Sun, An efficient optimization procedure for tetrahedral meshes by chaos search algorithm, Journal of Computer Science and Technology 18 (6) pp 796– (2003) · Zbl 1083.65517
[6] Chen, Construction of an objective function for optimization-based smoothing, Engineering with Computers 20 (3) pp 184– (2004)
[7] Joe, Construction of three-dimensional Delaunay triangulations using local transformations, Computer Aided Geometric Design 8 pp 123– (1991) · Zbl 0729.65120
[8] Joe, Construction of 3-dimensional improved-quality triangulations using local transformations, SIAM Journal on Scientific Computing 16 (6) pp 1292– (1995) · Zbl 0851.65081
[9] George PL, Borouchaki H. Back to edge flips in 3 dimensions. Proceedings of the 12th International Meshing Roundtable, Sandia National Laboratories, 2003; 393-402.
[10] Liu, Optimal tetrahedralization for small polyhedron: a new local transformation strategy for 3-D mesh generation and mesh improvement, CMES: Computer Modeling in Engineering and Sciences 14 (1) pp 31– (2006)
[11] Jin, Generation of unstructured tetrahedral meshes by advancing front technique, International Journal for Numerical Methods in Engineering 36 pp 1805– (1993) · Zbl 0771.76057
[12] Kennon, Generation of computational grids using optimization, AIAA Journal 24 (7) pp 1069– (1986) · Zbl 0601.76070
[13] Zhang, An algorithm for the optimization of directionally stretched triangulations, International Journal for Numerical Methods in Engineering 37 (9) pp 1481– (1994) · Zbl 0806.76074
[14] Lo, Volume discretization into tetrahedral-II. 3D-triangulation by advancing front approach, Computers and Structures 39 (5) pp 501– (1991) · Zbl 0764.65073
[15] Liu, Automatic mesh generation of 3-D geometric models, Acta Mechanica Sinica 19 (3) pp 285– (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.