Mesh optimization based on the centroidal voronoi tessellation

International Journal of Numerical Analysis and Modeling

Volumn 2, Issue , 2005, Pages 100-113

  Wang, Desheng ^a   Du, Qiang ^b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Centroidal voronoi tessellation; Delaunay triangulation; Mesh optimization; Mesh smoothing; Optimal tessellations; Voronoi tessellations

Indexed keywords

EID: 60949084667     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. R. Lohner and P. Parikh, Generation of three-dimensional grids by the advancing-front method. Int.J.Num.Method.Fluids 1988; 8: 1135-1149.
2. D. Marcum, and N. Weatherill, Unstructured Grid Generation using iterative point insertion and local reconnection. AIAA Journal 1995; 33: 1619-1625.
3. MS. Shephard and MK. Georges, Automatic three-dimensional mesh generation technique by the finite element octree technique. Int. J. Num. Method Engrg. 1991; 32: 709-749.
4. N. Weatherill and O. Hassan, Efficient three dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints, Int. J. Num. Method Engrg. 1994; 37: 2005-2039.
5. H. Borouchaki and SH. Lo, Fast Delaunay triangulation in three dimensions. Computer Methods in Applied Mechanics and Engineering 1995; 128: 153-167.
6. Q. Du, V. Faber and M. Gunzburger; Centroidal Voronoi tessellations, Applications and algorithms, SIAM Review, (1999), 41: pp.637-676.
7. Q. Du and M. Gunzburger, Grid Generation and Optimization Based on Centroidal Voronoi Tessellations, Applied and Computational Mathematics, 133 (2002), pp.591-607.
8. Q. Du, M. Gunzburger, and L. Ju, Meshfree, probabilistic determination of point sets and support regions for meshless computing, Comput. Methods Appl. Mech. Engrg., 191 (2002), pp 1349-1366.
9. Q. Du, M. Gunzburger, L. Ju and X. Wang, Centroidal Voronoi tessellation algorithms for image compression and segmentation, to appear in J. Math Imaging and Vision, 2006.
10. Q. Du, M. Gunzburger and L. Ju, Constrained Centroidal Voronoi Tessellations on General Surfaces, SIAM J. Sci. Comp, 24, pp.1499-1506, 2003.
11. Q. Du, M. Gunzburger, L. Ju, Probablistic methods for centroidal Voronoi tessellations and their parallel implementations, Journal of Parallel Computing, 28, pp.1477-1500, 2002.
12. Q. Du, and D. Wang, Tetrahedral mesh generation and optimization based on Centroidal Voronoi Tessellations. Int. J. Num. Method Engrg., 56, pp.1355-1373, 2002
13. Q. Du, and D. Wang, Boundary recovery for three dimensional conforming Delaunay triangulation. Computer Methods in Applied Mechanics and Engineering, 193,pp.2547-2563, 2004.
14. Q. Du, and D. Wang, Constrained boundary recovery for three dimensional Delaunay triangulation, Int. J. Num. Method Engrg., 2004, 61: 1471-1500.
15. Q. Du and D. Wang, Anisotropic Centroidal Voronoi Tessellations and their applications,SIAM SIAM J. Sci Comp., 26, pp.737-761, 2005.
16. Q. Du and D. Wang, On the Optimal Centroidal Voronoi Tessellation and the Gersho’s conjecture in the three dimensional space, Computers and Mathematics with Applications, 49, pp.1355-1373, 2005.
17. Q. Du and D. Wang, Approximate Constrained Centroidal Voronoi Tessellation on Surfaces and the Application to Surface Mesh Optimization, preprint, 2005.
18. Q. Du, and Desheng Wang, New progress in robust and quality Delaunay mesh generation, to appear in J. Computational Applied Mathematics, 2006.
19. Q. Du, M. Emelianenko and L. Ju, Convergence Properties of the Lloyd Algorithm for Computing the Centroidal Voronoi Tessellations, to appear in SIAM J. Numer. Anal., 2006.
20. Q. Du and M. Emelianenko, Uniform convergence of a nonlinear optimization-based multilevel quantization Scheme, preprint, 2005.
21. Q. Du and M. Emelianenko, Acceleration schemes for computing centroidal Voronoi tessellations, to appear in special issue of Numerical Linear Algebra with Applications, 2006
22. Q. Du, Z. Huang and Desheng Wang, Mesh and Solver Co-adaptation in Finite Element Methods for Anisotropic Problems, Numerical Methods for Differential Equations, 21, pp.859-874, 2005.
23. T. Kanungo, D. Mount, N. Netanyahu, C. Piatko, R. Silverman and A. Wu, An efficient k-means clustering algorithm: Analysis and implementation, IEEE Trans. Pattern Anal. Machl Intel. 24, (2002), pp.881-892.
24. D. Newman, The Hexagon theorem, IEEE Trans. Infor. theory, 28, 1982, pp.137-139.
25. E.S. Barnes and N.J.A. Sloane, The optimal Lattice quantizer in three dimensions, SIAM J. Algebraic Discrete Methods, 4, 30-41, 1983.
26. A. Gersho, Asymptotically optimal block quantization, IEEE Trans. Inform. Theory, 25, 1979, pp.373-380.
27. R. M. Gray and D. L. Neuhoff, Quantization, IEEE Trans. Inform. Theory, 44 (1998), 2325-2383.
28. S. Lloyd, Least square quantization in PCM, IEEE Trans. Infor. theory, 28, 1982, pp.129-137.
29. L. Freitag, P. Knupp, T. Munson, and S. Shontz. A Comparison of Optimization Software for Mesh Shape Quality Improvement Problems, p29-40, Proceedings of the 11th International Meshing Roundtable, Ithaca NY, 2002.
30. L. Freitag, P. Knupp, Tetrahedral mesh improvement via optimization of the element condition number, Int. J. Numer. Meth. Engr., 53:1377-1391, 2002.
31. P. Knupp, Matrix Norms and the Condition Number: A general framework to improvemesh quality via node-movement, 8th International Meshing RoundTable, Lake Tahoe, pp13-22, 1999.
32. L. Freitag and P. Knupp, Tetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number, 8th International Meshing RoundTable, Lake Tahoe, pp 247-258, 1999.
33. L. Freitag and C. Olliver-Gooch, Tetrahedral mesh improvement using swapping and smoothing. Int. J. Num. Method. Engrg. 1997; 40: 3979-4002.
34. EA. Dari and GC. Buscaglia, Mesh Optimization: how to obtain good unstructured 3-D finite element meshes with not-so-good mesh generators. Structural Optimization 1994; 8: 181-188.
35. PL. George, Delaunay Triangulation and Meshing: Application to Finite Elements. Editions HERMES, Paris, 1998.
36. H. Borouchaki and P. Frey, Adaptive Triangular-Quadrilateral Mesh Generation. Int. J. Num. Meth. Engrg. 1998; 41: 915-934.
37. N. Madsen, Divergence preserving discrete surface integral methods for Maxwell’s equations using nonorthogonal unstructured grids, J. Computational Physics, 1995;119: 35-45.
38. I. Sazonov, D. Wang, O. Hassan, K. Morgan and N. Weatherill, A stitching method for unstructured mesh generation for co-volume solution techniques, Computer Methods in Applied Mechanics and Engineering, 2005, in press.
39. A. G. Churbanov, A unified algorithm to predict compressible and imcompressible flows. In CD-Rom Proc. ECCOMAS Computational Fluid Dynamics Conf., Swansea, Wales, 2001.
40. T. D. Fawcett, Creating and validating heterogeneous tetrahedral finite element models of the femur from Computed Tomography (CT) images, Sept. 2004, Master thesis, Civil and Computational Engineering Centre, University of Wales Swansea.
41. C. A. Pridham(Bang)Hons, Tetrahedral finite element (FE) meshes to model femoral fractures generated from CT scans taken from the Visible Human Project.Sept. 2004, Master thesis, Civil and Computational Engineering Centre,University of Wales Swansea.
42. H. Edelsbrunner and D. Guoy, Sink Insertion for Mesh Improvement. International Journal of Foundations of Computer Science, 2002, 13: 223-242