Boundary recovery after 3D Delaunay tetrahedralization without adding extra nodes

International Journal for Numerical Methods in Engineering

Volumn 72, Issue 6, 2007, Pages 744-756

  Liu, Jianfei ^a   Chen, Bin ^a   Chen, Yongqiang ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Boundary recovery; Delaunay tetrahedralization; Local transformation; Sphere packing; SPR operation

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; MATHEMATICAL TRANSFORMATIONS;

BOUNDARY RECOVERY; DELAUNAY TETRAHEDRALIZATION; SMALL POLYHEDRON RECONNECTION OPERATION; SPHERE PACKING;

MESH GENERATION;

ALGORITHMS; BOUNDARY CONDITIONS; MATHEMATICAL TRANSFORMATIONS; MESH GENERATION;

EID: 35449001002     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2044     Document Type: Article

References (26)

1. Shewchuk JR. Constrained Delaunay tetrahedralizations and provably good boundary recovery. Proceedings of 11th International Meshing Roundtable, Ithaca, NY, U.S.A., 2002; 193-204.
2. Murphy M, Mount DM, Gable CW. A point-placement strategy for conforming Delaunay tetrahedralization. International Journal of Computational Geometry and Applications 2001; 11(6):669-682.
3. Cohen-Steiner D, Colin de Verdière È, Yvinec M. Conforming Delaunay triangulations in 3D. International Journal of Computational Geometry and Applications 2004; 28:217-233.
4. Shephard MS, Georges MK. Reliability of automatic 3-D mesh generation. Computer Methods in Applied Mechanics and Engineering 1992; 101:443-462.
5. George PL, Hecht F, Saltel E. Automatic mesh generator with specified boundary. Computer Methods in Applied Mechanics and Engineering 1991; 92:269-288.
6. Cavalcanti PR, Mello VT. 3-D constrained Delaunay triangulation: a minimalist approach. Proceedings of 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., 1999; 127-137.
7. Du Q, Wang D. Boundary recovery for three dimensional conforming Delaunay triangulation. Computer Methods in Applied Mechanics and Engineering 2004; 193:2547-2563.
8. Weatherill NP, Hassan O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constrains. International Journal for Numerical Methods in Engineering 1994; 37:2005-2039.
9. George PL, Borouchaki H, Saltel E. 'Ultimate' robustness in meshing an arbitrary polyhedron. International Journal for Numerical Methods in Engineering 2003; 58(7):1061-1089.
10. Owen S. An introduction to mesh generation algorithms. Proceedings of 12th International Meshing Roundtable. Sandia National Laboratories: Livermore, 2005.
11. Liu JF. Automatic triangulation of n-D domains. Proceedings of CAD/ Graphics, Hangzhou, China, 1991; 238-241.
12. Liu JF. Automatic mesh generation of 3-D geometric models. Acta Mechanica Sinica 2003; 19:285-288.
13. Shimada K. Physically based mesh generation: automated triangulation of surfaces and volumes via bubble packing. Ph.D. Thesis, MIT, Cambridge, MA, 1993.
14. Bern M, Eppstein D. Quadrilateral meshing by circle packing. International Journal of Computational Geometry and Applications 2000; 10(4):347-360.
15. Shimada K, Yamada A, Itoh T. Anisotropic triangulation of parametric surfaces via close packing of ellipsoids. International Journal of Computational Geometry and Applications 2000; 10(4):417-440.
16. Kim JH, Kim HG, Lee BC, Im S. Adaptive mesh generation by bubble packing method. Structural Engineering and Mechanics 2003; 15(1):135-149.
17. Li XY, Teng SH, Ungor A. Biting: advancing front meets sphere packing. International Journal for Numerical Methods in Engineering 2000; 49(1-2):61-81.
18. Chung SW, Kim SJ. A remeshing algorithm based on bubble packing method and its application to large deformation problems. Finite Elements in Analysis and Design 2003; 39(4):301-324.
19. Lo SH, Wang WX. Generation of finite element mesh with variable size over an unbounded 2D domain. Computer Methods in Applied Mechanics and Engineering 2005; 194:4668-4684.
20. Liu JF, Sun SL, Wang DC. 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 2006; 14:31-43.
21. Conraud J. Lazy constrained tetrahedralization. Proceedings of 4th International Meshing Roundtable, Albuquerque, NM, U.S.A., 1995; 55-62.
22. Quadros WR, Shimada K, Owen SJ. Skeleton-based computational method for the generation of a 3D finite element mesh sizing function. Engineering with Computers 2004; 20:249-264.
23. Ollivier-Gooch C, Boivin C. Guaranteed-quality simplical mesh generation with cell size and grading control. Engineering with Computers 2001; 17:269-286.
24. George PL, Borouchaki H. Back to edge flips in 3 dimensions. Proceedings of 12th International Meshing Roundtable, Santa Fe, NM, U.S.A., 2003; 393-402.
25. Joe B. Construction of 3-dimensional improved-quality triangulations using local transformations. SIAM Journal on Scientific Computing 1995; 16(6):1292-1307.
26. Lo SH. Optimization of tetrahedral meshes based on element shape measures. Computers and Structures 1997; 63(5):951-961.