High quality quadrilateral surface meshing without template restrictions: A new approach based on network flow techniques

International Journal of Computational Geometry and Applications

Volumn 10, Issue 3, 2000, Pages 285-307

  Müller Hannemann, Matthias ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

B matchings; Bidirected flows; Mesh decomposition; Mesh smoothing; Non manifold surfaces; Quadrilateral surface meshes

Indexed keywords

EID: 0034377966     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195900000176     Document Type: Article

References (33)

1. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network flows, Prentice Hall, 1993.
2. N. Amenta, M. Bern, and D. Eppstein, Optimal point placement for mesh smoothing, Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, 1997, pp. 528-537.
3. R. P. Anstee, A polynomial algorithm for b-matching: An alternative approach, Information Processing Letters 24 (1987), 153-157.
4. D. Applegate and W. Cook, Solving large-scale matching problems, Network Flows and Matching, DIMACS Series in Discrete Mathematics and Theoretical Computer Science (D. S. Johnson and C. C. McGeoch, eds.), vol. 12, 1993, pp. 557-576.
5. M. O. Ball and U. Derigs, An analysis of alternative strategies for implementing matching algorithms, Networks 13 (1983), 517-549.
6. M. Bern and D. Eppstein, Mesh generation and optimal triangulation, Computing in Euclidean Geometry, 2nd Edition (D.-Z. Du and F. Hwang, eds.), World Scientific, Singapore, 1995, pp. 47-123.
7. M. Bern and P. Plassmann, Mesh generation, Handbook of Computational Geometry (J. Sack and J. Urrutia, eds.), Elsevier Science, 1997, to appear.
8. T. D. Blacker and M. B. Stephenson, Paving: A new approach to automated quadrilateral mesh generation, Int. J. Numer. Methods in Eng. 32 (1991), 811-847.
9. H. Borouchaki, P. J. Frey, and P. L. George, Unstructured triangular-quadrilateral mesh generation. Application to surface meshing, Proceedings of the 5th International Meshing Roundtable, Sandia National Laboratories, Albuquerque, USA, 1996, pp. 229-242.
10. J. R. Brauer, ed., What every engineer should know about finite element analysis, Marcel Decker Inc., 1993.
11. CPLEX Optimization Inc., Using the CPLEX callable library, version 4.0, 1995.
12. U. Derigs, Programming in networks and graphs, Lecture Notes in Economics and Mathematical Systems, vol. 300, Springer-Verlag, Berlin, 1988.
13. J. Edmonds, An introduction to matching, Lecture notes, University of Michigan, Ann Arbor, 1967.
14. L. Freitag, M. Jones, and P. Plassmann, An efficient parallel algorithm for mesh smoothing, Proceedings of the 4th International Meshing Roundtable, Sandia National Laboratories, Albuquerque, USA, 1995, pp. 47-58.
15. L. Freitag, C. Ollivier-Gooch, Tetrahedral mesh improvement using swapping and smoothing, Int. J. Numer. Methods in Eng. 40 (1997), 3979-4002.
16. L. Freitag, C. Ollivier-Gooch, A cost/benefit analysis of simplicial mesh improvement techniques as measured by solution efficiency, Technical report ANL/MSC-P722-6598, Argonne National Laboratory, 1998.
17. A. M. H. Gerards, Matching, (M. O. Ball et al., ed.), Handbooks in Operations Research and Management Science, vol. 7, North-Holland, 1995, pp. 135-224.
18. K. Ho-Le, Finite element mesh generation methods: a review and classification, Computer-Aided Design 20 (1988), 27-38.
19. B. Joe, Quadrilateral mesh generation in polygonal regions, Computer-Aided Design 27 (1995), 209-222.
20. S. A. Mitchell, Choosing corners of rectangles for mapped meshing, Proceedings of the 13th Annual ACM Symposium on Computational Geometry, Nice, France, ACM, 1997, pp. 87-93.
21. S. A. Mitchell, High fidelity interval assignment, Proceedings of the 6th International Meshing Roundtable, Park City, Utah, Sandia National Laboratories, Albuquerque, USA, 1997, pp. 33-44.
22. R. H. Möhring and M. Müller-Hannemann, Complexity and modeling aspects of mesh refinement into quadrilaterals, Proceedings of the 8th Annual International Symposium on Algorithms and Computation, ISAAC'97, Singapore, Lecture Notes in Computer Science 1350, Springer-Verlag, 1997, pp. 263-273, journal version to appear in Algorithmica.
23. R. H. Möhring and M. Müller-Hannemann, Complexity and modeling aspects of mesh refinement into quadrilaterals, Proceedings of the 8th Annual International Symposium on Algorithms and Computation, ISAAC'97, Singapore, Lecture Notes in Computer Science 1350, Springer-Verlag, 1997, pp. 263-273, journal version to appear in Algorithmica.
24. R. H. Möhring, M. Müller-Hannemann, and K. Weihe, Mesh refinement via bidirected flows: Modeling, complexity, and computational results, Journal of the ACM 44 (1997), 395-426.
25. M. Müller-Hannemann, On the generation of finite element meshes with graph theoretical methods, Diploma thesis, Technische Universität Berlin, 1994.
26. M. Müller-Hannemann and K. Weihe, Minimum strictly convex quadrangulations of convex polygons, Proceedings of the 13th Annual ACM Symposium on Computational Geometry, Nice, France, ACM, 1997, pp. 193-202.
27. W. R. Pulleyblank, Faces of matching polyhedra, Ph.D. thesis, Faculty of Mathematics, University of Waterloo, 1973.
28. M. Rees, Combining quadrilateral and triangular meshing using the advancing front approach, Proceedings of the 6th International Meshing Roundtable, Park City, Utah, Sandia National Laboratories, Albuquerque, USA, 1997, pp. 337-348.
29. T. K. H. Tam and C. G. Armstrong, Finite element mesh control by integer programming, Int. J. Numer. Methods in Eng. 36 (1993), 2581-2605.
30. D. R. White and P. Kinney, Redesign of the paving algorithm: Robustness enhancements through element by element meshing, Proceedings of the 6th International Meshing Roundtable, Park City, Utah, Sandia National Laboratories, Albuquerque, USA, 1997, pp. 323-335.
31. D. R. White, L. Mingwu, S. E. Benzley, and G. D. Sjaardema, Automated hexahedral mesh generation by virtual decomposition, Proceedings of the 4th International Meshing Roundtable, Sandia National Laboratories, Albuquerque, USA, 1995, pp. 165-176.
32. J. Z. Zhu, O. C. Zienkiewicz, E. Hinton, and J. Wu, A new approach to the development of automatic quadrilateral mesh generation, Int. J. Numer. Methods in Eng. 32 (1991), 849-866.
33. O. C. Zienkiewicz and R. L. Taylor, The finite element method, McGraw Hill, London, 1989.