Adaptive and quality quadrilateral/hexahedral meshing from volumetric data

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 9-12, 2006, Pages 942-960

  Zhang, Yongjie ^a   Bajaj, Chandrajit ^a  

^a University of Texas at Austin   (United States)

Author keywords

Mesh adaptivity; Mesh quality; Quadrilateral hexahedral mesh; Topology preservation

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; FINITE ELEMENT METHOD; TOPOLOGY;

HEXAHEDRAL MESH; MESH ADAPTIVITY; MESH QUALITY; QUADRILATERAL MESH; TOPOLOGY PRESERVATION;

COMPUTER SIMULATION;

MATHEMATICAL METHOD;

EID: 28444442292     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.02.016     Document Type: Article

References (40)

1. Cubit mesh generation toolkit. Available from: .
2. P. Baehmann S. Wittchen M. Shephard K. Grice M. Yerry Robust geometrically based, automatic two-dimensional mesh generation Int. J. Numer. Methods Engrg. 24 1987 1043-1078
3. C. Bajaj J. Warren G. Xu A subdivision scheme for hexahedral meshes Visual Comput. 18 5-6 2002 343-356
4. T. Blacker R. Myers Seams and wedges in plastering: A 3d hexahedral mesh generation algorithm Engrg. Comput. 2 1993 83-93
5. T. Blacker M. Stephenson Paving: A new approach to automated quadrilateral mesh generation Int. J. Numer. Methods Engrg. 32 1991 811-847
6. S. Canann, Plastering and optismoothing: New approaches to automated, 3d hexahedral mesh generation and mesh smoothing. Ph.D. Dissertation, Brigham Young University, Provo, UT, 1991.
7. S. Canann, J. Tristano, M. Staten, An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral and quad-dominant meshes, in: 7th International Meshing Roundtable, 1998, pp. 479-494.
8. C. Charalambous A. Conn An efficient method to solve the minimax problem directly SIAM J. Numer. Anal. 15 1 1978 162-187
9. W.A. Cook W.R. Oakes Mapping methods for generating three-dimensional meshes Comput. Mech. Engrg. 1982 67-72
10. David Eppstein, Linear complexity hexahedral mesh generation, in: Symposium on Computational Geometry, 1996, pp. 58-67.
11. D. Field Laplacian smoothing and Delaunay triangulations Commun. Appl. Numer. Methods 4 1988 709-712
12. L. Freitag, On combining Laplacian and optimization-based mesh smoothing techniques, Trends in Unstructured Mesh Generation, AMD-Vol. 220, 1997, pp. 37-43.
13. L. Freitag C. Ollivier-Gooch Tetrahedral mesh improvement using swapping and smoothing Int. J. Numer. Methods Engrg. 40 1997 3979-4002
14. M. Garland, P. Heckbert, Simplifying surfaces with color and texture using quadric error metrics, in: IEEE Visualization, 1998, pp. 263-270.
15. T. Ju, F. Losasso, S. Schaefer, J. Warren, Dual contouring of Hermite data, in: Proceedings of SIGGRAPH, 2002, pp. 339-346.
16. P. Kinney, Cleanup: Improving quadrilateral finite element meshes, in: 6th International Meshing Roundtable, 1997, pp. 437-447.
17. P. Knupp Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part I: A framework for surface mesh optimization Int. J. Numer. Methods Engrg. 48 2000 401-420
18. P. Knupp Achieving finite element mesh quality via optimization of the Jacobian matrix norm and associated quantities. Part II: A framework for volume mesh optimization and the condition number of the Jacobian matrix Int. J. Numer. Methods Engrg. 48 2000 1165-1185
19. C. Kober, M. Matthias, Hexahedral mesh generation for the simulation of the human mandible, in: 9th International Meshing Roundtable, 2000, pp. 423-434.
20. C. Lee S. Lo A new scheme for the generation of a graded quadrilateral mesh Comput. Struct. 52 5 1994 847-857
21. S. Mitchell, T. Tautges, Pillowing doublets: Refining a mesh to ensure that faces share at most one edge, in: 4th International Meshing Roundtable, 1995, pp. 231-240.
22. A. Oddy, J. Goldak, M. McDill, M. Bibby, A distortion metric for isoparametric finite elements, Transactions of CSME, No. 38-CSME-32, Accession No. 2161, 1988.
23. S. Owen, A survey of unstructured mesh generation technology, in: 7th International Meshing Roundtable, 1998, pp. 26-28.
24. M. Price C. Armstrong Hexahedral mesh generation by medial surface subdivision: Part I Int. J. Numer. Methods Engrg. 38 19 1995 3335-3359
25. M. Price C. Armstrong Hexahedral mesh generation by medial surface subdivision: Part II Int. J. Numer. Methods Engrg. 40 1997 111-136
26. R. Schneiders A grid-based algorithm for the generation of hexahedral element meshes Engrg. Comput. 12 1996 168-177
27. R. Schneiders, Refining quadrilateral and hexahedral element meshes, in: 5th International Conference on Grid Generation in Computational Field Simulations, 1996, pp. 679-688.
28. R. Schneiders, An algorithm for the generation of hexahedral element meshes based on an octree technique, in: 6th International Meshing Roundtable, 1997, pp. 195-196.
29. R. Schneiders, R. Schindler, F. Weiler, Octree-based generation of hexahedral element meshes, in: 5th International Meshing Roundtable, 1996, pp. 205-216.
30. Y. Song Y. Zhang C.L. Bajaj N.A. Baker Continuum diffusion reaction rate calculations of wild type and mutant mouse acetylcholinesterase: adaptive finite element analysis Biophys. J. 87 3 2004 1558-1566
31. Y. Song Y. Zhang T. Shen C.L. Bajaj J.A. McCammon N.A. Baker Finite element solution of the steady-state Smoluchowski equation for rate constant calculations Biophys. J. 86 4 2004 2017-2029
32. M. Staten, S. Canann, Post refinement element shape improvement for quadrilateral meshes, Trends in Unstructured Mesh Generation, AMD-Vol. 220, 1997, pp. 9-16.
33. J. Talbert A. Parkinson Development of an automatic, two dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definitions Int. J. Numer. Methods Engrg. 29 1991 1551-1567
34. T. Tautges T. Blacker S. Mitchell The whisker-weaving algorithm: A connectivity based method for constructing all-hexahedral finite element meshes Int. J. Numer. Methods Engrg. 39 1996 3327-3349
35. S.-H. Teng C.W. Wong Unstructured mesh generation: Theory, practice, perspectives Int. J. Comput. Geometry Appl. 10 3 2000 227-266
36. F. Weiler, R. Schindler, R. schneiders, Automatic geometry-adaptive generation of quadrilateral and hexahedral element meshes for the FEM, Numerical Grid Generation in Computational Field Simulations, 1996, pp. 689-697.
37. Y. Zhang, C. Bajaj, Adaptive and quality quadrilateral/hexahedral meshing from volumetric data, in: 13th International Meshing Roundtable, 2004, pp. 365-376.
38. Y. Zhang, C. Bajaj, B.-S. Sohn, Adaptive and quality 3d meshing from imaging data, in: ACM Symposium on Solid Modeling and Applications, 2003, pp. 286-291.
39. Y. Zhang, C. Bajaj, B.-S. Sohn, 3D finite element meshing from imaging data, Comput. Methods Appl. Mech. Engrg., in press, doi:10.1016/ j.cma.2004.11.026.
40. J. Zhu O. Zienkiewicz E. Hinton J. Wu A new approach to the development of automatic quadrilateral mesh generation Int. J. Numer. Methods Engrg. 32 1991 849-866