Tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing-front-Delaunay triangulation

Computer Methods in Applied Mechanics and Engineering

Volumn 187, Issue 3-4, 2000, Pages 543-569

  Radovitzky, R ^a   Ortiz, M ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; CRYSTAL LATTICES; FINITE ELEMENT METHOD; INTERPOLATION; LATTICE CONSTANTS; MATHEMATICAL MODELS; POLYNOMIALS;

CRYSTAL LATTICES ARRANGEMENTS; DELAUNAY TRIANGULATION; FACE CENTERED CUBIC; NODAL DENSITY FUNCTION; SURFACE MESH; TETRAHEDRAL MESH GENERATION;

COMPUTER SIMULATION;

EID: 0034229154     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00339-4     Document Type: Article

References (65)

1. Amenta N., Bern M. Surface reconstruction by Voronoi filtering. Discret. Comput. Geom. 22:(4):1999;481-504.
2. Baker T.J. Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation. Engrg. Comput. 5:1989;161-175.
3. Beall M.W., Shephard M.S. A general topology-based mesh data structure. Int. J. Numer. Methods Engrg. 40:1997;1573-1596.
4. Borouchaki H., Lo S.H. Fast Delaunay triangulation in three dimensions. Comput. Methods Appl. Mech. Engrg. 128:1995;153-167.
5. Bowyer A. Computing Dirichlet tesslations. Comput. J. 24:(2):1981;162-166.
6. Buratynski E.G. Fully automatic three-dimensional mesh generator for complex geometries. Int. J. Numer. Methods Engrg. 30:1990;931-952.
7. Camacho G.T., Ortiz M. Adaptive Lagrangian modelling of ballistic penetration of metallic targets. Comput. Methods Appl. Mech. Engrg. 142:1997;269-301.
8. Cavendish J.C., Field D.A., Frey W.H. An approach to automatic three-dimensional finite element mesh generation. Int. J. Numer. Methods Engrg. 21:1985;329-347.
9. Chan C.T., Anastasiou K. An automatic tetrahedral mesh generation scheme by the advancing-front method. Commun. Appl. Numer. Methods. 13:1997;33-46.
10. Chazelle B., et al. Application challenges to computational geometry: Impact task force report. Technical Report TR-521-96. 1996;Princeton University.
11. Chew P. Constrained Delaunay Triangulations. 1987;ACM, New York.
12. Ciarlet P.G. Numerical Analysis of the Finite Element Method. 1976;Les Presses de L'Universite de Montreal, Quebec, Canada.
13. Dari E.A. Contribuciones a la triangulaci'on autom'atica de dominios tridimensionales. Ph.D. thesis. 1994;Instituto Balseiro, Bariloche, Argentina.
14. Delaunay B. Sur la sphere vide. Classe Sci. Mat. Nat. Vol.VII Bull. Acad. Sci. USSR. VIII:1934;793-800.
15. Dyn N., Levin D. A butterfly subdivision scheme for surface interpolation with tension control. AMC Trans. Graphics. 9:1990;160-169.
16. Farestam S., Simpson R.B. A framework for advancing-front techniques of finite element mesh generation. BIT. 35:1995;210-232.
17. Fleischmann P., Selberherr S. Three-dimensional Delaunay mesh generator using a modified advancing-front approach. Proceeding of the Sixth International Meshing Roundtable. 1997;267-276 Sandia National Laboratories, Park City, Utah.
18. Freitag L., Ollivier-Gooch C. A comparison of tetrahedral mesh improvement techniques. Proceedings of the Fifth International Meshing Roundtable. October 1996;87-100 Sandia National Laboratories, Pittsburgh, Pennsylvania.
19. George P.L., Hermeline F. Delaunay's mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra. Int. J. Numer. Methods Engrg. 33:1992;975-995.
20. Guillemin V., Pollack A. Differential Topology. 1974;Prentice-Hall, Englewood Cliffs, NJ.
21. Hammond C. Introduction to crystallography. 1990;Oxford University Press, Oxford.
22. Hazlewood C. Approximating constrained tetrahedrizations. Comput. Aided Geometric Design. 10:1993;67-87.
23. Hoffmann C.M. Geometric and Solid Modeling. 1989;Morgan Kaufmann Publishers, San Mateo, California.
24. Hull D., Bacon D.J. third edition Introduction to Dislocations, International Series on Materials Science and Technology. 37:1984;Elsevier, Amsterdam.
25. Jin H., Tanner R.I. Generation of unstructured tetrahedral meshes by advancing-front technique. Int. J. Numer. Methods Engrg. 36:1993;1805-1823.
26. Joe B. Three-dimensional triangulations from local transformations. SIAM J. Scientific Statist. Comput. 10:1989;718-741.
27. Joe B. Construction of three-dimensional improved-quality triangulations using local transformations. SIAM J. Scientific Comput. 16:(6):1995;1292-1307.
28. Lau T.S., Lo S.H. Finite element mesh generation over analytical curved surfaces. Comput. Struct. 59:(2):1996;301-309.
29. Liu A., Joe B. Relation between tetrahedron shape measures. BIT. 34:1994;268-287.
30. Lo S.H. Finite element mesh generation over curved surfaces. Comput. Struct. 29:(5):1988;731-742.
31. Lo S.H. Volume discretization into tetrahedra - II. 3D triangulation by advancing-front approach. Comput. Struct. 39:(5):1991;501-511.
32. Lo S.H. Volume discretization into tetrahedra - I. Verification and orientation of boundary surfaces. Comput. Struct. 39:(5):1991;493-500.
33. Lo S.H. Automatic mesh generation over intersecting surfaces. J. Numer. Methods Engrg. 38:1995;943-954.
34. Löhner R. Some useful data structures for the generation of unstructured grids. Commun. Appl. Numer. Methods. 4:1988;123-135.
35. Löhner R. Finite elements in CFD: grid generation, adaptivity and parallelization. AGARD Report. vol. 787:1992;. (Chapter 8).
36. Löhner R. Regridding surface triangulations. J. Comput. Phys. 126:1996;1-10.
37. Löhner R., Parikh P. Generation of three-dimensional unstructure grids by the advancing-front method. Int. J. Numer. Methods Fluids. 8:1988;1135-1149.
38. Mantyla M. An Introduction to Solid Modeling. 1988;Computer Science Press, Rockville, Maryland.
39. Mavriplis D.J. An advancing-front Delaunay triangulation algorithm designed for robustness, paper 93-0671. AIAA. 1993.
40. Mavriplis D.J. Unstructured mesh generation and adaptivity, Technical Report 95-26. NASA. 1995.
41. Merriam M.L. An efficient advancing-front algorithm for Delaunay triangulation, paper 91-0792. AIAA. 1991.
42. Möller P., Hansbo P. An advancing-front mesh generation in three dimensions. Int. J. Numer. Methods Engrg. 38:1995;3551-3569.
43. Ortiz M., Pandolfi A. Finite-deformation cohesive elements for three-dimensional crack-propagation. Int. J. Numer. Meth. Eng. 44:(9):1999;1267-1282.
44. Pandolfi A., Ortiz M. Solid modeling aspects of three-dimensional fragmentation. Eng. Comput. 14:(4):1998;287-308.
45. Parthasarathy V.N., Graichen C.M., Hathaway A.F. A comparison of tetrahedron quality measures, Finite Elements and Design. 15:1993;225-261.
46. Peraire J., Peiro J., Formaggia L., Morgan K., Zienkiewicz O.C. Finite element Euler computations in three dimensions. Int. J. Numer. Methods Engrg. 26:1988;2135-2159.
47. Peraire J., Vahdati M., Morgan K., Zienkiewicz O.C. Adaptive remeshing for compressible flow computations. J. Comput. Phys. 72:1987;449-466.
48. Perucchio R., Saxena M., Kela A. Automatic mesh generations from solid models based on recursive spatial decompositions. Int. J. Numer. Methods Engrg. 28:1989;2469-2501.
49. Radovitzky R., Ortiz M. Lagrangian finite element analysis of Newtonian fluid flows. Int. J. Numer. Methods Engrg. 43:1998;607-619.
50. Radovitzky R., Ortiz M. Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Comput. Methods Appl. Mech. Engrg. 172:1999;203-240.
51. d, Discrete & Computational Geometry. 12:1994;189-202.
52. Requicha A.A.G. Representations for rigid solids: Theory methods and systems. Comput. Surveys. 12:1980;437-465.
53. Rypl D., Krysl P. Triangulation of 3d surfaces. Engrg. Comput. 13:(2):1997;87-98.
54. Samet H. The Design and Analysis of Spatial Data Structures. 1990;Addison-Wesley, New York.
55. Schroeder W.J., Shephard M.S. Geometry-based fully automatic mesh generation and the Delaunay triangulation. Int. J. Numer Methods Engrg. 26:1988;2503-2515.
56. Schroeder W.J., Shephard M.S. A combined octree/Delaunay method for fully automatic 3-d mesh generation. Int. J. Numer. Methods Engrg. 29:1990;37-55.
57. Shephard M.S., Georges M.K. Automatic three-dimensional mesh generation by the finite octree technique. Int. J. Numer. Methods Engrg. 32:(4):1991;709-749.
58. Standish T.A. Data Structures, Algorithms and Software Principles in C. 1995;Addison-Wesley, New York.
59. Tanemura M., Ogawa T., Ogita N. A new algorithm for three-dimensional Voronoi tesselation. J. Comput. Phys. 51:(2):1983;191-207.
60. Watson D.F. Computing the n-dimensional Delaunay tesslation with application to Voronoi polytopes. Comput. J. 24:(2):1981;167-172.
61. Weatherill N.P., Hassan O. Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints. Int. J. Numer. Methods Engrg. 37:1994;2005-2039.
62. Weatherill N.P. The reconstruction of boundary contours and surfaces in arbitrary unstructured triangular and tetrahedral grids. Engrg. Comput. 13:(8):1996;66-81.
63. Wright J.P., Jack A.G. Aspects of three-dimensional constrained Delaunay meshing. Int. J. Numer. Methods Engrg. 37:1994;1841-1861.
64. Yerry M.A., Shephard M.S. Automatic mesh generation for three-dimensional solids. Comput. Struct. 20:1985;211-223.
65. Zorin D., Schroeder P., Sweldens W. Interpolating subdivision for meshes with arbitrary topology. SIGGRAPH '96. 1996.