Automatic mesh generation and finite element computation

Handbook of Numerical Analysis

Volumn 4, Issue , 1996, Pages 69-190

  George, P L ^a  

^a INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350511699     PISSN: 15708659     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-8659(96)80003-2     Document Type: Review

References (117)

1. Aho A., Hopcroft J., and Ullman J. Data Structures and Algorithms (1983), Addison-Wesley, New York
2. Arcilla A.S., Hauser J., Eiseman P.R., and Thompson J.F. Numerical grid generation in computational fluid dynamics and related fields. Proc. Conf. Barcelona (1991), North-Holland, Reading, MA 841-854
3. Aurenhamer F. Voronoï diagrams. A survey of a fundamental data structure. ACM Computing Surveys 23 3 (1991) 345-405
4. Baker T.J. Three dimensional mesh generation by triangulation of arbitrary point sets. AIAA Paper 87-1124 (1987)
5. Baker T.J. Mesh generation by a sequence of transformations. Proc. AIAA 8th Comp. Fluid Dynamics Conf. Honolulu, HI (1987)
6. Baker T.J. Generation of tetrahedral meshes around complete aircraft. Proc. Numerical Grid Generation in Computational Fluid Mechanics '88. Miami (1988)
7. Baker T.J. Unstructured mesh generation and its application to the calculation of flows over complete aircraft. Proc. Tennessee Univ. Space Institute Workshop (1988)
8. Baker T.J. Developments and trends in three-dimensional mesh generation. Appl. Numer. Math. 5 (1989) 275-309
9. Baker T.J. Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation. Engrg. Comput. 5 (1989) 161-175
10. Baker T.J. Shape reconstruction and volume meshing for complex solids. Internat. J. Numer. Methods Engrg. 32 (1991) 665-675
11. Bathe K.J., and Chae S.W. On automatic mesh construction and mesh refinement in finite element analysis. Computers & Structures 32 3/4 (1989) 911-936
12. Berger M. Géométrie Tome 3: Convexes et Polytopes, Polyèdres Réguliers, Aires et Volumes (1978), Fernand Nathan, Amsterdam
13. Bernadou M., George P.L., Hassim A., Joly P., Laug P., Perronnet A., Saltel E., Steer D., Vanderborck G., and Vidrascu M. Modulef: A Modular Library of Finite Elements (1988), INRIA, Paris
14. Bowyer A. Computing Dirichlet tesselations. Comput. J. 24 2 (1981) 162-167
15. Cabello J., Löhner R., and Jacquotte O.P. A variational method for the optimization of directionally stretched elements generated by the advancing front method. In: Arcilla A.S., Hauser J., Eiseman P.R., and Thompson J.F. (Eds). Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, Conf. Barcelona (1991), North-Holland 521-532
16. Cabello J., Löhner R., and Jacquotte O.P. A variational method for the optimization of two- and three-dimensional unstructured meshes. 30th Aerospace Sciences Meeting. Reno (1992)
17. Castillo J.E. The discrete grid generation on curves and surfaces. In: Arcilla A.S., Hauser J., Eiseman P.R., and Thompson J.F. (Eds). Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, Conf. Barcelona (1991), North-Holland, Amsterdam 915-924
18. Castillo J.E. Mathematical Aspects of Numerical Grid Generation (1991), SIAM, Amsterdam
19. Caughey D.A. A systematic procedure for generating useful conformal coordinates mappings. Internat. J. Numer. Methods Engrg. 12 (1978) 1651-1657
20. Cavendish J.C., Field D.A., and Frey W.H. An approach to automatic three-dimensional finite element mesh generation. Internat. J. Numer. Methods Engrg. 21 (1985) 329-347
21. Cendes Z.J., Shenton D.N., and Shahnasser H. Magnetic field computations using Delaunay triangulations and complementary finite element methods. IEEE Trans. Magnetics 21 (1985)
22. Cherfils C., and Hermeline F. Diagonal swap procedures and characterizations of 2D-Delaunay triangulations. RAIRO Modél. Math. Anal. Numér. 24 5 (1990) 613-626
23. Chew L.P. Constrained Delauny triangulations. Algorithmica 4 (1989)
24. ACM 0-89791-163-6. Chew L.P., and Drysdale R.L. Voronoï diagrams based on convex distance functions (1985) 235-244
25. Ciarlet P.G. Basic error estimates for elliptic problems. In: Ciarlet P.G., and Lions J.L. (Eds). Finite Element Methods. Handbook of Numerical Analysis Vol. II (1991), North-Holland, Philadelphia, PA 17-351
26. Cook W.A. Body oriented coordinates for generating 3-dimensional meshes. Internat. J. Numer. Methods Engrg. 8 (1974) 27-43
27. Coulomb J.L. Maillage 2D et 3D. Experimentation de la triangulation de Delaunay. Proc. Conf. on Automated Mesh Generation and Adaptation. Grenoble (1987)
28. Coxeter H.S.M., Few L., and Rogers C.A. Covering space with equal spheres. Mathematika 6 (1959) 147-151
29. Delaunay B. Sur la sphère vide. Bull. Acad. Sci. URSS Class. Sci. Nat. (1934) 793-800
30. Dirichlet G.L. Uber die Reduction der positiven quadratischen formen mit drei understimmten ganzen Zahlen. Z. Angew. Math. Mech. 40 3 (1850) 209-227
31. Dwyer R.A. A faster divide-and-conquer algorithm for constructing Delaunay triangulations. Algorithmica 2 (1987) 137-151
32. Ecer A., Spyropoulos J.T., and Maul J.D. A three-dimensional block-structured finite element grid generation scheme. AIAA J. 23 (1985) 1483-1490
33. Field D.A. Laplacian smoothing and Delaunay triangulations. Comm. Appl. Numer. Methods 4 (1988) 709-712
34. Field D.A., and Smith W.D. Graded tetrahedral finite element meshes. Internat. J. Numer. Methods Engrg. 31 (1991) 413-425
35. and ACM, New York. Field D.A., and Yarnall K. Three dimensional Delaunay triangulations on a Cray X-MP. Proc. Supercomputing 88. Science et Applications Vol. 2 (1989), IEEE Computer Soc. Press, Amsterdam
36. Frey W.H., and Field D.A. Mesh relaxation: A new technique for improving triangulations. Internat. J. Numer. Methods Engrg. 31 (1991) 1121-1133
37. Fritz W. Two-dimensional and three-dimensional block structured grid generation techniques. Conf. on Automated Mesh Generation and Adaption. Grenoble (1987)
38. Garey D.M.R., Johnson S., Preparata F.P., and Tarjan R.E. Triangulating a simple polygon. Inform. Process Lett. 7 (1978)
39. Stan-CS, Ph.D. George J.A. Computer implementation of the finite element method (1971)
40. also as. George P.L. Génération Automatique de Maillages, Applications aux Méthodes d'Elements Finis. RMA no. 16 (1990), Masson, Silver Spring MD
41. also as. George P.L. Génération Automatique de Maillages, Applications aux Méthodes d'Elements Finis. Automatic Mesh Generation, Applications to Finite Element Methods (1991), Wiley, Paris
42. George P.L. Génération de maillages par une méthode de type Voronoï. Rapport de Recherche INRIA no. 1398 (1991)
43. George P.L. Génération de maillages par une méthode de type Voronoï, Partie 2: Le cas tridimensionnel. Rapport de Recherche INRIA no. 1664 (1992)
44. George P.L. Transformation d'un maillage en un maillage aigu. J. Phys. 3 (1993) 55-68
45. George P.L., Hecht F., and Saltel E. Constraint of the boundary and automatic mesh generation. Numerical Grid Generation in Computational Fluid Mechanics (1988), Prineridge Press, New York
46. George P.L., Hecht F., and Saltel E. Automatic triangulations by a pseudo-Voronoï technique in 3D. Proc. Workshop on Computational Mathematics and Applications. Pavie, Italie (1989)
47. George P.L., Hecht F., and Saltel E. Fully automatic mesh generator for 3D domains of any shape. Impact Comput. Sci. Engrg. 2 3 (1990) 187-218
48. George P.L., Hecht F., and Saltel E. Automatic 3D mesh generation with prescribed meshed boundaries. IEEE Trans. Magnetics 26 2 (1990) 771-774
49. George P.L., Hecht F., and Saltel E. Automatic mesh generation with specified boundary. Comput. Methods Appl. Mech. Engrg. 92 (1991) 269-288
50. George P.L., Hecht F., and Vallet M.G. Creation of internal points in Voronoï type method, control adaption. Adv. Engrg. Software 13 5/6 (1991) 303-313
51. George P.L., and Hermeline F. Delaunay's mesh of a convex polyhedron in dimension d. Application for arbitrary polyhedra. Internat. J. Numer. Methods Engrg. 33 (1992) 975-995
52. George P.L., and Seveno E. Génération de maillages par une méthode de type frontal. Rapport de Recherche INRIA no. 1725 (1992)
53. Gilding B. A numerical grid generation technique. Comput. & Fluids 16 (1988) 47-58
54. Golgolab A. Mailleur tridimensionnel automatique pour des géométries complexes. Rapport de Recherche INRIA no. 1004 (1989)
55. Gordon W.J., and Hall C.A. Construction of curvilinear co-ordinate systems and applications to mesh generation. Internat. J. Numer. Methods Engrg. 7 (1973) 461-477
56. Hall C.A. Transfinite interpolation and applications to engineering problems. In: Law A.G., and Sahney B.N. (Eds). Theory of Approximation (1976), Academic Press, Swansea 308-331
57. Hauser J., and Taylor C. Numerical Grid Generation in Computational Fluid Mechanics CFD 86 (1986), Pineridge, New York
58. Hecht F. Thèse d'habilitation (1992), Université Pierre et Marie Curie, Swansea
59. Hecht F., and Saltel E. Emc2: Un logiciel d'édition de maillages et de contours bidimensionnels. Rapport Technique INRIA no. 118 (1990)
60. Hermeline F. Une méthode automatique de maillage en dimension n. Thèse (1980), Université Paris 6, Paris
61. Hermeline F. Triangulation automatique d'un polyèdre en dimension N. RAIRO Anal. Numér. 16 3 (1982) 211-242
62. Ho Le K. Finite element mesh generation methods: A review and classification. Comput. Aided Design 20 (1988) 27-38
63. Holmes D.G., and Snyder D.D. The generation of unstructured triangular meshes using Delaunay triangulation. Numerical Grid Generation in Computational Fluid Mechanics (1988), Pineridge, Paris
64. Joe B. Delaunay versus max-min solid angle triangulations for three-dimensional mesh generation. Internat. J. Numer. Methods Engrg. 31 (1991) 987-997
65. Joe B. Construction of three-dimensional Delaunay triangulations using local transformations. Comput. Aided Geom. Design 8 (1991) 123-142
66. Johnston B.P., and Sullivan M. Fully automatic two dimensional mesh generation using normal offsetting. Internat. J. Numer. Methods Engrg. 33 (1992) 425-442
67. Lawson C.L. Properties of n-dimensional triangulations. Comput. Aided Design 3 (1986) 231-246
68. Lee D.T. Two-dimensional Voronoï diagrams in Lp-Metric. J. ACM 27 4 (1980) 604-618
69. Lo S.H. A new mesh generation scheme for arbitrary planar domains. Internat. J. Numer. Methods Engrg. 21 (1985) 1403-1426
70. Lo S.H. Delaunay triangulation of non-convex planar domains. Internat. J. Numer. Methods Engrg. 28 (1989) 2695-2707
71. Lo S.H. Automatic mesh generation and adaptation by using contours. Internat. J. Numer. Methods Engrg. 31 (1991) 689-707
72. Lo S.H. Volume discretization into tetrahedra - I: Verification and orientation of boundary surfaces. Comput. Struct. 39 (1991) 493-500
73. Lo S.H. Volume discretization into tetrahedra - II: 3D triangulation by advancing front approach. Comput. Struct. 39 (1991) 501-511
74. Löhner R. Some useful data structures for the generation of unstructured grids. Comm. Appl. Numer. Methods 4 (1988) 123-135
75. Löhner R., Camberos J., and Merriam M. Parallel unstructured grid generation. Comput. Meth. Appl. Mech. Engrg. 95 (1992) 343-357
76. Löhner R., and Parikh P. Three-dimensional grid generation by the advancing-front method. Internat. J. Numer. Methods Fluids 8 (1988) 1135-1149
77. Löhner R., and Parikh P. Generation of 3D unstructured grids by the advancing front method. Proc. AIAA 88 0515, 26th Aerospace Sciences Meeting. Reno, NV (1988)
78. Mavriplis D.J. Unstructured and adaptive mesh generation method. In: Arcilla A.S., Hauser J., Eiseman P.R., and Thompson J.F. (Eds). Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, Conf. Barcelona (1991), North-Holland, Swansea 79-92
79. Mavriplis D.J. An advancing front Delaunay triangulation algorithm designed for robustness. Icase Report no 92-49 (1992)
80. Meshkat S., Ruppert J., and Li H. Three-dimensional automatic unstructured grid generation based on Delaunay tetrahedrization. In: Arcilla A.S., Hauser J., Eiseman P.R., and Thompson J.F. (Eds). Numerical Grid Generation in Computational Fluid Dynamics and Related Fields, Conf. Barcelona (1991), North-Holland, Amsterdam 841-854
81. Reno, NV. Peraire J., and Peiro J. A 3D Finite Element Multigrid Solver for the Euler Equations. AIAA (1992)
82. Peraire J., Peiro J., Formaggia L., Morgan K., and Zienkiewicz O.C. Finite element Euler computations in three dimensions. Internat. J. Numer. Methods Engrg. 26 (1988) 2135-2159
83. Peraire J., Peiro J., and Morgan K. Adaptive remeshing for three-dimensional compressible flow computations. J. of Comp. Phys. 103 (1992) 269-285
84. Peraire J., Vahdati M., Morgan K., and Zienkiewicz O.C. Adaptive remeshing for compressible flow computations. J. Comput. Phys. 72 2 (1987) 449-466
85. Perronnet A. Logical and physical representation of an object, modularity for the programming of finite element methods. Proc. IFIP Working Group 2.5 on Numerical Software. Soderkoping, Sweden (1983)
86. Perronnet A. A generator of tetrahedral finite elements for multi-material object and fluids. Numerical Grid Generation in Computational Fluid Mechanics (1988), Pineridge, Amsterdam
87. Preparata F.P., and Shamos M.I. Computational Geometry, an Introduction (1985), Springer, Swansea
88. no. 18. Risler J.J. Méthodes Mathématiques pour la C.A.O. RMA (1991), Masson, Berlin
89. Samet H. The quadtree and related hierarchical data structures. Comput. Surveys 16 2 (1984) 187-285
90. Schroeder W.J., and Shephard M.S. A combined Octree-Delaunay method for fully automatic 3D mesh generation. Internat. J. Numer. Methods Engrg. 29 (1990) 37-55
91. Sengupta S., Hauser J., Eiseman P.R., and Thompson J.F. Numerical Grid Generation in Computational Fluid Mechanics 88 (1988), Pineridge, Paris
92. Shaw J.A., and Weatherill N.P. Automatic topology generation for multiblock grids. Appl. Math. Comput. 52 (1992) 355-388
93. Shephard M.S. Approaches to the automatic generation and control of finite element meshes. Appl. Mech. Rev. 41 (1988) 169-185
94. Shephard M.S., and Georges M.K. Reliability of automatic 3D mesh generation. Comput. Methods Appl. Mech. Engrg. 101 (1992) 443-462
95. Shephard M.S., Grice K.R., Lo J.A., and Schroeder W.J. Trends in automatic three-dimensional mesh generation. Comput. & Structures 30 1/2 (1988) 421-429
96. Shephard M.S., Guerinoni F., Flaherty J.E., Ludwig R.A., and Baehmann P.L. Adaptive solutions of the Euler equations using finite quadtree and octree grids. Comput. Structures 30 (1988) 327-336
97. Shephard M.S., and Yerri M.A. An approach to automatic finite element mesh generation. Comput. Engrg. 3 (1982) 21-28
98. Sloan S.W. A fast algorithm for constructing Delaunay triangulations in the plane. Adv. Engrg. Software 9 1 (1987) 34-55
99. Sloan S.W., and Houlsby G.T. An implementation of Watson's algorithm for computing 2-dimensional Delaunay triangulations. Adv. Engrg. Software 6 4 (1984) 192-197
100. Thacker W.C. A brief review of techniques for generating irregular computational grids. Internat. J. Numer. Methods Engrg. 15 (1980) 1335-1341
101. Thompson J.F. A general three dimensional elliptic grid generation system on a composite block-structure. Comput. Methods Appl. Mech. Engrg. 64 (1987) 377-411
102. Thompson J.F., Warsi Z.U.A., and Mastin C.W. Numerical Grids Generation, Foundations and Applications (1985), North-Holland, Swansea
103. Vallet M.G. Génération de maillages anisotropes adaptés - Application à la capture de couches limites. Rapport de Recherche INRIA no. 1360 (1990)
104. Vallet M.G., Hecht F., and Mantel B. Anisotropic control of mesh generation based upon a Voronoï type method. Numerical Grid Generation in Computational Fluid Dynamics and Related Fields (1991), North-Holland, Amsterdam
105. Voronoï G. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Recherches sur les parallélloedres primitifs. J. Angew. Math. 134 (1908)
106. Watson D.F. Computing the n-dimensional Delaunay tesselation with applications to Voronoï polytopes. Comput. J. 24 2 (1981) 167-172
107. Weatherill N.P. The generation of unstructured grids using Dirichlet tesselation. MAE report no. 1715 (1985), Princeton Univ., Amsterdam
108. Weatherill N.P. A method for generating irregular computational grids in multiply connected planar domains. Internat. J. Numer. Methods Fluids 8 (1988) 181-197
109. Weatherill N.P. The integrity of geometrical boundaries in the 2-dimensional Delaunay triangulation. Comm. Appl. Numer. Methods 6 (1990) 101-109
110. Weatherill N.P. Numerical grid generation. Lecture Series 1990-06 (1990), Von Karman Institute for Fluid Dynamics
111. Weatherill N.P. Delaunay triangulation in computational fluid dynamics. Comput. Math. Appl. 24 5/6 (1992) 129-150
112. Wordenweber B. Finite element mesh generation. Comput. Aided Design 16 (1984) 285-291
113. Yerri M.A., and Shephard M.S. A modified quadtree approach to finite element mesh generation. IEEE Comput. Graphics Appl. 3 (1983) 36-46
114. Yerri M.A., and Shephard M.S. Automatic mesh generation for three-dimensional solids. Comput. & Structures 20 (1985) 211-223
115. Zhu J.Z., Zienkiewicz O.C., Hinton E., and Wu J. A new approach to the development of automatic quadrilateral mesh generation. Internat. J. Numer. Methods Engrg. 32 (1991) 849-866
116. Zienkiewicz O.C., and Phillips D.V. An automatic mesh generation scheme for plane and curved surfaces by isoparametric co-ordinates. Internat. J. Numer. Methods Engrg. 3 (1971) 519-528
117. Zienkiewicz O.C., and Zhu J.Z. Adaptivity and mesh generation. Internat. J. Numer. Methods Engrg. 32 (1991) 783-810