Unstructured tetrahedral mesh generation technology
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 1, pp. 146-163 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present a robust unstructured tethahedra mesh generation technology. This technology is a combination of boundary discretization methods, an advancing front technique and a Delaunay-based mesh generation technique. For boundary mesh generation we propose four different approaches using analytical boundary parameterization, interface with CAD systems, surface mesh refinement, and constructive solid geometry. These methods allow us to build a flexible grid generation technology with a user friendly interface.
@article{ZVMMF_2010_50_1_a11,
     author = {A. A. Danilov},
     title = {Unstructured tetrahedral mesh generation technology},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {146--163},
     year = {2010},
     volume = {50},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a11/}
}
TY  - JOUR
AU  - A. A. Danilov
TI  - Unstructured tetrahedral mesh generation technology
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 146
EP  - 163
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a11/
LA  - en
ID  - ZVMMF_2010_50_1_a11
ER  - 
%0 Journal Article
%A A. A. Danilov
%T Unstructured tetrahedral mesh generation technology
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 146-163
%V 50
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a11/
%G en
%F ZVMMF_2010_50_1_a11
A. A. Danilov. Unstructured tetrahedral mesh generation technology. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 1, pp. 146-163. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a11/

[1] Schönhardt E., “Über die Zerlegung von Dreieckspolyedern in Tetraeder”, Math. Ann., 1928, no. 98, 309–312 | DOI | MR

[2] Joe B., “Three-dimensional boundary-constrained triangulations”, Proc. 13th IMACS World Congress, 1992, 215–222

[3] George P.-L., Borouchaki H., “Maillage simplicial d'un polyèdre arbitraire”, C. R. Acad. Sci. Paris. Ser. I, 338 (2004), 735–740 | MR | Zbl

[4] Borouchaki H., Hecht F., Saltel E., George P.-L., “Reasonably efficient Delaunay based mesh generator in 3 dimensions”, Proc. 4th Internat. Meshing Roundtable, 1995, 3–14

[5] Du Q., Wang D., “Recent progress in robust and quality Delaunay mesh generation”, J. Comput. and Appl. Math., 195 (2006), 8–23 | DOI | MR | Zbl

[6] Shewchuk J. R., “Constrained Delaunay tetrahedralizations and provably good boundary recovery”, Proc. 11th Internat. Meshing Roundtable, 2002, 193–204

[7] Ito Y., Shih A., Soni B., “Reliable isotropic tetrahedral mesh generation based on an advancing front method”, Proc. 13th Internat. Meshing Roundtable, 2004, 95–106 | Zbl

[8] Yang Y., Yong J., Sun J., “An algorithm for tetrahedral mesh generation based on conforming constrained Delaunay tetrahedralization”, Comput. and Graphics, 29 (2005), 606–615 | DOI

[9] George P.-L., Borouchaki H., Saltel E., ““Ultimate” robustness in meshing an arbitrary polyhedron”, Internat. J. Numer. Meth. Engng., 58 (2003), 1061–1089 | DOI | MR | Zbl

[10] 3D Generator of Anisotropic Meshes, http://sourceforge.net/projects/ani3d/

[11] 2D Generator of Anisotropic Meshes, http://sourceforge.net/projects/ani2d/

[12] The Common Geometry Module, http://cubit.sandia.gov/cgm.html

[13] Open CASCADE Technology, http://opencascade.org/

[14] Vassilevski Yu., Vershinin A., Danilov A., Plenkin A., Tetrahedral mesh generation in domains defined in CAD systems, Inst. Numer. Math. Moscow, 2005, 21–32 (in Russian)

[15] Nikitin K., Surface meshing technology for domains composed of primitives, Diploma thesis, MSU, Dept. Mech. Math., Moscow, 2007 (in Russian)

[16] George P.-L., Borouchaki H., Delaunay triangulation and meshing. Application to finite elements, Hermes, 1998 | MR

[17] Ivanenko S. A., “Variatsionnye metody postroeniya adaptivnykh setok”, Zh. vychisl. matem. i matem. fiz., 43:6 (2003), 830–844 | MR | Zbl

[18] Garanzha V., “Max-norm optimization of spatial mappings with application to grid generation, construction of surfaces and shape design”, Proc. Minisymp. in Int. Conf. OFEA, 2001, 61–74

[19] Agouzal A., Lipnikov K., Vassilevski Yu., “Adaptive generation of quasi-optimal tetrahedral meshes”, East-West Journal, 7 (1999), 223–244 | MR | Zbl