[en] This article presents a methodology aiming at easing considerably the generation of high-quality meshes for complex three-dimensional (3D) domains. To this end, a mesh size field h(x) is computed, taking surface curvatures and geometric features into account. The size field is tuned by five intuitive parameters and yields quality meshes for arbitrary geometries. Mesh size is initialized on a surface triangulation of the domain based on discrete curvatures and medial axis transform computations. It is then propagated into the volume while ensuring the size gradient ∇h is controlled so as to obtain a smoothly graded mesh. As the size field is stored in an independent octree data structure, it can be computed separately, then plugged into any mesh generator able to respect a prescribed size field. The procedure is automatic, in the sense that minimal interaction with the user is required. Applications of our methodology on CAD models taken from the very large ABC dataset are presented. In particular, all presented meshes were obtained with the same generic set of parameters, demonstrating the universality of the technique.
Disciplines :
Computer science
Author, co-author :
Bawin, Arthur ; Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium ; Département de Génie Mécanique, École Polytechnique de Montréal, Montréal, Canada
Henrotte, François ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE) ; Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium
Remacle, Jean-François ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Electrotechnique (électricité appliquée) ; Institute of Mechanics, Materials and Civil Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium
Language :
English
Title :
Automatic feature-preserving size field for three-dimensional mesh generation
Publication date :
30 September 2021
Journal title :
International Journal for Numerical Methods in Engineering
The authors would like to thank the Belgian Fund for Scientific Research (FRIA/FC 29571) for their support. Financial support from the Simulation‐based Engineering Science (Génie Par la Simulation) program funded through the CREATE program from the Natural Sciences and Engineering Research Council of Canada is also gratefully acknowledged. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (grant agreement ERC‐2015‐AdG‐694020).information Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada, Fonds pour la Formation ? la Recherche dans l'Industrie et dans l'Agriculture, FRIA/FC 29571; H2020 European Research Council, ERC-2015-AdG-694020The authors would like to thank the Belgian Fund for Scientific Research (FRIA/FC 29571) for their support. Financial support from the Simulation-based Engineering Science (G?nie Par la Simulation) program funded through the CREATE program from the Natural Sciences and Engineering Research Council of Canada is also gratefully acknowledged. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (grant agreement ERC-2015-AdG-694020).Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada, Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture, FRIA/FC 29571; H2020 European Research Council, ERC‐2015‐AdG‐694020 Funding information
Geuzaine C, Remacle JF. Gmsh: a 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng. 2009;79(11):1309-1331. https://doi.org/10.1002/nme.2579.
Cunha A, Canann S, Saigal S. Automatic boundary sizing for 2D and 3D meshes. ASME Appl Mech Div-Publ-AMD. 1997;220:65-72.
Owen SJ, Saigal S. Neighborhood-based element sizing control for finite element surface meshing. Proceedings of the 6th International Meshing Roundtable, Park City, Utah: Sandia; 1997:143-154.
Chen J, Xiao Z, Zheng Y, Zheng J, Li C, Liang K. Automatic sizing functions for unstructured surface mesh generation. Int J Numer Methods Eng. 2017;109(4):577-608. https://doi.org/10.1002/nme.5298.
Chen J, Liu Z, Zheng Y, et al. Automatic sizing functions for 3D unstructured mesh generation. Proc Eng. 2017;203:245-257. https://doi.org/10.1016/j.proeng.2017.09.804.
Pirzadeh S. Structured background grids for generation of unstructured grids by advancing-front method. AIAA J. 1993;31(2):257-265.
Zhu J, Blacker TD, Smith R. Background overlay grid size functions. In: Chrisochoides N, ed. Proceedings of the 11th International Meshing Roundtable, IMR 2002, September 15-18. Vol 2002. Ithaca, New York, Sandia; 2002:65-73.
Tchon KF, Khachan M, Guibault F, Camarero R. Three-dimensional anisotropic geometric metrics based on local domain curvature and thickness. Comput Aided Des. 2005;37(2):173-187. https://doi.org/10.1016/j.cad.2004.05.007.
Quadros WR, Vyas V, Brewer M, Owen SJ, Shimada K. A computational framework for automating generation of sizing function in assembly meshing via disconnected skeletons. Eng Comput. 2010;26(3):231-247. https://doi.org/10.1007/s00366-009-0164-z.
Persson PO. Mesh size functions for implicit geometries and PDE-based gradient limiting. Eng Comput. 2006;22(2):95-109. https://doi.org/10.1007/s00366-006-0014-1.
Chen J, Cao B, Zheng Y, Xie L, Li C, Xiao Z. Automatic surface repairing, defeaturing and meshing algorithms based on an extended B-rep. Adv Eng Softw. 2015;86:55-69. https://doi.org/10.1016/j.advengsoft.2015.04.004.
Shan J, Li Y, Guo Y, Guan Z. A robust backward search method based on walk-through for point location on a 3D surface mesh. Int J Numer Methods Eng. 2008;73(8):1061-1076. https://doi.org/10.1002/nme.2098.
Zhang Y, Wang W, Liang X, et al. High-fidelity tetrahedral mesh generation from medical imaging data for fluid-structure interaction analysis of cerebral aneurysms. Comput Model Eng Sci. 2009;42(2):131.
Liang X, Zhang Y. An octree-based dual contouring method for triangular and tetrahedral mesh generation with guaranteed angle range. Eng Comput. 2014;30(2):211-222.
Burstedde C, Wilcox LC, Ghattas O. p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees. SIAM J Sci Comput. 2011;33(3):1103-1133. https://doi.org/10.1137/100791634.
Zhang Y, Bajaj C, Sohn BS. 3D finite element meshing from imaging data. Comput Methods Appl Mech Eng. 2005;194(48-49):5083-5106.
Turner M, Moxey D, Peiró J. Automatic mesh sizing specification of complex three dimensional domains using an octree structure. In: Ledoux F, Lewis K, eds. Research Note, 24th International Meshing Roundtable, October 11-14. Austin, Texas; Elsevier: 2015.
Deister F, Tremel U, Hassan O, Weatherill NP. Fully automatic and fast mesh size specification for unstructured mesh generation. Eng Comput. 2004;20(3):237-248. https://doi.org/10.1007/s00366-004-0291-5.
Rusinkiewicz S. Estimating curvatures and their derivatives on triangle meshes. Paper presented at: Proceedings of the 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 3DPVT 2004,>Thessaloniki, Greece; vol. 2004, 2004:486-493; IEEE.
Dey TK, Zhao W. Approximating the medial axis from the voronoi diagram with a convergence guarantee. Algorithmica. 2004;38(1):179-200. https://doi.org/10.1007/s00453-003-1049-y.
Beckmann N, Kriegel HP, Schneider R, Seeger B. The R*-tree: an efficient and robust access method for points and rectangles. Paper presented at: Proceedings of the 19 of ACM SIGMOD Record; 1990:322-331; ACM, New York, NY.
Koch S, Matveev A, Jiang Z, et al. ABC: a big CAD model dataset for geometric deep learning. Paper presented at: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Computer Vision Foundation / IEEE, Long Beach, CA; 2019:9601-9611.
Frey PJ, George PL. Maillages: Applications Aux Éléments Finis. Paris, France: Hermès Science Publications; 1999.
Marot C, Verhetsel K, Remacle JF. Reviving the search for optimal tetrahedralizations. In: Peirò J, Viertel R, eds. Proceedings of the 28th International Meshing Roundtable, IMR 2019, October 14-17. Vol 2019. Buffalo, New York; 2019:326-336.
