Abstract
This paper is motivated by the problem of subdividing a prismatic mesh to a tetrahedral mesh with prescribed boundary conditions and without inserting Steiner points. We show that this 3D subdivision problem can be modeled as a 2D cutting flow problem. Then we propose a complete solution to the cutting flow problem, covering all possible combinations of base domain topology and boundary condition. We not only provide provable sufficient and necessary conditions for existence of solutions, but also provide linear algorithms to compute a solution whenever there is one.
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Albertelli, G., Crawfis, R.A.: Efficient subdivision of finite-element datasets into consistent tetrahedra. In: Proceedings of the 8th Conference on Visualization, VIS 1997, pp. 213–219. IEEE Computer Society Press, Los Alamitos (1997)
Au, P., Dompierre, J., Labbé, P., Guibault, F., Camarero, R.: Proposal of benchmarks for 3D unstructured tetrahedral mesh optimization. In: Proceedings of the 7th International Meshing, pp. 459–478 (1998)
Connell, S.D., Braaten, M.E.: Semi-structured mesh generation for 3d Navier-Stokes calculations. In: AIAA 12th Computational Fluid Dynamics Conference, pp. 369–380 (1995)
Dompierre, J., Labbé, P., Vallet, M.-G., Camarero, R.: How to subdivide pyramids, prisms, and hexahedra into tetrahedra. In: 8th International Meshing Roundtable, pp. 195–204 (1999)
Freitag, L.A., Ollivier-Gooch, C.: Tetrahedral mesh improvement using swapping and smoothing. International Journal for Numerical Methods in Engineering 40(21), 3979–4002 (1998)
Jiao, X.: Face offsetting: A unified approach for explicit moving interfaces. J. Comput. Phys. 220, 612–625 (2006)
Loehner, R.: Matching semi-structured and unstructured grids for Navier-Stokes calculations. In: AIAA 11th Computational Fluid Dynamics Conference, pp. 555–564 (1993)
Longest, W., Kleinstreuer, C.: Comparison of blood particle deposition models for non-parallel flow domains. Journal of Biomechanics 36(3), 421–430 (2003)
Max, N., Becker, B., Crawfis, R.: Flow volumes for interactive vector field visualization. In: Proceedings of the 4th Conference on Visualization, VIS 1993, pp. 19–24. IEEE Computer Society, Washington, DC (1993)
N’dri, D., Garon, A., Fortin, A.: A new stable space-time formulation for two-dimensional and three-dimensional incompressible viscous flow. International Journal for Numerical Methods in Fluids 37(8), 865–884 (2001)
Pirzadeh, S.: Unstructured viscous grid generation by advancing layers method. In: AIAA 12th Computational Fluid Dynamics Conference (1993)
Pirzadeh, S.: Three-dimensional unstructured viscous grids by the advancing-layers method. AIAA Journal 34(1), 43–49 (1996)
Taylor, C.A., Hughes, T.J.R., Zarins, C.K.: Finite element modeling of blood flow in arteries. Computer Methods in Applied Mechanics and Engineering 158(1-2), 155–196 (1998)
Yin, X., Han, W., Gu, X., Yau, S.-T.: The cutting pattern problem for tetrahedral mesh generation. In: Quadros, W.R. (ed.) Proceedings of the 20th International Meshing Roundtable, vol. 90, pp. 217–236. Springer, Heidelberg (2011)
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Yin, X., Han, W., Gu, X., Yau, ST. (2014). Subdividing Prismatic Meshes by Cutting Flow. In: Zhang, Y.J., Tavares, J.M.R.S. (eds) Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications. CompIMAGE 2014. Lecture Notes in Computer Science, vol 8641. Springer, Cham. https://doi.org/10.1007/978-3-319-09994-1_19
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DOI: https://doi.org/10.1007/978-3-319-09994-1_19
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