Level set method Sharp feature; Implicit representation; Boolean operatio; Sharp feature; Implicit representation; Boolean operation; Finite elements
Abstract :
[en] The present contribution enriches the nowadays “classical” level set implicit representation of geometries with topological information in order to correctly represent sharp features. For this, sharp features are classified according to their positions within elements of the level set support. Based on this additional information, sub-elements and interface-mesh used in a finite element context for integration and application of boundary conditions are modified to match exactly to the sharp features. In order to analyze evolving geometries, Boolean operations on these semi-implicit representations are derived so that the minimal additional information to represent correctly the new geometry is stored. This approach has been successfully applied to complex two-dimensional geometries. It computes in a robust way numerous Boolean operations and guarantees the precision and the convergence rate of the numerical simulations.
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Bibliography
[1] Osher, S., Sethian, J.A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79:1 (1988), 12–49.
[2] Sethian, J.A., Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, 1999, Cambridge University Press, Cambridge.
[3] S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, vol. 153, Springer Science & Business Media, New York, 2006.
[4] Chen, S., Merriman, B., Osher, S., Smereka, P., A simple level set method for solving Stefan problems. J. Comput. Phys. 135:1 (1997), 8–29.
[5] Osher, S., Fedkiw, R.P., Level set methods: an overview and some recent results. J. Comput. Phys. 169:2 (2001), 463–502.
[6] Duflot, M., A study of the representation of cracks with level sets. Int. J. Numer. Methods Eng. 70:11 (2007), 1261–1302.
[7] Vese, L.A., Chan, T.F., A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 50:3 (2002), 271–293.
[8] Sussman, M., Fatemi, E., Smereka, P., Osher, S., An improved level set method for incompressible two-phase flows. Comput. Fluids 27:5 (1998), 663–680.
[9] Olsson, E., Kreiss, G., A conservative level set method for two phase flow. J. Comput. Phys. 210:1 (2005), 225–246.
[10] Sethian, J.A., Wiegmann, A., Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163:2 (2000), 489–528.
[11] Wang, M.Y., Wang, X., Guo, D., A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192:1 (2003), 227–246.
[12] Allaire, G., Jouve, F., Toader, A.-M., Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194:1 (2004), 363–393.
[13] Cheng, K.W., Fries, T.-P., Higher-order xfem for curved strong and weak discontinuities. Int. J. Numer. Methods Eng. 82:5 (2010), 564–590.
[14] Fries, T.-P., Omerović, S., Higher-order accurate integration of implicit geometries. Int. J. Numer. Methods Eng. 106:5 (2016), 323–371.
[15] Kästner, M., Müller, S., Goldmann, J., Spieler, C., Brummund, J., Ulbricht, V., Higher-order extended fem for weak discontinuities—level set representation, quadrature and application to magneto-mechanical problems. Int. J. Numer. Methods Eng. 93:13 (2013), 1403–1424.
[16] Legrain, G., Chevaugeon, N., Dréau, K., High order x-fem and levelsets for complex microstructures: uncoupling geometry and approximation. Comput. Methods Appl. Mech. Eng. 241 (2012), 172–189.
[17] Legrain, G., Geuzaine, C., Remacle, J.-F., Moës, N., Cresta, P., Gaudin, J., Numerical simulation of cad thin structures using the extended finite element method and level sets. Finite Elem. Anal. Des. 77 (2013), 40–58.
[18] Moumnassi, M., Belouettar, S., Béchet, É., Bordas, S.P., Quoirin, D., Potier-Ferry, M., Finite element analysis on implicitly defined domains: an accurate representation based on arbitrary parametric surfaces. Comput. Methods Appl. Mech. Eng. 200:5 (2011), 774–796.
[19] Tran, A., Yvonnet, J., He, Q.-C., Toulemonde, C., Sanahuja, J., A multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within xfem. Int. J. Numer. Methods Eng. 85:11 (2011), 1436–1459.
[20] Brönnimann, H., Melquiond, G., Pion, S., The design of the boost interval arithmetic library. Theoret. Comput. Sci. 351:1 (2006), 111–118.
[21] W.R. Franklin, Pnpoly-point Inclusion in Polygon Test, Web site: 〈 http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html〉.
[22] Ertl, O., Selberherr, S., A fast level set framework for large three-dimensional topography simulations. Comput. Phys. Commun. 180:8 (2009), 1242–1250.
[23] Pierard, O., Barboza, J., Duflot, M., D׳Alvise, L., Perez-Duarte, A., Distortions prediction during multi-pass machining simulations by using the level-set method. Int. J. Mater. Form. 1:1 (2008), 563–565.
[25] K. Museth, D.E. Breen, R.T. Whitaker, A.H. Barr, Level set surface editing operators, in: ACM Transactions on Graphics (TOG), vol. 21, ACM, New York, 2002, pp. 330–338.
[26] Williams, M., Stress singularities resulting from various boundary conditions. J. Appl. Mech. 19:4 (1952), 526–528.
[27] Szabo, B.A., Babuška, I., Finite element analysis. 1991, John Wiley & Sons, New York.
[28] González-Estrada, O.A., Natarajan, S., Ródenas, J.J., Nguyen-Xuan, H., Bordas, S.P., Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity. Comput. Mech. 52:1 (2013), 37–52.
[29] B. Szabó, I. Babuška, Introduction to Finite Element Analysis: Formulation, Verification and Validation, vol. 35, John Wiley & Sons, New York, 2011.
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