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Issue No.05 - May (2012 vol.18)
pp: 717-728
B. Fierz , Comput. Vision Lab., ETH Zurich, Zurich, Switzerland
J. Spillmann , Comput. Vision Lab., ETH Zurich, Zurich, Switzerland
Iker Aguinaga Hoyos , CELT, Tecnun, Donostia, Spain
M. Harders , Comput. Vision Lab., ETH Zurich, Zurich, Switzerland
We present a novel hybrid method to allow large time steps in explicit integrations for the simulation of deformable objects. In explicit integration schemes, the time step is typically limited by the size and the shape of the discretization elements as well as by the material parameters. We propose a two-step strategy to enable large time steps for meshes with elements potentially destabilizing the integration. First, the necessary time step for a stable computation is identified per element using modal analysis. This allows determining which elements have to be handled specially given a desired simulation time step. The identified critical elements are treated by a geometric deformation model, while the remaining ones are simulated with a standard deformation model (in our case, a corotational linear Finite Element Method). In order to achieve a valid deformation behavior, we propose a strategy to determine appropriate parameters for the geometric model. Our hybrid method allows taking much larger time steps than using an explicit Finite Element Method alone. The total computational costs per second are significantly lowered. The proposed scheme is especially useful for simulations requiring interactive mesh updates, such as for instance cutting in surgical simulations.
pattern matching, computer animation, finite element analysis, surgical simulation, time step maintenance, explicit finite element simulation, shape matching, deformable object simulation, explicit integration scheme, discretization element, material parameter, modal analysis, simulation time step, geometric deformation model, standard deformation model, corotational linear finite element method, deformation behavior, interactive mesh update, Computational modeling, Deformable models, Finite element methods, Solid modeling, Mathematical model, Estimation, Sockets, stability and instability., Physically based modeling, virtual reality, real time
B. Fierz, J. Spillmann, Iker Aguinaga Hoyos, M. Harders, "Maintaining Large Time Steps in Explicit Finite Element Simulations Using Shape Matching", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 5, pp. 717-728, May 2012, doi:10.1109/TVCG.2011.105
[1] M. Desbrun, P. Schröder, and A. Barr, "Interactive Animation of Structured Deformable Objects," Proc. Conf. Graphics Interface, pp. 1-8, 1999.
[2] J.R. Shewchuk, "What Is a Good Linear Element? Interpolation, Conditioning, and Quality Measures," Proc. Int'l Meshing Roundtable, pp. 115-126, 2002.
[3] M. Müller and M. Gross, "Interactive Virtual Materials," Proc. Graphics Interface, pp. 239-246, 2004.
[4] M. Müller, B. Heidelberger, M. Teschner, and M. Gross, "Meshless Deformations Based on Shape Matching," ACM Trans. Graphics, vol. 24, no. 3, pp. 471-478, 2005.
[5] A.R. Rivers and D.L. James, "FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation," ACM Trans. Graphics, vol. 26, no. 3, pp. 82:1-82:6, 2007.
[6] P. Gurfil and I. Klein, "Stabilizing the Explicit Euler Integration of Stiff and Undamped Linear Systems," J. Guidance, Control, and Dynamics, vol. 30, no. 6, pp. 1659-1667, 2007.
[7] M. Shinya, "Stabilizing Explicit Methods in Spring-Mass Simulation," Proc. Computer Graphics Int'l, pp. 528-531, 2004.
[8] J.R. Shewchuk, "Tetrahedral Mesh Generation by Delaunay Refinement," Proc. Symp. Computational Geometry, pp. 86-95, 1998.
[9] P. Alliez, D. Cohen-Steiner, M. Yvinec, and M. Desbrun, "Variational Tetrahedral Meshing," ACM Trans. Graphics, vol. 24, no. 3, pp. 617-625, 2005.
[10] J. Schöberl, "NETGEN An Advancing Front 2D/3D-Mesh Generator Based on Abstract Rules," Computing and Visualization in Science, vol. 1, no. 1, pp. 41-52, July 1997.
[11] F. Labelle and J.R. Shewchuk, "Isosurface Stuffing: Fast Tetrahedral Meshes with Good Dihedral Angles," ACM Trans. Graphics, vol. 26, no. 3, pp. 57.1-57.10, 2007.
[12] B.M. Klingner and J.R. Shewchuk, "Aggressive Tetrahedral Mesh Improvement," Proc. Int'l Meshing Roundtable, pp. 3-23, 2008.
[13] M. Wicke, D. Ritchie, B.M. Klingner, S. Burke, J.R. Shewchuk, and J.F. O'Brien, "Dynamic Local Remeshing for Elastoplastic Simulation," ACM Trans. Graphics, vol. 29, no. 4, p. 49, 2010.
[14] A. Pentland and J. Williams, "Good Vibrations: Modal Dynamics for Graphics and Animation," ACM SIGGRAPH Computer Graphics, vol. 23, no. 3, pp. 207-214, 1989.
[15] K.K. Hauser, C. Shen, and J.F. O'Brien, "Interactive Deformation Using Modal Analysis with Constraints," Proc. Graphics Interface, pp. 247-256, 2003.
[16] G. Debunne, M. Desbrun, M.-P. Cani, and A.H. Barr, "Dynamic Real-Time Deformations Using Space & Time Adaptive Sampling," ACM SIGGRAPH Computer Graphics, p. 31, 2001.
[17] E. Grinspun, P. Krysl, and P. Schröder, "CHARMS: A Simple Framework for Adaptive Simulation," ACM Trans. Graphics, vol. 21, no. 3, pp. 281-290, 2002.
[18] D. Steinemann, M.A. Otaduy, and M. Gross, "Fast Adaptive Shape Matching Deformations," Proc. Symp. Computer Animation, pp. 87-94, 2008.
[19] B. Fierz, J. Spillmann, and M. Harders, "Stable Explicit Integration of Deformable Objects by Filtering High Modal Frequencies," J. WSCG, vol. 18, nos. 1-3, pp. 81-88, 2010.
[20] B. Klein, FEM - Grundlagen der Anwendungen der Finite-Elemente-Methode im Maschinen- und Flugzeugbau, Vieweg, 2007.
[21] G. Irving, J. Teran, and R. Fedkiw, "Invertible Finite Elements for Robust Simulation of Large Deformation," Proc. Symp. Computer Animation, pp. 131-140, 2004.
[22] H. Si, "TetGen: A Quality Tetrahedral Mesh Generator and Three-Dimensional Delaunay Triangulator," http:/, 2009.
[23] J. Spillmann, M. Becker, and M. Teschner, "Non-Iterative Computation of Contact Forces for Deformable Objects," J. WSCG, vol. 15, nos. 1-3, pp. 33-40, 2007.
[24] D. Steinemann, M. Harders, M. Gross, and G. Szekely, "Hybrid Cutting of Deformable Solids," Proc. Virtual Reality Conf., pp. 35-42, 2006.
[25] A.J. Wathan, "Realistic Eigenvalue Bounds for the Galerkin Mass Matrix," IMA J. Numerical Analysis, vol. 7, no. 4, pp. 449-457, Oct. 1987.
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