A time-integration method for stable simulation of extremely deformable hyperelastic objects
This paper presents a time integration method for realtime simulation of extremely deformable objects subject to geometrically nonlinear hyperelasticity. In the presented method, the equation of motion of the system is discretized by the backward Euler method, and linearly approximated through the f...
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| Published in | The Visual computer Vol. 33; no. 10; pp. 1335 - 1346 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2017
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0178-2789 1432-2315 |
| DOI | 10.1007/s00371-016-1225-0 |
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| Abstract | This paper presents a time integration method for realtime simulation of extremely deformable objects subject to geometrically nonlinear hyperelasticity. In the presented method, the equation of motion of the system is discretized by the backward Euler method, and linearly approximated through the first-order Taylor expansion. The approximate linear equation is solved with the quasi-minimal residual method (QMR), which is an iterative linear equation solver for non-symmetric or indefinite matrices. The solution is then corrected considering the nonlinear term that is omitted at the Taylor expansion. The method does not demand the constitutive law to guarantee the positive definiteness of the stiffness matrix. Experimental results show that the presented method realizes stable behavior of the simulated model under such deformation that the tetrahedral elements are almost flattened. It is also shown that QMR outperforms the biconjugate gradient stabilized method (BiCGStab) in this application. |
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| AbstractList | This paper presents a time integration method for realtime simulation of extremely deformable objects subject to geometrically nonlinear hyperelasticity. In the presented method, the equation of motion of the system is discretized by the backward Euler method, and linearly approximated through the first-order Taylor expansion. The approximate linear equation is solved with the quasi-minimal residual method (QMR), which is an iterative linear equation solver for non-symmetric or indefinite matrices. The solution is then corrected considering the nonlinear term that is omitted at the Taylor expansion. The method does not demand the constitutive law to guarantee the positive definiteness of the stiffness matrix. Experimental results show that the presented method realizes stable behavior of the simulated model under such deformation that the tetrahedral elements are almost flattened. It is also shown that QMR outperforms the biconjugate gradient stabilized method (BiCGStab) in this application. |
| Author | Kikuuwe, Ryo |
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| Cites_doi | 10.1145/1073204.1073300 10.1109/TVCG.2007.1055 10.1016/j.cag.2009.10.005 10.1007/BFb0080116 10.1137/0910004 10.1111/cgf.12351 10.1007/BF01385726 10.1162/105474601753132696 10.1145/1599470.1599492 10.1016/S1524-0703(03)00045-6 10.1080/10255840500295852 10.1145/2601097.2601116 10.1016/j.cag.2014.01.003 10.1137/0915022 10.1145/1477926.1477934 10.1145/2010324.1964932 10.1016/j.gmod.2005.03.007 10.1137/1.9780898718003 10.1145/1028523.1028541 10.1016/j.gmod.2010.10.001 10.1137/0907058 10.1007/s00371-008-0243-y 10.1145/2366145.2366216 10.1145/280814.280821 10.1007/s10916-006-9021-4 10.1137/0913035 10.1007/978-3-540-70521-5_5 10.1111/j.1467-8659.2012.03230.x 10.1145/1073368.1073394 10.1145/1964921.1964986 10.1109/ARITH.2007.25 10.1145/1778765.1778775 |
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Comput.1994152313337126145610.1137/09150220803.65036 P Sonneveld (1225_CR40) 1989; 10 I Chao (1225_CR8) 2010; 29 1225_CR18 R Schmedding (1225_CR37) 2008; 24 C Song (1225_CR39) 2014; 40 RW Freund (1225_CR13) 1991; 60 R Kikuuwe (1225_CR19) 2009; 28 1225_CR30 HA van der Vorst (1225_CR43) 1992; 13 RW Freund (1225_CR14) 1994; 15 BA Lloyd (1225_CR21) 2007; 13 1225_CR16 1225_CR36 O Civit-Flores (1225_CR9) 2014; 33 1225_CR11 1225_CR12 1225_CR34 1225_CR10 G Irving (1225_CR17) 2006; 68 T Liu (1225_CR20) 2013; 32 T Patterson (1225_CR31) 2012; 31 1225_CR28 K Hirota (1225_CR15) 2001; 10 1225_CR29 S Natsupakpong (1225_CR26) 2010; 72 H Wang (1225_CR44) 2015; 34 M Nakao (1225_CR25) 2006; 30 G Picinbono (1225_CR33) 2003; 65 S Bouaziz (1225_CR6) 2014; 33 FS Sin (1225_CR38) 2013; 32 J Barbič (1225_CR3) 2005; 24 H Zhong (1225_CR45) 2005; 8 1225_CR4 1225_CR5 1225_CR41 1225_CR2 I Peterlík (1225_CR32) 2010; 34 1225_CR7 1225_CR27 Y Saad (1225_CR35) 1986; 7 1225_CR24 1225_CR22 1225_CR1 1225_CR23 1225_CR42 |
| References_xml | – reference: SaadYSchultzMHGMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systemsSIAM J. Sci. Comput.19867385686984856810.1137/09070580599.65018 – reference: ZhongHWachowiakMPPetersTMA real time finite element based tissue simulation method incorporating nonlinear elastic behaviorComput. Methods Biomech. Biomed. Eng.20058317718910.1080/10255840500295852 – reference: Nesme, M., Payan, Y., Faure, F.: Efficient, physically plausible finite elements. In: Eurographics, short presentations, pp. 77–80 (2005) – reference: Stomakhin, A., Howes, R., Schroeder, C., Teran, J.M.: Energetically consistent invertible elasticity. In: Proceedings of ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 25–32 (2012) – reference: McAdams, A., Zhu, Y., Selle, A., Empey, M., Tamstorf, R., Teran, J., Sifakis, E.: Efficient elasticity for character skinning with contact and collisions. ACM Trans. Graph. 30(4), 37 (2011) (article 37) – reference: Nienhuys, H.W., van der Stappen, F.A.: Combining finite element deformation with cutting for surgery simulations. In: Proceedings of Eurographics, pp. 43–52 (2000) – reference: Bickel, B., Wicke, M., Gross, M.: Adaptive simulation of electrical discharges. In: Proceedings of Vision, Modeling, and Visualization, pp. 209–216 (2006) – reference: IrvingGTeranJFedkiwRTetrahedral and hexahedral invertible finite elementsGraph. Models2006682668910.1016/j.gmod.2005.03.0071125.74050 – reference: Fletcher, R.: Conjugate gradient methods for indefinite systems. In: Dold, A., Eckmann, B. (eds.) Numerical Analysis. Lecture Notes in Mathematics, vol. 506, pp. 73–89. Springer, New York (1976) – reference: FreundRWNachtigalNMQMR: a quasi-minimal residual method for non-Hermitian linear systemNumer. Math.1991601315339113719710.1007/BF013857260754.65034 – reference: van der VorstHABi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systemsSIAM J. Sci. Comput.1992132631644114911110.1137/09130350761.65023 – reference: Myronenko, A., Song, X.: On the closed-form solution of the rotation matrix arising in computer vision problems (2009). arXiv:0904.1613 – reference: Desbrun, M., Schröder, P., Barr, A.H.: Interactive animation of structured deformable objects. In: Proceedings of the 1999 Conference on Graphics Interface, pp. 1–8 (1999) – reference: Nocedal, J., Wright, S.J.: Numerical optimization, 2nd edn. Springer Series in Operations Research and Financial Engineering. Springer, New York (2006) – reference: PicinbonoGDelingetteHAyacheNNon-linear anisotropic elasticity for real-time surgery simulationGraph. Models200365530532110.1016/S1524-0703(03)00045-61054.68165 – reference: SonneveldPCGS, a fast Lanczos-type solver for nonsymmetric linear systemsSIAM J. Sci. Stat. Comput.1989101365297616010.1137/09100040666.65029 – reference: Teran, J., Sifakis, E., Irving, G., Fedkiw, R.: Robust quasistatic finite elements and flesh simulation. In: Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 181–190 (2005) – reference: FreundRWNachtigalNMAn implementation of the QMR method based on coupled two-term recurrencesSIAM J. Sci. Comput.1994152313337126145610.1137/09150220803.65036 – reference: PattersonTMitchellNSifakisESimulation of complex nonlinear elastic bodies using lattice deformersACM Trans. Graph.201231619710.1145/2366145.2366216 – reference: WangHA Chebyshev semi-iterative approach for accelerating projective and position-based dynamicsACM Trans. Graph.2015346246 – reference: KikuuweRTabuchiHYamamotoMAn edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elementsACM Trans. Graph.2009281810.1145/1477926.1477934 – reference: NatsupakpongSÇavuşoğluMCDetermination of elasticity parameters in lumped element (mass-spring) models of deformable objectsGraph. Models2010726617310.1016/j.gmod.2010.10.001 – reference: SinFSSchroederDBarbičJVega: Non-linear FEM deformable object simulatorComput. Graph. Forum2013321364810.1111/j.1467-8659.2012.03230.x – reference: HirotaKKanekoTHaptic representation of elastic objectsPresence200110552553610.1162/105474601753132696 – reference: Baraff, D., Witkin, A.: Large steps in cloth simulation. In: Proceedings of ACM SIGGRAPH, pp. 43–54 (1998) – reference: ChaoIPinkallUSananPSchröderPA simple geometric model for elastic deformationsACM Trans. 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| SubjectTerms | Algorithms Approximation Artificial Intelligence Computer Graphics Computer Science Deformation Equations of motion Formability Haptics Image Processing and Computer Vision Iterative methods Linear equations Mathematical analysis Original Article Simulation Stiffness matrix Taylor series Time integration |
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| Title | A time-integration method for stable simulation of extremely deformable hyperelastic objects |
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