zbMATH — the first resource for mathematics

Using Nesterov’s method to accelerate multibody dynamics with friction and contact. (English) Zbl 1333.68258

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68U20 Simulation (MSC2010)
70E55 Dynamics of multibody systems
Full Text: DOI
[1] V. Acary, F. Cadoux, C. Lemarechal, and J. Malick. 2011. A formulation of the linear discrete Coulomb friction problem via convex optimization. ZAMM- J. Appl. Math. Mechan./Zeitschrift fur Angewandte Mathematik und Mechanik 91, 2, 155–175. · Zbl 1370.74114 · doi:10.1002/zamm.201000073
[2] M. A. Ambroso, C. R. Santore, A. R. Abate, and D. J. Durian. 2005. Penetration depth for shallow impact cratering. Phys. Rev. E71, 051305. · doi:10.1103/PhysRevE.71.051305
[3] E. Andersen and K. Andersen. 2000. The mosek interior point optimizer for linear programming: An implementation of the homogeneous algorithm. In High Performance Optimization, H. Frenk, K. Roos, T. Terlaky, and S. Zhang, Eds., Springer, 197–232. · Zbl 1028.90022 · doi:10.1007/978-1-4757-3216-0_8
[4] E. Andersen, C. Roos, and T. Terlaky. 2003. On implementing a primal-dual interior-point method for conic quadratic optimization. Math. Program. 95, 2, 249–277. · Zbl 1030.90137 · doi:10.1007/s10107-002-0349-3
[5] M. Anitescu. 2006. Optimization-based simulation of nonsmooth rigid multibody dynamics. Math. Program. 105, 1, 113–143. · Zbl 1085.70008 · doi:10.1007/s10107-005-0590-7
[6] M. Anitescu, J. F. Cremer, and F. A. Potra. 1996. Formulating 3D contact dynamics problems. Mechan. Struct. Mach. 24, 4, 405–437. · doi:10.1080/08905459608905271
[7] M. Anitescu and G. D. Hart. 2004. A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction. Int. J. Numer. Meth. Engin. 60, 14, 2335–2371. · Zbl 1075.70501 · doi:10.1002/nme.1047
[8] M. Anitescu and A. Tasora. 2010. An iterative approach for cone complementarity problems for nonsmooth dynamics. Comput. Optim. Appl. 47, 2, 207–235. · Zbl 1200.90160 · doi:10.1007/s10589-008-9223-4
[9] A. Beck and M. Teboulle. 2009. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2, 1, 183–202. · Zbl 1175.94009 · doi:10.1137/080716542
[10] S. R. Becker, E. J. Candes, and M. C. Grant. 2011. Templates for convex cone problems with applications to sparse signal recovery. Math. Program. Comput. 3, 3, 165–218. · Zbl 1257.90042 · doi:10.1007/s12532-011-0029-5
[11] F. Bertails-Descoubes, F. Cadoux, G. Daviet, and V. Acary. 2011. A nonsmooth Newton solver for capturing exact Coulomb friction in fiber assemblies. ACM Trans. Graph. 30, 1, 6.
[12] D. Bertsekas. 1976. On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans. Autom. Control 21, 2, 174–184. · Zbl 0326.49025 · doi:10.1109/TAC.1976.1101194
[13] K. Bodin, C. Lacoursiere, and M. Servin. 2012. Constraint fluids. IEEE Trans. Visual. Comput. Graph. 18, 3, 516–526. · doi:10.1109/TVCG.2011.29
[14] O. Bonnefon and G. Daviet. 2011. Quartic formulation of Coulomb 3D frictional contact. Tech. rep. Rapport Technique RT-0400, INRIA.
[15] R. Bridson, R. Fedkiw, and J. Anderson. 2002. Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. Graph. 21, 3, 594–603. · Zbl 05457161 · doi:10.1145/566654.566623
[16] N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, and T. Poschel. 1996. Model for collisions in granular gases. Phys. Rev. E53, 5, 5382.
[17] F. Cadoux. 2009. An optimization-based algorithm for Coulomb’s frictional contact. ESAIM: Proc. 27, 54–69. · Zbl 1167.74049 · doi:10.1051/proc/2009019
[18] Cauchy, A. 1847. Methode generale pour la resolution des systemes d’equations simultanees. Comput. Rend. Sci. Paris 25, 1847, 536–538.
[19] R. W. Cottle, J.-S. Pang, and R. E. Stone. 2009. The Linear Complementarity Problem. Academic Press, New York. · Zbl 1192.90001 · doi:10.1137/1.9780898719000
[20] P. Cundall. 1971. A computer model for simulating progressive large-scale movements in block rock mechanics. In Proceedings of the International Symposium on Rock Mechanics.
[21] P. Cundall. 1988. Formulation of a three-dimensional distinct element model-Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int. J. Rock Mechan. Mining Sci. Geomechan. Abstr. 25, 3, 107–116. · doi:10.1016/0148-9062(88)92293-0
[22] P. Cundall and O. Strack. 1979. A discrete element model for granular assemblies. Geotechniq. 29, 47–65. · doi:10.1680/geot.1979.29.1.47
[23] G. Daviet, F. Bertails-Descoubes, and L. Boissieux. 2011. A hybrid iterative solver for robustly capturing Coulomb friction in hair dynamics. ACM Trans. Graph. 30, 139. · doi:10.1145/2070781.2024173
[24] G. De Saxce and Z.-Q. Feng. 1998. The bipotential method: A constructive approach to design the complete contact law with friction and improved numerical algorithms. Math. Comput. Model. 28, 4, 225–245. · Zbl 1126.74341 · doi:10.1016/S0895-7177(98)00119-8
[25] R. Delannay, M. Louge, P. Richard, N. Taberlet, and A. Valance. 2007. Towards a theoretical picture of dense granular flows down inclines. Nature Mater. 6, 2, 99–108. · doi:10.1038/nmat1813
[26] J. W. Demmel. 2011. SuperLu users’ guide. http://crd.lbl.gov/∼xiaoye/SuperLU/superlu_ug.pdf.
[27] S. P. Dirkse and M. C. Ferris. 1995. The PATH solver: A nonmonotone stabilization scheme for mixed complementarity problems. Optim. Meth. Softw. 5, 2, 123–156. · doi:10.1080/10556789508805606
[28] K. Erleben. 2007. Velocity-based shock propagation for multibody dynamics animation. ACM Trans. Graph. 26, 2, 12.
[29] A. Filippov. 1967. Classical solutions of differential equations with multi-valued right-hand side. SIAM J. Control 5, 4, 609–621. · Zbl 0238.34010 · doi:10.1137/0305040
[30] D. M. Flickinger, J. Williams, and J. Trinkle. 2013. What’s wrong with collision detection in multibody dynamic simulation? In Proceedings of the IEEE International Conference on Robotics and Automation (ICRA’13). 959–964.
[31] C. Glocker and F. Pfeiffer. 2006. An LCP-approach for multibody systems with planar friction. In Proceedings of the International Symposium on Contact Mechanics (CMIS’06). 13–20.
[32] E. Guendelman, R. Bridson, and R. Fedkiw. 2003. Nonconvex rigid bodies with stacking. ACM Trans. Graph. 22, 871–878. · Zbl 05457319 · doi:10.1145/882262.882358
[33] E. J. Haug. 1989. Computer-Aided Kinematics and Dynamics of Mechanical Systems, Vol. 1. Prentice-Hall, Englewood Cliffs, NJ.
[34] T. Heyn. 2013. On the modeling, simulation, and visualization of many-body dynamics problems with friction and contact. Ph.D. thesis. Department of Mechanical Engineering, University of Wisconsin-Madison.
[35] T. Heyn, M. Anitescu, A. Tasora, and D. Negrut. 2013. Using Krylov subspace and spectral methods for solving complementarity problems in many-body contact dynamics simulation. Int. J. Numer. Meth. Engin. 95, 7, 541–561. · Zbl 1352.74206 · doi:10.1002/nme.4513
[36] Intel. 2013. The Intel math kernel library sparse matrix vector multiply format prototype package. http://software.intel.com/en-us/article/the-intel-math-kernel-library-sparse-matrix-vector-multiply-format-prot otype-package.
[37] H. M. Jaeger, S. R. Nagel, and R. P. Behringer. 1996. Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1273. · doi:10.1103/RevModPhys.68.1259
[38] K. L. Johnson. 1987. Contact Mechanics. Cambridge University Press. · Zbl 0599.73108
[39] C. Kane, E. Repetto, M. Ortiz, and J. Marsden. 1999. Finite element analysis of nonsmooth contact. Comput. Meth. Appl. Mechan. Engin. 180, 1, 1–26. · Zbl 0963.74061 · doi:10.1016/S0045-7825(99)00034-1
[40] D. M. Kaufman and D. K. Pai. 2012. Geometric numerical integration of inequality constrained, nonsmooth Hamiltonian systems. SIAM J. Sci. Comput. 34, 5, A2650–A2703. · Zbl 1259.65202 · doi:10.1137/100800105
[41] A. Li, R. Serban, and D. Negrut. 2013. A SPIKE-based approach for the parallel solution of sparse linear systems on GPU cards. Tech. rep. TR-2013-05, University of Wisconsin-Madison. http://sbel.wisc.edu/documents/TR-2013-05.pdf. · Zbl 1366.65050
[42] S. Luding. 2005. Molecular dynamics simulations of granular materials. In The Physics of Granular Media, H. Hinrichsen and D. E. Wolf, Eds., Wiley-VCH, Weinheim, Germany. 299–324. · doi:10.1002/352760362X.ch13
[43] H. Mazhar, J. Bollman, E. Forti, A. Praeger, T. Osswald, and D. Negrut, 2013a. Studying the effect of powder geometry of the selective laser sintering process. Tech. rep. TR-2013-03, Simulation-Based Engineering Laboratory, University of Wisconsin-Madison. http://sbel.wisc.edu/documents/TR-2013-03.pdf.
[44] H. Mazhar, T. Heyn, A. Pazouki, D. Melanz, A. Seidl, A. Bartholomew, A. Tasora, and D. Negrut. 2013b. Chrono: A parallel multi-physics library for rigid-body, flexible-body, and fluid dynamics. Mechan. Sci. 4, 1, 49–64. · doi:10.5194/ms-4-49-2013
[45] H. Mazhar, D. Melanz, M. Ferris, and D. Negrut. 2014a. An analysis of several methods for handling hard-sphere frictional contact in rigid multibody dynamics. Tech. rep. TR-2014-11, Simulation-Based Engineering Laboratory, University of Wisconsin-Madison. http://sbel.wisc.edu/documents/TR-2014-11.pdf.
[46] H. Mazhar, J. Schneider, and D. Negrut. 2014b. Preliminary results for helical anchoring project. Tech. rep. TR-2014-10, Simulation-Based Engineering Laboratory. University of Wisconsin-Madison, http://sbel.wisc.edu/documents/TR-2014-10.pdf.
[47] H. Mazhar, T. Heyn, and D. Negrut. 2011. A scalable parallel method for large collision detection problems. Multibody Syst. Dynam. 26, 37–55. · Zbl 1287.70004 · doi:10.1007/s11044-011-9246-y
[48] J. J. Moreau and M. Jean. 1996. Numerical treatment of contact and friction: The contact dynamics method. In Proceedings of the 3rdBiennial Joint Conference on Engineering Systems and Analysis (ESDA’96). 201–208.
[49] A. Nemirovsky and D. B. Yudin. 1983. Problem Complexity and Method Efficiency in Optimization. John Wiley and Sons.
[50] Y. Nesterov. 2003. A method of solving a convex programming problem with convergence rate O (1/k2). Soviet Math. Doklady 27, 2, 372–376.
[51] Y. Nesterov. 2003. Introductory Lectures on Convex Optimization: A Basic Course, Vol. 87. Springer. · Zbl 1086.90045
[52] B. O’Donoghue and E. Candes. 2012. Adaptive restart for accelerated gradient schemes. ArXiv e-prints.
[53] T. Poschel and T. Schwager. 2005. Computational Granular Dynamics: Models and Algorithms. Springer.
[54] T. M. Preclik, K. I. Iglberger, and U. Rude. 2009. Iterative rigid multi-body dynamics. In Proceedings of the Thematic Conference on Multibody Dynamics (ECCOMAS’09).
[55] T. M. Preclik and U. Rude. 2011. Solution existence and non-uniqueness of Coulomb friction. Tech. rep. 4, Friedrich-Alexander University Erlangen-Nurnberg, Institut fur Informatik, Nurnberg, Germany.
[56] O. Schenk and K. Gartner. 2004. Solving unsymmetric sparse systems of linear equations with Pardiso. Future Generat. Comput. Syst. 20, 3, 475–487. · doi:10.1016/j.future.2003.07.011
[57] Z. Shojaaee, M. R. Shaebani, L. Brendel, J. Toeroek, and D. E. Wolf. 2012. An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials. J. Comput. Phys. 231, 2, 612–628. · Zbl 1285.74016 · doi:10.1016/j.jcp.2011.09.024
[58] B. Smith, D. M. Kaufman, G. Vouga, R. Tamstorf, and E. Grinspun. 2012. Reflections on simultaneous impact. ACM Trans. Graph. 31, 4, 106:1–106:12.
[59] D. E. Stewart. 2000. Rigid-body dynamics with friction and impact. SIAM Rev. 42, 1, 3–39. · Zbl 0962.70010 · doi:10.1137/S0036144599360110
[60] D. E. Stewart and J. C. Trinkle. 1996. An implicit time-stepping scheme for rigid-body dynamics with inelastic collisions and Coulomb friction. Int. J. Numer. Meth. Engin. 39, 2673–2691. · Zbl 0882.70003 · doi:10.1002/(SICI)1097-0207(19960815)39:15<2673::AID-NME972>3.0.CO;2-I
[61] B.-Y. Su and K. Keutzer. 2012. clSpMV: A cross-platform OpenCL SpMV framework on GPUs. In Proceedings of the 26thACM International Conference on Supercomputing (ICS’12). ACM Press, New York, 353–364. · doi:10.1145/2304576.2304624
[62] A. Tasora and M. Anitescu. 2013. A complementarity-based rolling friction model for rigid contacts. Meccanica 48, 7, 1643–1659. · Zbl 1293.70052 · doi:10.1007/s11012-013-9694-y
[63] A. Tasora, M. Anitescu, S. Negrini, and D. Negrut. 2013. A compliant visco-plastic particle contact model based on differential variational inequalities. Int. J. Non-Linear Mechan. 53, SI, 2–12.
[64] A. Tasora, D. Negrut, and M. Anitescu. 2008. Large-scale parallel multi-body dynamics with frictional contact on the graphical processing unit. J. Multi-Body Dynam. 222, 4, 315–326. · doi:10.1243/14644193JMBD154
[65] R. Tonge, F. Benevolenski, and A. Voroshilov. 2012. Mass splitting for jitter-free parallel rigid body simulation. ACM Trans. Graph. 31, 4, 105.
[66] J. C. Trinkle. 2003. Formulation of multibody dynamics as complementarity problems. In Proceedings of the 19thBiennial Conference on Mechanical Vibration and Noise, Parts A, B, and C (ASME’03). Vol. 5. ASME.
[67] J. S. Uehara, M. A. Ambroso, R. P. Ojha, and D. J. Durian. 2003. Low-speed impact craters in loose granular media. Phys. Rev. Lett. 90, 194301. · doi:10.1103/PhysRevLett.90.194301
[68] L. Vu-Quoc, L. Lesburg, and X. Zhang. 2004. An accurate tangential force-displacement model for granular-flow simulations: Contacting spheres with plastic deformation, force-driven formulation. J. Comput. Phys. 196, 1, 298–326. · Zbl 1115.76416 · doi:10.1016/j.jcp.2003.10.025
[69] L. Vu-Quoc and X. Zhang. 1999. An elastoplastic contact force-displacement model in the normal direction: Displacement-driven version. Proc. Royal Soc. London Series A: Math. Phys. Engin. Sci. 455, 1991, 4013–4044. · Zbl 0984.74057 · doi:10.1098/rspa.1999.0488
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.