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Remarks on the gluing algorithm for multibody systems co-simulation

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper briefs a part of authors’ study on co-simulation techniques and their application to multibody system dynamics. The main concern of the study is on construction and properties of algorithms that are suitable for such purpose. One of the proposed methods from literature is so-called “gluing-algorithm” by Wang et al. These authors proposed Newton iteration to couple several simulators of mechanical subsystems through constraints/reactions, and provided numerical examples to suggest efficiency of the method. Here we re-investigate the method in order to underline some problems that one might meet when using the “gluingalgorithm”.
Rocznik
Strony
19--32
Opis fizyczny
Bibliogr. 37 poz., rys., tab., wykr.
Twórcy
autor
  • IAAM, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland
autor
  • IAAM, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland
Bibliografia
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  • [2] Lelarasmee, Ekachai. The Waveform Relaxation Method for Time Domain Analysis of Large Scale Integrated Circuits: Theory and Applications. PhD thesis. Berkeley, CA: University of California, 1982.
  • [3] Harchel Gary D., and Alberto L. Sangiovanni-Vincentelli. “A survey of third-generation simulation techniques”. Proceedings of the IEEE 69 (1981): 1264–1280.
  • [4] Bae, Dae Sung, Jon G. Kuhl, and Edward J. Haug. “A recursive formulation for constrained mechanical system dynamics. Part III: Parallel processor implementa tion”. Mechanics of Structures and Machines 16(2), 1988: 249–269.
  • [5] Bae, Dae Sung, and Edward J. Haug. “A recursive formulation for constrained mechanical system dynamics. Part I: Open loop systems”. Mechanics of Structures and Machines, 15(3), 1987: 383–393.
  • [6] Bae, Dae Sung, and Edward J. Haug. “A recursive formulation for constrained mechanical system dynamics. Part II: Closed loop systems”. Mechanics of Structures and Machines 15(4), 1987: 481–506.
  • [7] Featherstone, Roy. “A divide-and-conquer articulated--body algorithm for parallel O(log(n)) calculation of rigid--body dynamics. Part 1: Basic algorithm”. The International Journal of Robotics Research 18(9), 1999: 867–875.
  • [8] Featherstone, Roy. “A divide-and-conquer articulated-body algorithm for parallel O(log(n)) calculation of rigid-body dynamics. Part 1: Trees, loops, and accuracy”. The International Journal of Robotics Research 18(9), 1999: 876–892.
  • [9] Kim, Sung-Soo. “A subsystem synthesis method for efficient vehicle multibody dynamics”. Multibody System Dynamics 7 (2002): 189–207.
  • [10] Anderson Kurt S., and S. Duan. “Highly parallelizable low order dynamics simulation algorithm for multi-rigid--body systems”. Journal of Guidance, Control and Dynamics 23(2), 2000: 355–364.
  • [11] Andrus, J.F. “Numerical solution of systems of ordinary differential equations separated into subsystems”. SIAM Journal on Numerical Analysis 16(4), 1979: 605–611.
  • [12] Wells, Daniel Raymond. Multirate linear multistep methods for the solution of systems of ordinary diff erential equations. PhD thesis. Champaign, IL, USA, 1982.
  • [13] Gear, C.W., and D.R. Wells. “Multirate linear multistep methods”. BIT 24(4), 1984: 484–502.
  • [14] Hippmann, Gerhard, Martin Arnold, and Marcus Schittenhelm. “Efficient simulation of bush and roller chain drives”. In: Multibody Dynamics 2005, ECCOMAS Thematic Conference, Madrid, Spain, June 2005.
  • [15] Arnold, Martin. “Multi-rate time integration for large scale multibody system models”. In: IUTAM Symposium on Multiscale Problems in Multibody System Contacts 1 (2007): 1–10.
  • [16] Lelarasmee, Ekachai, Albert E. Ruehli, and Alberto L. Sangiovanni-Vincentelli. “The waveform relaxation method for time-domain analysis of large scale integrated circuits”. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 1(3), 1982: 131–145.
  • [17] Hale, Jack K. Ordinary Differential Equations. Mineola, N.Y.: Dover Publications, Inc., 2009 [Originally published: New York: Wiley, 1969].
  • [18] White, J., et al. Waveform relaxation: Theory and practice. Technical Report UCB/ERL M85/65, Berkeley: EECS Department, University of California, 1985.
  • [19] Miekkala, Ulla, and Nevanlinna Olavi. “Convergence of dynamic iteration methods for initial value problems”. SIAM Journal of Scientifi c and Statistical Computing 8(4), 1987: 459–482.
  • [20] Miekkala, Ulla, and Olavi Nevanlinna. “Sets of convergence and stability regions”. BIT Numerical Mathematics 27 (1987): 554–584. 10.1007/BF01937277.
  • [21] Nevanlinna, Olavi. “Remarks on Picard-Lindelöf iteration”. BIT Numerical Mathematics 29 (1989): 328--346. 10.1007/BF01952687.
  • [22] Nevanlinna, Olavi. “Remarks on Picard-Lindelöf iteration”. BIT Numerical Mathematics 29 (1989): 535--562. 10.1007/BF02219239.
  • [23] Nevanlinna, Olavi. “Power bounded prolongations and Picard-Lindelöf iteration”. Numerische Mathematik 58 (1990): 479–501. 10.1007/BF01385637.
  • [24] Miekkala, Ulla. “Dynamic iteration methods applied to linear DAE systems”. Journal of Computation and Applied Mathematics 25(2), 1989: 133–151.
  • [25] Leimkühler, Ben. “Estimating waveform relaxation convergence”. SIAM Journal of Scientifi c Computing 14 (1993): 872–889.
  • [26] Leimkühler, Ben. “Relaxation techniques in multi-body dynamics”. Transactions of Canadian Society for Mechanical Engineering 17(4A), 1993: 459–471.
  • [27] Arnold, Martin, and Michael Günther. “Preconditioned dynamic iteration for coupled differential-algebraic systems”. BIT Numerical Mathematics 41 (2001): 1–25. 10.1023/A:1021909032551.
  • [28] Sun, Wei, Jian-Hua Zou, and Xiao-Guang Fan. “Convergence of parallel dynamic iteration methods for nonlinear daes of index-2”. In: Automation Science and Engineering, 2006. CASE ’06. IEEE International Conference, Oct. 2006: 129–133.
  • [29] Burrage, Kevin. Parallel and Sequential Methods for Ordinary Diff erential Equations. Oxford: Clarendon Press, 1995.
  • [30] Wang, Jinzhong, Zheng-Dong Ma, and Gregory Hulbert. “A gluing algorithm for distributed simulation of multibody systems”. Nonlinear Dynamics 34 (2003): 159–188.
  • [31] Wang, Jinzhong, Zheng-Dong Ma, and Gregory Hulbert. “Gluing for dynamic simulation of distributed mechanical systems”. Advances in Computational Multibody Systems 5 (2005): 69–94.
  • [32] Wang, Jinzhong, Zheng-Dong Ma, and Gregory Hulbert. “A distributed mechanical system simulation platform based on a ‘gluing algorithm’”. Journal of Computing and Information Science in Engineering 5 (2005): 71–76.
  • [33] Gu, Bei, W. Gordon, and H. Harry Asada. “Co--simulation of coupled dynamic subsystems: A differential--algebraic approach using singularly perturbed sliding manifolds”. In: Proceedings of the American Control Conference, Chicago, Illinois, June 2000.
  • [34] Gu, Bei, and H. Harry Asada. “Co-simulation of algebraically coupled dynamic subsystems”. In: Proceedings of the American Control Conference, Arlington,VA, June 2001.
  • [35] Gu, Bei, and Harry H. Asada. “Co-simulation of algebraically coupled dynamic subsystems without disclosure of proprietary subsystem models”. ASME Journal of Dynamic Systems, Measurement and Control 126(1), 2004: 1–13.
  • [36] Gear, C.W., G.K. Gupta, and B. Leimkühler. “Automatic integration of Euler-Lagrange equations with constraints”. Journal of Computational and Applied Mathematics 12 (1985): 77–90.
  • [37] The MathWorks, Inc. MATLAB function reference.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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