Preconditioned dynamic iteration for coupled differential-algebraic systems

BIT Numerical Mathematics

Volumn 41, Issue 1, 2001, Pages 1-25

  Arnold, Martin ^a   Günther, Michael ^b  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Coupled problems; Differential algebraic systems; Dynamic iteration; Waveform relaxation

Indexed keywords

EID: 0012659861     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021909032551     Document Type: Article

References (23)

1. M. Arnold, A pre-conditioned method for the dynamical simulation of coupled mechanical multibody systems, to appear in: Z. Angew. Math. Mech.
2. M. Arnold and B. Simeon, Pantograph and catenary dynamics: A benchmark problem and its numerical solution, Appl. Numer. Math., 34 (2000), pp. 345-362.
3. K. Brenan, S. Campbell, and L. Petzold, Numerical Solution of Initial-value Problems in Differential-algebraic Equations, 2nd ed., SIAM, Philadelphia, 1996.
4. K. Burrage, Z. Jackiewicz, S. Nørsett, and R. Renaut, Preconditioning waveform relaxation iterations for differential systems, BIT, 36 (1996), pp. 54-76.
5. P. Deuflhard, E. Hairer, and J. Zugck, One-step and extrapolation methods for differential-algebraic systems, Numer. Math., 51 (1987), pp. 501-516.
6. W. Duffek, Ein Fahrbahnmodell zur Simulation der dynamischen Wechselwirkung zwischen Fahrzeug und Fahrweg, Tech. Report IB 515-91-18, DLR, D-5000 Köln 90, 1991.
7. C. W. Gear and D. R. Wells, Multirate linear multistep methods, BIT, 24 (1984), pp. 484-502.
8. G. Gristede, C. Zukowski, and A. Ruehli, Measuring error propagation in waveform relaxation analysis, IEEE Trans. Circuits Systems Fund. Theory Appl., 46 (1999), pp. 337-348.
9. M. Günther and M. Arnold, Coupled simulation of partitioned differential-algebraic network models, in preparation.
10. M. Günther and P. Rentrop, Multirate ROW methods and latency of electric circiuts, Appl. Numer. Math., 13 (1993), pp. 83-102.
11. E. Hairer, S. Nørsett, and G. Wanner, Solving Ordinary Differential Equations. I. Nonstiff Problems, 2nd ed, Springer-Verlag, Berlin, 1993.
12. E. Hairer and G. Wanner, Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems, 2nd ed., Springer-Verlag, Berlin, 1996.
13. M. Hoschek, P. Rentrop, and Y. Wagner, Network approach and differential-algebraic systems in technical applications, Surveys Math. Indust., 9 (1999), pp. 49-75.
14. Z. Jackiewicz and M. Kwapisz, Convergence of waveform relaxation methods for differential-algebraic systems, SIAM J. Numer. Anal., 33 (1996), pp. 2303-2317.
15. R. Kübler and W. Schiehlen, Two methods of simulator coupling, Math. Comput. Modelling Dynamical Syst., 6 (2000), pp. 93-113.
16. E. Lelarasmee, A. Ruehli, and A. Sangiovanni-Vincentelli, The waveform relaxation method for time domain analysis of large scale integrated circuits, IEEE Trans. CAD of IC and Syst., 1 (1982), pp. 131-145.
17. R. Lewis, P. Bettess, and E. Hinton, eds., Numerical Methods in Coupled Systems, Wiley Series in Numerical Methods in Engineering, Wiley, Chichester, 1984.
18. U. Miekkala and O. Nevanlinna, Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 459-482.
19. P. Rentrop, Partitioned Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations, Numer. Math., 47 (1985), pp. 545-564.
20. R. Roberson and R. Schwertassek, Dynamics of Multibody Systems, Springer-Verlag, Berlin, 1988.
21. A. Veitl and M. Arnold, Coupled simulation of multibody systems and elastic structures, in Advances in Computational Multibody Dynamics, J. Ambrósio and W. Schiehlen, eds., IDMEC/IST, Lisbon, Portugal, 1999, pp. 635-644.
22. U. Wever and Q. Zheng, Parallel transient simulation on workstation clusters, in Progress in Industrial Mathematics at ECMI 94, H. Neunzert, ed., Wiley & Teubner, Chichester, 1996, pp. 274-284.
23. M. Witting and T. Pröpper, Cosimulation of electromagnetic fields and electrical networks in the time domain, Surveys Math. Indust., 9 (1999), pp. 101-116.