Abstract
We consider prediction strategies in a parallel coupling scheme for modular co-simulation: local extrapolation and a linear-implicit stabilization technique based on model information. That is, concerning local extrapolation, instead of using data points at the macro time points for generating the extrapolation polynomial (as it is done in the conventional global case), we use local data points only within the last macro time step. The linear-implicit stabilization technique predicts coupling quantities based on model information in terms of Jacobian matrices by performing a linear-implicit Euler step forward in time. We introduce and discuss these two prediction strategies and analyze their numerical properties, stability and accuracy, based on a simple test model.
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References
Arnold, M.: Multi-rate time integration for large scale multibody system models. In: IUTAM Symposium on Multiscale Problems in Multibody System Contacts, held in Stuttgart, Germany (2006)
Arnold, M.: Stability of sequential modular time integration methods for coupled multibody system models. J. Comput. Nonlinear Dyn. 5, 031003 (2010)
Arnold, M., Clauß, C., Schierz, T.: Error analysis and error estimates for co-simulation in FMI for model exchange and co-simulation v2.0. Arch. Mech. Eng. LX, 75–94 (2013)
Arnold, M., Günther, M.: Preconditioned dynamic iteration for coupled differential-algebraic systems. BIT Numer. Math. 41(1), 001–025 (2001)
Bartel, A., Brunk, M., Schüps, S.: On the convergence rate of dynamic iteration for coupled problems with multiple subsystems. J. Comput. Appl. Math. 262, 14–24 (2014). Selected Papers from NUMDIFF-13
Burger, M., Gerdts, M.: A survey on numerical methods for the simulation of initial value problems with DAEs. In: Ilchmann, A., Reis, T. (eds.) Surveys in Differential-Algebraic Equations IV. Differential-Algebraic Equations Forum, pp. 221–300. Springer International Publishing, Cham (2017)
Busch, M.: Zur Effizienten Kopplung von Simulationsprogrammen. Kassel University Press (2012)
Busch, M., Schweizer, B.: Numerical stability and accuracy of different co-simulation techniques: Analytical investigations based on a 2-dof test model. In: The 1st Joint International Conference on Multibody System Dynamics, Lappeenranta, Finland, 25–27 May 2010
Jackson, K.R.: A survey of parallel numerical methods for initial value problems for ordinary differential equations. IEEE Trans. Mag. 27(5), 3792–3797 (1991)
Kübler, R., Schiehlen, W.: Two methods of simulator coupling. Math. Comput. Model. Dyn. Syst. 6(2), 93–113 (2000)
Schierz, T., Arnold, M.: Stabilized overlapping modular time integration of coupled differential-algebraic equations. Appl. Numer. Math. 62(10), 1491–1502 (2012). Selected Papers from NUMDIFF-12
Veitl, A., Gordon, T., van de Sand, A., Howell, M., Valášek, M., VaculÃn, O., Steinbauer, P.: Methodologies for coupling simulation models and codes in mechatronic system analysis and design. In: Proceedings of the 16th IAVSD-Symposium on Dynamics of Vehicles on Roads and Tracks. Pretoria, volume 33 of Supplement to Vehicle System Dynamics, pp. 231–243. Swets & Zeitlinger (1999)
Viel, A.: Implementing stabilized co-simulation of strongly coupled systems using the functional mock-up interface 2.0. In: Proceedings of the 10th International Modelica Conference, Lund, Sweden (2014)
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Burger, M., Steidel, S. (2019). Local Extrapolation and Linear-Implicit Stabilization in a Parallel Coupling Scheme. In: Schweizer, B. (eds) IUTAM Symposium on Solver-Coupling and Co-Simulation. IUTAM Bookseries, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-030-14883-6_3
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DOI: https://doi.org/10.1007/978-3-030-14883-6_3
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