Abstract
In engineering, it is a common desire to couple existing simulation tools together into one big system by passing information from subsystems as parameters into the subsystems under influence. As executed at fixed time points, this data exchange gives the global method a strong explicit component. Globally, such an explicit co-simulation schemes exchange time step can be seen as a step of an one-step method which is explicit in some solution components. Exploiting this structure, we give a convergence proof for such schemes. As flows of conserved quantities are passed across subsystem boundaries, it is not ensured that system-wide balances are fulfilled: the system is not solved as one single equation system. These balance errors can accumulate and make simulation results inaccurate. Use of higher-order extrapolation in exchanged data can reduce this problem but cannot solve it. The remaining balance error has been handled in past work by recontributing it to the input signal in next coupling time step, a technique labeled balance correction methods. Convergence for that method is proven. Further, the lack of stability for co-simulation schemes with and without balance correction is stated.
References
[1] M. Arnold, C. Bausch, T. Blochwitz, C. Clauß, M. Monteiro, T. Neidhold, J.-V. Peetz, and S. Wolf, Functional Mock-up Interface for Co-Simulation, 2010.Search in Google Scholar
[2] M. Arnold, C. Clauss, and T. Schierz, Error analysis and error estimates for co-simulation in FMI for model exchange and co-simulation v2.0, The Archive of Mechanical Engineering60 (2013), No. 1, 75–94.10.2478/meceng-2013-0005Search in Google Scholar
[3] M. Arnold and M. Günther, Preconditioned dynamic iteration for coupled differential-algebraic systems, BIT Numer. Math. 41 (2001), 1–25.10.1023/A:1021909032551Search in Google Scholar
[4] M. Busch, Zur effizienten Kopplung von Simulationsprogrammen, Ph.D. thesis, Kassel Univ., 2012.Search in Google Scholar
[5] P. Deuflhard and F. Bornemann, Numerische Mathematik, II, de Gruyter, Berlin, 1994.Search in Google Scholar
[6] R. Kossel, Hybride Simulation thermischer Systeme am Beispiel eines Reisebusses, Ph.D. thesis, Braunschweig, Techn. Univ., 2012, 112 p.Search in Google Scholar
[7] R. Kübler and W. Schiehlen, Modular simulation in multibody system dynamics, Multibody System Dynamics4 (2000), 107–127.10.1023/A:1009810318420Search in Google Scholar
[8] U. Miekkala and O. Nevanlinna, Convergence of dynamic iteration methods for initial value problems, SIAM J. Sci. Stat. Comput. 8 (1987), 459–482.10.1137/0908046Search in Google Scholar
[9] D. Scharff, C. Kaiser, W. Tegethoff, and M. Huhn, Ein einfaches Verfahren zur Bilanzkorrektur in Kosimulationsumgebungen. In: SIMVEC Berechnung, Simulation und Erprobung im Fahrzeugbau. 2012, Baden-Baden, Germany, VDI-Berichte, 2169 (2012), 581–596.Search in Google Scholar
[10] D. Scharff, T. Moshagen, and J. Vondřejc, Treating smoothness and balance during data exchange in explicit simulator coupling or cosimulation, arXiv: 1703.05522, (2017), 30 p.Search in Google Scholar
[11] S. Sicklinger, V. Belsky, B. Engelmann, H. Elmqvist, H. Olsson, R. Wüchner, and K.-U. Bletzinger, Interface Jacobian-based co-simulation, Int. J. Numer. Meth. Engrg. 98 (2014), No. 6, 418–444.10.1002/nme.4637Search in Google Scholar
[12] M. Wells, J. Hasan, and C. Lucas, Predictive hold with error correction techniques that maintain signal continuity in co-simulation environments, SAE Int. J. Aerosp. 5 (2012), No. 2, 481–493.10.4271/2012-01-2205Search in Google Scholar
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