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Performance Improvement of Explicit Co-simulation Methods Through Continuous Extrapolation

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IUTAM Symposium on Solver-Coupling and Co-Simulation

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 35))

Abstract

In order to couple several simulation models, the corresponding software tools can be interconnected by means of a co-simulation. The inputs and outputs of the models depend on each other and have to be updated during the time integration process of the numerical solvers. Since the tools can only communicate at discrete macro-time points, the model inputs are mostly approximated, e.g., by using polynomial interpolation and extrapolation techniques. As a drawback of classical extrapolation methods, discontinuities occur at the macro-time points. This can slow down the solvers and reduces the efficiency of the co-simulation. The current paper considers continuous approximation techniques of \(C^0\), \(C^1\) and \(C^2\) type which are capable to overcome the discontinuity issues. The approaches are analyzed regarding numerical stability, global error and performance. To show the benefit of the continuity, the methods are implemented in a master-slave co-simulation and a comparison with the classical discontinuous approach is done. The \(C^2\)-continuous approach mostly outperforms the methods of lower continuity. The \(C^0\)-continuous method fails due to a limitation of the error order. With a here-presented enhancement the order drop of the \(C^0\)-continuous method can be avoided.

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Notes

  1. 1.

    www.modelisar.org.

  2. 2.

    www.tlk-thermo.com.

  3. 3.

    Using a sequential Gauss-Seidel method for the co-simulation, one subsystem obtains extrapolated and the other subsystem obtains interpolated coupling variables while both subsystems obtain extrapolated coupling variables if a parallel Jacobi method is applied.

  4. 4.

    For constraint couplings, the zero-stability of the co-simulation method depends on the structure of the submodels, e.g., on the ratio of masses. Several stabilization techniques exist to generate zero-stable explicit methods for constraint couplings, see e.g. the overlapping technique in Ref. [5]. However, these methods are mostly based on an adaption of the model equations in the subsystems which is hardly realizable in commercial simulation tools. In contrast, for applied-force couplings the zero-stability of explicit co-simulation methods is always guaranteed as long as the subsystem solvers are zero-stable and the applied forces do not depend on accelerations, see Refs. [9, 25].

  5. 5.

    The approximation error is only limited at 1e-12 due to round-off errors in the computer arithmetic.

  6. 6.

    For a classical co-simulation, where both subsystems are solved on different process instances, the coupling has to be accomplished with inter-process communication which is more difficult to implement. The numerical approximation methods can however be applied in the same way.

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  1. Wiesenstraße 28, 91469, Hagenbüchach, Germany

    Martin Busch

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  1. Institut für Angewandte Dynamik, Technische Universität Darmstadt, Darmstadt, Germany

    Bernhard Schweizer

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Busch, M. (2019). Performance Improvement of Explicit Co-simulation Methods Through Continuous Extrapolation. 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_4

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  • DOI: https://doi.org/10.1007/978-3-030-14883-6_4

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  • Online ISBN: 978-3-030-14883-6

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