Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics

Abstract : In this paper we use step size adjustment and extrapolation methods to improve Moreau's time-stepping scheme for the numerical integration of non-smooth mechanical systems, i.e. systems with impact and friction. The scheme yields a system of inclusions, which is transformed into a system of projective equations. These equations are solved iteratively. Switching points are time instants for which the structure of the mechanical system changes, for example, time instants for which a sticking friction element begins to slide. We show how switching points can be localized and how these points can be resolved by choosing a minimal step size. In order to improve the integration of non-smooth systems in the smooth parts, we show how the time-stepping method can be used as a base integration scheme for extrapolation methods, which allow for an increase in the integration order. Switching points are processed by a small time step, while time intervals during which the structure of the system does not change are computed with a larger step size and improved integration order. The overall algorithm, which consists of a time-stepping module, an extrapolation module and a step size adjustment module, is discussed in detail and some examples are given.
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Christian Studer, Remco Leine, Christoph Glocker. Step size adjustment and extrapolation for time-stepping schemes in non-smooth dynamics. International Journal for Numerical Methods in Engineering, Wiley, 2008, 76 (11), ⟨10.1002/nme.2383⟩. ⟨hal-01352897⟩

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