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S. Wolff:
"On time transformations in (a)synchronous variational integrators";
Talk: 8th International Conference on Structural Dynamics (EURODYN2011), Leuven; 2011-07-04 - 2011-07-06; in: "Proceedings of the 8th International Conference on Structural Dynamics (EURODYN2011)", (2011), ISBN: 978-90-760-1931-4; 3615 - 3622.

In order to improve stability and accuracy of explicit AVIs, the usage of adaptive time steps is studied. Previous approaches to variable time steps in asynchronous integration are based on symplectic-energy-momentum schemes which may generate unsolvable equations rendering the scheme unstable. This article studies the application of general time transformations to variational integrators. The resulting schemes are momentum preserving and symplectic. The method is extended to the asynchronous case. It turns out that there exist more restrictions on the choice of the time step function than in the synchronous setting. Suitable time step functions are proposed. The resulting system of equation is symplectic and explicit, but involves the solution of a scalar quadratic equation and the computation of higher order derivatives. Examples focus on single degree of freedom systems. Simulations illustrate the possible advantages and dangers of variable time steps in synchronous/asynchronous integration.

time stepping schemes; symplectic-momentum integration; multiple time stepping; asynchronous variational integration; variable time steps

Project Head Christian Bucher:
Formulierung und Test eines glatten zeitadaptiven Raum-Zeit-Integrators