Computing time investigations of variational multi rate integrators

Gail T, Leyendecker S, Ober-Blöbaum S (2013)

Publication Type: Conference contribution, Conference Contribution

Publication year: 2013

Pages Range: DVD

Conference Proceedings Title: Proceedings of the ECCOMAS Thematic Conference on Mutlibody Dynamics

Event location: Zagreb HR

DOI: 10.1002/pamm.201310017

Abstract

Consider a mechanical system that contains slow and fast dynamics. Let it be possible, to split the potential energy into a slow and a fast potential and the configuration vector into slow and fast variables. For such systems, multirate schemes simulate the different parts using different time steps with the goal to save computing time. For the proposed multirate scheme, a time grid consisting of micro and macro nodes is used and the integrator is derived from a discrete variational principle. Variational integrators conserve properties like symplecticity and momentum maps and have good energy behavior. To solve the resulting system of coupled nonlinear equations, a Newton-Raphson iteration with an analytical Jacobian is used. It is demonstrated that the multirate approach leads to less computing time compared to singlerate simulation by means of three example systems, the Fermi-Pasta-Ulam problem, a triple spherical pendulum and a simple atomistic model, where the latter two are subject to constraints. Computing times are compared for different numbers of micro and macro nodes for dynamic simulations during a certain time interval. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Authors with CRIS profile

Tobias Gail Institute of Applied Dynamics Sigrid Leyendecker Institute of Applied Dynamics

Related research project(s)

Numerical investigations on optimal control and variational integrators for multirate systems Jan. 1, 2012 - Dec. 31, 2017 Simulation and optimal control of the dynamics of multibody systems in biomechanics and robotics Dec. 1, 2008 - Dec. 1, 2011

Involved external institutions

Universität Paderborn DE Germany (DE)

How to cite

APA:

Gail, T., Leyendecker, S., & Ober-Blöbaum, S. (2013). Computing time investigations of variational multi rate integrators. In Proceedings of the ECCOMAS Thematic Conference on Mutlibody Dynamics (pp. DVD). Zagreb, HR.

MLA:

Gail, Tobias, Sigrid Leyendecker, and Sina Ober-Blöbaum. "Computing time investigations of variational multi rate integrators." Proceedings of the ECCOMAS Thematic Conference on Mutlibody Dynamics, Zagreb 2013. DVD.

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