A Variational Approach to Multirate Integration for Constrained Systems

  • Sigrid Leyendecker
  • Sina Ober-Blöbaum
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 28)


The simulation of systems with dynamics on strongly varying time scales is quite challenging and demanding with regard to possible numerical methods. A rather naive approach is to use the smallest necessary time step to guarantee a stable integration of the fast frequencies. However, this typically leads to unacceptable computational loads. Alternatively, multirate methods integrate the slow part of the system with a relatively large step size while the fast part is integrated with a small time step. In this work, a multirate integrator for constrained dynamical systems is derived in closed form via a discrete variational principle on a time grid consisting of macro and micro time nodes. Being based on a discrete version of Hamilton’s principle, the resulting variational multirate integrator is a symplectic and momentum preserving integration scheme and also exhibits good energy behaviour. Depending on the discrete approximations for the Lagrangian function, one obtains different integrators, e.g. purely implicit or purely explicit schemes, or methods that treat the fast and slow parts in different ways. The performance of the multirate integrator is demonstrated by means of several examples.


Time Grid Time Step Scheme Multirate System Discrete Trajectory Lagrangian Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This chapter was partly developed and published in the course of the Collaborative Research Centre 614 “Self-Optimizing Concepts and Structures in Mechanical Engineering” funded by the German Research Foundation (DFG) under grant number SFB 614.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Chair of Applied DynamicsUniversity of Erlangen-NurembergErlangenGermany
  2. 2.Computational Dynamics and Optimal ControlUniversity of PaderbornPaderbornGermany

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