Variational integrators of mixed order for constrained and unconstrained systems acting on multiple time scales

Variational integrators of mixed order for constrained and unconstrained systems acting on... The considered systems contain dynamics on different time scales caused by different types and stiffnesses in potentials. For the slow motion, a coarse approximation suffices, but to resolve the fast motion, high accuracy is required. To avoid unnecessarily high computational costs, the idea here is to use polynomials of different degrees to approximate the slow and fast dynamics and quadrature formulas of different orders to approximate the different action terms. The approach is extended to holonomically constrained systems, where the Lagrange multiplier theorem is used to introduce constraint forces constraining the motion to the constraint manifold. The computational efficiency of the integrators is shown by means of two examples. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Variational integrators of mixed order for constrained and unconstrained systems acting on multiple time scales

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710057
Publisher site
See Article on Publisher Site

Abstract

The considered systems contain dynamics on different time scales caused by different types and stiffnesses in potentials. For the slow motion, a coarse approximation suffices, but to resolve the fast motion, high accuracy is required. To avoid unnecessarily high computational costs, the idea here is to use polynomials of different degrees to approximate the slow and fast dynamics and quadrature formulas of different orders to approximate the different action terms. The approach is extended to holonomically constrained systems, where the Lagrange multiplier theorem is used to introduce constraint forces constraining the motion to the constraint manifold. The computational efficiency of the integrators is shown by means of two examples. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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