Gagarina, E, Ambati, VR, Nurijanyan, S et al. (2 more authors) (2016) On variational and symplectic time integrators for Hamiltonian systems. Journal of Computational Physics, 306. pp. 370-389. ISSN 0021-9991
Abstract
Various systems in nature have a Hamiltonian structure and therefore
accurate time integrators for those systems are of great practical use. In this paper, a fi nite element method will be explored to derive symplectic time stepping schemes for (non-)autonomous systems in a systematic way. The technique used is a variational discontinuous Galerkin nite element method in time. This approach provides a uni ed framework to derive known and new symplectic time integrators. An extended analysis for the new time integrators will be provided. The analysis shows that a novel third order time integrator presented in this paper has excellent dispersion properties. These new time stepping schemes are necessary to get accurate and stable simulations of (forced) water waves and other non-autonomous variational systems, which we illustrate in our numerical results.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) |
Keywords: | nonlinear water waves; finite element Galerkin method; (non)autonomous variational formulation; symplectic time integration |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/L025388/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Nov 2015 11:23 |
Last Modified: | 03 Mar 2020 17:02 |
Published Version: | http://dx.doi.org/10.1016/j.jcp.2015.11.049 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jcp.2015.11.049 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92166 |