On variational and symplectic time integrators for Hamiltonian systems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:306

Article

Gagarina, E.¹  Ambati, V. R.¹  Nurijanyan, S.¹  van der Vegt, J. J. W.¹  Bokhove, O.² 

[1] Univ Twente, Dept Appl Math, Math Computat Sci Grp, NL-7500 AE Enschede, Netherlands

[2] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

关键词: Nonlinear water waves;    Finite element Galerkin method;    (Non-)autonomous variational formulation;    Symplectic time integration;   

DOI  :  10.1016/j.jcp.2015.11.049

来源: Elsevier

【 摘 要 】

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 finite 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 finite element method in time. This approach provides a unified 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. (C) 2015 The Authors. Published by Elsevier Inc.

【 授权许可】

Free