Advanced

Geometric integration of Hamiltonian systems perturbed by Rayleigh damping

Modin, Klas LU and Söderlind, Gustaf LU (2011) BIT50 Conference In Bit Numerical Mathematics 51(4). p.977-1007
Abstract
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter epsilon, and the schemes under study preserve the symplectic structure in the case epsilon=0. In the case 0 <epsilon a parts per thousand(a)1 the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3D pendulum.... (More)
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter epsilon, and the schemes under study preserve the symplectic structure in the case epsilon=0. In the case 0 <epsilon a parts per thousand(a)1 the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Geometric numerical integration, Splitting methods, Weakly dissipative, systems
in
Bit Numerical Mathematics
volume
51
issue
4
pages
977 - 1007
publisher
Springer
conference name
BIT50 Conference
external identifiers
  • wos:000297362000010
  • scopus:81755161517
ISSN
0006-3835
DOI
10.1007/s10543-011-0345-1
language
English
LU publication?
yes
id
c8446f11-7261-4fbb-a6e5-6f7c1153877d (old id 2272234)
date added to LUP
2011-12-29 12:30:15
date last changed
2017-09-03 04:20:45
@inproceedings{c8446f11-7261-4fbb-a6e5-6f7c1153877d,
  abstract     = {Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter epsilon, and the schemes under study preserve the symplectic structure in the case epsilon=0. In the case 0 &lt;epsilon a parts per thousand(a)1 the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation of relative equilibria for small enough step sizes is conducted. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order.},
  author       = {Modin, Klas and Söderlind, Gustaf},
  booktitle    = {Bit Numerical Mathematics},
  issn         = {0006-3835},
  keyword      = {Geometric numerical integration,Splitting methods,Weakly dissipative,systems},
  language     = {eng},
  number       = {4},
  pages        = {977--1007},
  publisher    = {Springer},
  title        = {Geometric integration of Hamiltonian systems perturbed by Rayleigh damping},
  url          = {http://dx.doi.org/10.1007/s10543-011-0345-1},
  volume       = {51},
  year         = {2011},
}