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Geometric Integration of Weakly Dissipative Systems

Modin, Klas LU ; Führer, Claus LU and Söderlind, Gustaf LU (2009) International Conference on Numerical Analysis and Applied Mathematics, 2009 In Numerical Analysis and Applied Mathematics, Vols 1 and 2 1168. p.877-877
Abstract
Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
weakly dissipative systems, Geometric integration, splitting methods, adaptive geometric integration
in
Numerical Analysis and Applied Mathematics, Vols 1 and 2
volume
1168
pages
877 - 877
publisher
American Institute of Physics
conference name
International Conference on Numerical Analysis and Applied Mathematics, 2009
external identifiers
  • wos:000273023600211
  • scopus:70450202224
ISSN
1551-7616
0094-243X
language
English
LU publication?
yes
id
24a2f60e-626a-4f1f-bb33-91fec407fb73 (old id 1531687)
date added to LUP
2010-01-28 16:10:25
date last changed
2017-02-13 13:10:00
@inproceedings{24a2f60e-626a-4f1f-bb33-91fec407fb73,
  abstract     = {Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.},
  author       = {Modin, Klas and Führer, Claus and Söderlind, Gustaf},
  booktitle    = {Numerical Analysis and Applied Mathematics, Vols 1 and 2},
  issn         = {1551-7616},
  keyword      = {weakly dissipative systems,Geometric integration,splitting methods,adaptive geometric integration},
  language     = {eng},
  pages        = {877--877},
  publisher    = {American Institute of Physics},
  title        = {Geometric Integration of Weakly Dissipative Systems},
  volume       = {1168},
  year         = {2009},
}