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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 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.
Please use this url to cite or link to this publication:
author
; and
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
host publication
Numerical Analysis and Applied Mathematics, Vols 1 and 2
volume
1168
pages
877 - 877
publisher
American Institute of Physics (AIP)
conference name
International Conference on Numerical Analysis and Applied Mathematics, 2009
conference location
Rethymno, Greece
conference dates
2009-09-18 - 2009-09-22
external identifiers
  • wos:000273023600211
  • scopus:70450202224
ISSN
0094-243X
1551-7616
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
24a2f60e-626a-4f1f-bb33-91fec407fb73 (old id 1531687)
date added to LUP
2016-04-01 11:51:20
date last changed
2024-01-07 23:04:01
@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         = {{0094-243X}},
  keywords     = {{weakly dissipative systems; Geometric integration; splitting methods; adaptive geometric integration}},
  language     = {{eng}},
  pages        = {{877--877}},
  publisher    = {{American Institute of Physics (AIP)}},
  title        = {{Geometric Integration of Weakly Dissipative Systems}},
  volume       = {{1168}},
  year         = {{2009}},
}