Geometric Integration of Weakly Dissipative Systems
(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:
https://lup.lub.lu.se/record/1531687
- author
- Modin, Klas LU ; Führer, Claus LU and Söderlind, Gustaf LU
- organization
- publishing date
- 2009
- 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
- 1551-7616
- 0094-243X
- 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 = {{1551-7616}}, 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}}, }