Geometric integration of Hamiltonian systems perturbed by Rayleigh damping
(2011) BIT50 Conference 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:
https://lup.lub.lu.se/record/2272234
- author
- Modin, Klas LU and Söderlind, Gustaf LU
- organization
- publishing date
- 2011
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- Geometric numerical integration, Splitting methods, Weakly dissipative, systems
- host publication
- Bit Numerical Mathematics
- volume
- 51
- issue
- 4
- pages
- 977 - 1007
- publisher
- Springer
- conference name
- BIT50 Conference
- conference location
- Lund, Sweden
- conference dates
- 2010-06-17 - 2010-06-20
- external identifiers
-
- wos:000297362000010
- scopus:81755161517
- ISSN
- 0006-3835
- DOI
- 10.1007/s10543-011-0345-1
- 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
- c8446f11-7261-4fbb-a6e5-6f7c1153877d (old id 2272234)
- date added to LUP
- 2016-04-01 14:38:21
- date last changed
- 2022-01-28 01:41:37
@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 <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}}, keywords = {{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}}, doi = {{10.1007/s10543-011-0345-1}}, volume = {{51}}, year = {{2011}}, }