Geometric integration of Hamiltonian systems perturbed by Rayleigh damping
(2011) BIT50 Conference In Bit Numerical Mathematics 51(4). p.9771007 Abstract
 Explicit and semiexplicit 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 semiexplicit 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 RungeKutta method of the same order. (Less)
Please use this url to cite or link to this publication:
http://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
 in
 Bit Numerical Mathematics
 volume
 51
 issue
 4
 pages
 977  1007
 publisher
 Springer
 conference name
 BIT50 Conference
 external identifiers

 wos:000297362000010
 scopus:81755161517
 ISSN
 00063835
 DOI
 10.1007/s1054301103451
 language
 English
 LU publication?
 yes
 id
 c8446f1172614fbba6e56f7c1153877d (old id 2272234)
 date added to LUP
 20111229 12:30:15
 date last changed
 20170903 04:20:45
@inproceedings{c8446f1172614fbba6e56f7c1153877d, abstract = {Explicit and semiexplicit 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 RungeKutta method of the same order.}, author = {Modin, Klas and Söderlind, Gustaf}, booktitle = {Bit Numerical Mathematics}, issn = {00063835}, keyword = {Geometric numerical integration,Splitting methods,Weakly dissipative,systems}, language = {eng}, number = {4}, pages = {9771007}, publisher = {Springer}, title = {Geometric integration of Hamiltonian systems perturbed by Rayleigh damping}, url = {http://dx.doi.org/10.1007/s1054301103451}, volume = {51}, year = {2011}, }