A variational principle for computing slow invariant manifolds in dissipative dynamical systems
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing such manifolds for finite-dimensional dynamical systems using...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2011
|
| In: |
SIAM journal on scientific computing
Year: 2011, Jahrgang: 33, Heft: 2, Pages: 703-720 |
| ISSN: | 1095-7197 |
| DOI: | 10.1137/100790318 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1137/100790318 Verlag, lizenzpflichtig, Volltext: https://epubs.siam.org/doi/10.1137/100790318 
|
| Verfasserangaben: | Dirk Lebiedz, Jochen Siehr, and Jonas Unger |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1813313067 | ||
| 003 | DE-627 | ||
| 005 | 20230710123514.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 220805s2011 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1137/100790318 |2 doi | |
| 035 | |a (DE-627)1813313067 | ||
| 035 | |a (DE-599)KXP1813313067 | ||
| 035 | |a (OCoLC)1389793442 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Lebiedz, Dirk |d 1974- |e VerfasserIn |0 (DE-588)123431565 |0 (DE-627)082552134 |0 (DE-576)293706433 |4 aut | |
| 245 | 1 | 2 | |a A variational principle for computing slow invariant manifolds in dissipative dynamical systems |c Dirk Lebiedz, Jochen Siehr, and Jonas Unger |
| 264 | 1 | |c 2011 | |
| 300 | |a 18 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 04.08.2022 | ||
| 520 | |a A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing such manifolds for finite-dimensional dynamical systems using trajectory optimization. The corresponding objective functional reflects a variational principle that characterizes trajectories on slow invariant manifolds. For a two-dimensional linear system and a common nonlinear test problem we show analytically that the variational approach asymptotically exactly identifies the slow invariant manifold in the limit of either an infinite time horizon of the variational problem with fixed spectral gap or infinite spectral gap with a fixed finite time horizon. Numerical results are presented for the linear and nonlinear model problems as well as for a more realistic higher-dimensional chemical reaction mechanism. | ||
| 650 | 4 | |a 37M99 | |
| 650 | 4 | |a 37N40 | |
| 650 | 4 | |a 80A30 | |
| 650 | 4 | |a 92E20 | |
| 650 | 4 | |a calculus of variations | |
| 650 | 4 | |a chemical kinetics | |
| 650 | 4 | |a extremum principle | |
| 650 | 4 | |a model reduction | |
| 650 | 4 | |a optimization | |
| 650 | 4 | |a slow invariant manifold | |
| 700 | 1 | |a Siehr, Jochen |e VerfasserIn |0 (DE-588)1034649574 |0 (DE-627)746139993 |0 (DE-576)382289331 |4 aut | |
| 700 | 1 | |a Unger, Jonas |d 1986- |e VerfasserIn |0 (DE-588)1093434872 |0 (DE-627)853494061 |0 (DE-576)46123534X |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |a Society for Industrial and Applied Mathematics |t SIAM journal on scientific computing |d Philadelphia, Pa. : SIAM, 1993 |g 33(2011), 2, Seite 703-720 |h Online-Ressource |w (DE-627)266885292 |w (DE-600)1468391-X |w (DE-576)078589967 |x 1095-7197 |7 nnas |
| 773 | 1 | 8 | |g volume:33 |g year:2011 |g number:2 |g pages:703-720 |g extent:18 |a A variational principle for computing slow invariant manifolds in dissipative dynamical systems |
| 856 | 4 | 0 | |u https://doi.org/10.1137/100790318 |x Verlag |x Resolving-System |z lizenzpflichtig |3 Volltext |
| 856 | 4 | 0 | |u https://epubs.siam.org/doi/10.1137/100790318 |x Verlag |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20220805 | ||
| 993 | |a Article | ||
| 994 | |a 2011 | ||
| 998 | |g 1034649574 |a Siehr, Jochen |m 1034649574:Siehr, Jochen |d 110000 |e 110000PS1034649574 |k 0/110000/ |p 2 | ||
| 999 | |a KXP-PPN1813313067 |e 4175946527 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"name":{"displayForm":["Dirk Lebiedz, Jochen Siehr, and Jonas Unger"]},"origin":[{"dateIssuedKey":"2011","dateIssuedDisp":"2011"}],"id":{"eki":["1813313067"],"doi":["10.1137/100790318"]},"physDesc":[{"extent":"18 S."}],"relHost":[{"title":[{"title":"SIAM journal on scientific computing","title_sort":"SIAM journal on scientific computing"}],"language":["eng"],"corporate":[{"display":"Society for Industrial and Applied Mathematics","roleDisplay":"VerfasserIn","role":"aut"}],"recId":"266885292","type":{"media":"Online-Ressource","bibl":"periodical"},"disp":"Society for Industrial and Applied MathematicsSIAM journal on scientific computing","note":["Gesehen am 02.07.2021"],"part":{"year":"2011","issue":"2","pages":"703-720","text":"33(2011), 2, Seite 703-720","volume":"33","extent":"18"},"titleAlt":[{"title":"Journal on scientific and statistical computing"},{"title":"Journal on scientific computing"}],"pubHistory":["14.1993 -"],"name":{"displayForm":["Society for Industrial and Applied Mathematics"]},"id":{"eki":["266885292"],"zdb":["1468391-X"],"issn":["1095-7197"]},"origin":[{"dateIssuedKey":"1993","publisher":"SIAM","dateIssuedDisp":"1993-","publisherPlace":"Philadelphia, Pa."}],"physDesc":[{"extent":"Online-Ressource"}]}],"person":[{"role":"aut","display":"Lebiedz, Dirk","roleDisplay":"VerfasserIn","given":"Dirk","family":"Lebiedz"},{"given":"Jochen","family":"Siehr","role":"aut","roleDisplay":"VerfasserIn","display":"Siehr, Jochen"},{"roleDisplay":"VerfasserIn","display":"Unger, Jonas","role":"aut","family":"Unger","given":"Jonas"}],"title":[{"title":"A variational principle for computing slow invariant manifolds in dissipative dynamical systems","title_sort":"variational principle for computing slow invariant manifolds in dissipative dynamical systems"}],"note":["Gesehen am 04.08.2022"],"type":{"bibl":"article-journal","media":"Online-Ressource"},"language":["eng"],"recId":"1813313067"} | ||
| SRT | |a LEBIEDZDIRVARIATIONA2011 | ||