Smoothed dynamics of highly oscillatory Hamiltonian systems:
Abstract: "We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partia...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin-Wilmersdorf
Konrad-Zuse-Zentrum für Informationstechnik
1994
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| Schriftenreihe: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC
1994,28 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step-size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been succesfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods [sic] fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method." |
| Beschreibung: | 22 S. graph. Darst. |
Internformat
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| 100 | 1 | |a Reich, Sebastian |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Smoothed dynamics of highly oscillatory Hamiltonian systems |c Sebastian Reich |
| 264 | 1 | |a Berlin-Wilmersdorf |b Konrad-Zuse-Zentrum für Informationstechnik |c 1994 | |
| 300 | |a 22 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1994,28 | |
| 520 | 3 | |a Abstract: "We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step-size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been succesfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods [sic] fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method." | |
| 650 | 4 | |a Hamiltonian systems | |
| 830 | 0 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1994,28 |w (DE-604)BV004801715 |9 1994,28 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006614206 | ||
Datensatz im Suchindex
| _version_ | 1804124353871216640 |
|---|---|
| any_adam_object | |
| author | Reich, Sebastian |
| author_facet | Reich, Sebastian |
| author_role | aut |
| author_sort | Reich, Sebastian |
| author_variant | s r sr |
| building | Verbundindex |
| bvnumber | BV009980526 |
| ctrlnum | (OCoLC)32499018 (DE-599)BVBBV009980526 |
| format | Book |
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| id | DE-604.BV009980526 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:44:19Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006614206 |
| oclc_num | 32499018 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| physical | 22 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| series2 | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| spelling | Reich, Sebastian Verfasser aut Smoothed dynamics of highly oscillatory Hamiltonian systems Sebastian Reich Berlin-Wilmersdorf Konrad-Zuse-Zentrum für Informationstechnik 1994 22 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1994,28 Abstract: "We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step-size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been succesfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods [sic] fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method." Hamiltonian systems Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1994,28 (DE-604)BV004801715 1994,28 |
| spellingShingle | Reich, Sebastian Smoothed dynamics of highly oscillatory Hamiltonian systems Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC Hamiltonian systems |
| title | Smoothed dynamics of highly oscillatory Hamiltonian systems |
| title_auth | Smoothed dynamics of highly oscillatory Hamiltonian systems |
| title_exact_search | Smoothed dynamics of highly oscillatory Hamiltonian systems |
| title_full | Smoothed dynamics of highly oscillatory Hamiltonian systems Sebastian Reich |
| title_fullStr | Smoothed dynamics of highly oscillatory Hamiltonian systems Sebastian Reich |
| title_full_unstemmed | Smoothed dynamics of highly oscillatory Hamiltonian systems Sebastian Reich |
| title_short | Smoothed dynamics of highly oscillatory Hamiltonian systems |
| title_sort | smoothed dynamics of highly oscillatory hamiltonian systems |
| topic | Hamiltonian systems |
| topic_facet | Hamiltonian systems |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT reichsebastian smootheddynamicsofhighlyoscillatoryhamiltoniansystems |