Stabilized Integration of Hamiltonian Systems with Hard-Sphere Inequality Constraints
We consider numerical methods for resolving the dynamics of a Hamiltonian N-body problem subject to hard-sphere inequality constraints. The dynamics of these mixed systems consists of smooth flow of a Hamiltonian system between collisions with an impulsive momentum exchange at the points of collisio...
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| Published in | SIAM journal on scientific computing Vol. 30; no. 1; pp. 134 - 147 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1064-8275 1095-7197 |
| DOI | 10.1137/06066552X |
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| Abstract | We consider numerical methods for resolving the dynamics of a Hamiltonian N-body problem subject to hard-sphere inequality constraints. The dynamics of these mixed systems consists of smooth flow of a Hamiltonian system between collisions with an impulsive momentum exchange at the points of collision. The inclusion of these impulses makes traditional backward error analysis inappropriate since the flow is discontinuous and cannot be interpreted using a single modified smooth Hamiltonian system. We introduce two methods which respect the underlying modified smooth Hamiltonian system through the use of a modified map and collision operator at points of collision. In numerical experiments, these new methods show dramatically improved energy conservation over long time intervals. |
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| AbstractList | We consider numerical methods for resolving the dynamics of a Hamiltonian N-body problem subject to hard-sphere inequality constraints. The dynamics of these mixed systems consists of smooth flow of a Hamiltonian system between collisions with an impulsive momentum exchange at the points of collision. The inclusion of these impulses makes traditional backward error analysis inappropriate since the flow is discontinuous and cannot be interpreted using a single modified smooth Hamiltonian system. We introduce two methods which respect the underlying modified smooth Hamiltonian system through the use of a modified map and collision operator at points of collision. In numerical experiments, these new methods show dramatically improved energy conservation over long time intervals. |
| Author | Bond, Stephen D. Leimkuhler, Benedict J. |
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| CitedBy_id | crossref_primary_10_1016_j_jcp_2012_01_017 crossref_primary_10_1038_s41467_025_57688_8 crossref_primary_10_3390_separations10090499 crossref_primary_10_1016_j_triboint_2023_108694 crossref_primary_10_1002_nme_3236 crossref_primary_10_1016_j_corsci_2024_112194 crossref_primary_10_1021_acsmacrolett_9b00935 crossref_primary_10_1209_0295_5075_118_20006 crossref_primary_10_1016_j_jcp_2021_110846 crossref_primary_10_1039_D0CP02796K crossref_primary_10_1002_nme_4980 crossref_primary_10_1016_j_dt_2023_01_014 crossref_primary_10_1002_nme_3266 crossref_primary_10_1016_j_actamat_2024_120408 crossref_primary_10_1016_j_ijheatmasstransfer_2018_06_152 crossref_primary_10_1137_100800105 |
| Cites_doi | 10.1016/0301-0104(90)89081-Z 10.1063/1.443025 10.1103/PhysRevE.66.021402 10.1080/00268978100100921 10.1063/1.1743957 10.1007/BF02510253 10.1063/1.532892 10.1016/j.cam.2006.05.036 10.1002/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-W 10.1103/PhysRev.159.98 10.1007/BF02188219 10.1080/00268970009483294 10.1063/1.1501124 10.1016/0301-0104(82)88142-1 10.1017/S096249290100006X 10.1137/S0036142997329797 10.1137/S1111111102406038 10.1080/00268979300102631 10.1023/A:1022344502818 |
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| SubjectTerms | Algorithms Energy Error analysis Lagrange multiplier Methods Numerical analysis Spheres |
| Title | Stabilized Integration of Hamiltonian Systems with Hard-Sphere Inequality Constraints |
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