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URN: urn:nbn:de:kobv:517-opus-15639
URL: http://opus.kobv.de/ubp/volltexte/2007/1563/

Reich, Sebastian

Smoothed dynamics of highly oscillatory Hamiltonian systems

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Kurzfassung auf Englisch

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 successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods 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.

Institut: Institut für Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: c Postprint
Schriftenreihe: Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe, ISSN 1866-8372
Band Nummer: paper 031
Sprache: Englisch
Erstellungsjahr: 1995
Publikationsdatum: 16.11.2007
first published in:
Physica D: Nonlinear Phenomena - 89 (1995), 1-2, p. 28-42
ISSN: 0167-2789
doi: 10.1016/0167-2789(95)00212-X

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