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Symplectic Numerical Integrators in Constrained Hamiltonian Systems (1994)
| Citations: | 61 - 8 self |
BibTeX
@MISC{Skeel94symplecticnumerical,
author = {Robert D. Skeel and Benedict J. Leimkuhler and Benedict J. Leimkuhler},
title = {Symplectic Numerical Integrators in Constrained Hamiltonian Systems},
year = {1994}
}
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Abstract
: Recent work reported in the literature suggests that for the long-time integration of Hamiltonian dynamical systems one should use methods that preserve the symplectic (or canonical) structure of the flow. Here we investigate the symplecticness of numerical integrators for constrained dynamics, such as occur in molecular dynamics when bond lengths are made rigid in order to overcome stepsize limitations due to the highest frequencies. This leads to a constrained Hamiltonian system of smaller dimension. Previous work has shown that it is possible to have methods which are symplectic on the constraint manifold in phase space. Here it is shown that the very popular Verlet method with SHAKE-type constraints is equivalent to the same method with RATTLE-type constraints and that the latter is symplectic and time reversible. (This assumes that the iteration is carried to convergence.) We also demonstrate the global convergence of the Verlet scheme in the presence of SHAKE--type and RATTLE-...
Keyphrases
symplectic numerical integrator constrained hamiltonian system rattle-type constraint molecular dynamic hamiltonian system popular verlet method constrained dynamic phase space shake type bond length hamiltonian dynamical system global convergence long-time integration shake-type constraint constraint manifold numerical integrator verlet scheme stepsize limitation previous work recent work
