Exact and non-stiff sampling of highly oscillatory systems: an implicit mass-matrix penalization approach

Details Exact and non-stiff sampling of highly oscillatory systems: an implicit mass-matrix penalization approach Exact and non-stiff sampling of highly oscillatory systems: an implicit mass-matrix penalization approach

2008-05-08

arxiv.org/abs/0805.1092v2

Mathematics

Numerical Analysis

32 pages, 5 figures

Scientific paper

We propose and analyze an implicit mass-matrix penalization (IMMP) technique which enables efficient and exact sampling of the (Boltzmann/Gibbs) canonical distribution associated to Hamiltonian systems with fast degrees of freedom (fDOFs). The penalty parameters enable arbitrary tuning of the timescale for the selected fDOFs, and the method is interpreted as an interpolation between the exact Hamiltonian dynamics and the dynamics with infinitely slow fDOFs (equivalent to geometrically corrected rigid constraints). This property translates in the associated numerical methods into a tunable trade-off between stability and dynamical modification. The penalization is based on an extended Hamiltonian with artificial constraints associated with each fDOF. By construction, the resulting dynamics is statistically exact with respect to the canonical distribution in position variables. The algorithms can be easily implemented with standard geometric integrators with algebraic constraints given by the expected fDOFs, and has no additional complexity in terms of enforcing the constraint and force evaluations. The method is demonstrated on a high dimensional system with non-convex interactions. Prescribing the macroscopic dynamical timescale, it is shown that the IMMP method increases the time-step stability region with a gain that grows linearly with the size of the system. The latter property, as well as consistency of the macroscopic dynamics of the IMMP method is proved rigorously for linear interactions. Finally, when a large stiffness parameter is introduced, the IMMP method can be tuned to be asymptotically stable, converging towards the heuristically expected Markovian effective dynamics on the slow manifold.

Affiliated with

Also associated with

No associations

Rating

Exact and non-stiff sampling of highly oscillatory systems: an implicit mass-matrix penalization approach does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Exact and non-stiff sampling of highly oscillatory systems: an implicit mass-matrix penalization approach, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact and non-stiff sampling of highly oscillatory systems: an implicit mass-matrix penalization approach will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-52354