Title: Stabilized Multiple Time Stepping Method for Coupling Multiple Time Scales in Molecular Dynamics

Speaker: Dr. Phani Nukala, Computer Science and Mathematics Division, ORNL

Date/Time: Thursday, June 7, 2007, 1:00pm - 2:00pm

Location: CSRI Building, Room 95 (Sandia NM)

Brief Abstract: Classical molecular dynamics simulations contain fast bond stretching and bending (high frequency) modes and a relatively slow (low frequency) motion in the remaining degrees of motion. In a typical MD simulation, the high-frequency bond vibrational modes are associated with time scales on the order of 10-14 s (10 fs). For numerical integration, the Verlet method (reversible and symplectic) is typically used with a time step size on the order of 10-15 s (1 fs) to resolve the fast bond stretching/bending modes. However, the large-scale motions of interest are characterized by timescales on the order of pico-seconds, which are three orders of magnitude larger than those of high-frequency vibrational timescales. Consequently, various approaches based on constrained dynamics, reversible multiple time stepping (MTS) schemes, and mollified techniques have been used to increase the time step. However, the MTS schemes are often plagued by parametric resonance effects, which limit the largest time step that can be used in the simulations.
 
In this project, we developed a stabilized multiple time stepping (SMTS) scheme based on the nonlinear variation of constants formula, an auxiliary problem and a variational equation. In particular, the fast response is evolved through an auxiliary problem and the mollification function for the slow response of the system is obtained as the time-averaged force response of the variational equation. The resulting SMTS method is stable and eliminates the usual parametric resonance effects associated with the traditional MTS methods. Since the allowable slow frequency time step size is not linked with the fastest time period, the SMTS method allows significantly large time step sizes to integrate the slow frequency response of the system.