EXTRAPOLATION VERSUS IMPULSE IN MULTIPLE-TIMESTEPPING SCHEMES - II - LINEAR-ANALYSIS AND APPLICATIONS TO NEWTONIAN AND LANGEVIN DYNAMICS

Force splitting or multiple timestep (MTS) methods are effective techn iques that accelerate biomolecular dynamics simulations by updating th e fast and slow forces at different frequencies. Since simple extrapol ation formulas for incorporating the slow forces into the, discretizat ion produced notable energy drifts, symplectic MTS variants based on p eriodic impulses became more popular. However, the efficiency gain pos sible with these impulse approaches, is limited by a timestep barrier due to resonance-a numerical artifact occurring when the timestep is r elated to the period of the fastest motion present in the dynamics. Th is limitation is lifted substantially for MTS methods based on extrapo lation in combination with stochastic dynamics, as demonstrated for th e LN method in the companion paper for protein dynamics. To explain ou r observations on those complex nonlinear systems, we examine here the stability of extrapolation and impulses to force-splitting in Newtoni an and Langevin dynamics. We analyze for a simple linear test system t he energy drift of the former and the resonance-related artifacts of t he latter technique. We show that two-class impulse methods are genera lly stable except at integer multiples of half the period of the faste st motion, with the severity of the instability worse at larger timest eps. Extrapolation methods are generally unstable for the Newtonian mo del problem, but the instability is bounded for increasing timesteps. This boundedness ensures good long-timestep behavior of extrapolation methods for Langevin dynamics with moderate values of the collision pa rameter. We thus advocate extrapolation methods for efficient integrat ion of the stochastic Langevin equations of motion, as in the LN metho d described in paper I. (C) 1998 American Institute of Physics.