EU Regional School - Tuckerman Seminar
Prof. Tuckerman - Multiple Time-Stepping in Molecular Dynamics: Challenges, Solutions, and Applications
New York University
The inherent separation of time scales that is a ubiquitous feature in a wide variety of complex dynamical systems can be exploited to generate efficient algorithms for numerically integrating the classical equations of motion of such systems. The basic strategy is to assign the force component associated with each time scale its own time step and then to devise multiple time-step solvers based on this division of forces. The underlying assumption of such schemes is that fast forces arise from potentials that are computationally inexpensive to evaluate while the slower forces contain the major computational bottlenecks. Consequently, if the slower forces can be integrated with a larger time step and evaluated less frequently, the computational cost of the calculation will be significantly reduced. In the talks I will give, I will review this basic strategy and point out that the cost savings are limited by phenomena known as resonances. I will then present several solutions to the resonance problem that allow the full time-scale separation to be exploited by the multiple time-step solver. Finally, I will present some application areas to which multiple time-stepping approaches can be applied, including rare-event sampling techniques for biomolecular and crystal structure prediction, fixed- charge and polarizable models, and in coarse-grained approaches such as dissipative- particle dynamics.