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An Isaac Newton Institute Workshop

Effective Computational Methods for Highly Oscillatory Problems: The Interplay between Mathematical Theory and Applications

Treatment of Oscillations in Classical Molecular Dynamics

Author: Robert D. Skeel (Purdue University)

Abstract

Atomic oscillations present in classical molecular dynamics (MD) restrict the step size that can be used. These oscillations are decidedly nonlinear, and there is only a modest separation of temporal scales. For reasons to be explained, amplitudes of the highest frequency oscillations are small, and, hence, MD is an example of a (mildly) stiff oscillatory problem. Actually, getting accurate trajectories is not usually the aim of MD; instead, time averages or time correlation functions are sought, and the implications of this are examined. Two techniques for lengthening the step size have found general use: multiple time stepping and bond-length constraints. Accuracy and stability of these techniques is discussed.

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