Multiple timestep molecular dynamics

T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comput. Chem., 18 1785-1791, 1997. 

The stringency of the timestep threshold and the failure of implicit methods to address the issue have led to alternative proposals for ameliorating the instability in molecular dynamics, in particular the method of multiple timestepping which we next describe. Variants of this method were described in a series of papers in the early 1990s by Tuckerman and Berne [374] and Tuckerman et al. [375, 377]. A simultaneous development by Grubmiiller et al. [158] most closely matches the presentation given here. The first resonance analysis is due to Biesiadecki and Skeel [35]. 

It is important to emphasize the tremendous complexity of molecular dynamics in relation to the simple model scenario presented here. In [22, 29], multiple timestepping was used effectively to treat large scale systems where the force spUtting is defined in the context of particle-mesh Ewald long-ranged force computations. We also point out that where additional constraints are present, the prospects for multiple timestepping may be significantly better, as, in the previously mentioned work [118] and in Sect. 8.6 of the next chapter, where isokinetic constraints are used to stabilize the system. 

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