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Overcoming Instabilities in Verlet-I/r-RESPA with the Mollified Impulse Method

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Computational Methods for Macromolecules: Challenges and Applications

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 24))

Abstract

The primary objective of this paper is to explain the derivation of symplectic mollified Verlet-I/r-RESPA (MOLLY) methods that overcome linear and nonlinear instabilities that arise as numerical artifacts in Verlet-I/r-RESPA. These methods allow for lengthening of the longest time step used in molecular dynamics (MD). We provide evidence that MOLLY methods can take a longest time step that is 50% greater than that of Verlet-I/r-RESPA, for a given drift, including no drift. A 350% increase in the timestep is possible using MOLLY with mild Langevin damping while still computing dynamic properties accurately. Furthermore, longer time steps also enhance the scalability of multiple time stepping integrators that use the popular Particle Mesh Ewald method for computing full electrostatics, since the parallel bottleneck of the fast Fourier transform associated with PME is invoked less often. An additional objective of this paper is to give sufficient implementation details for these mollified integrators, so that interested users may implement them into their MD codes, or use the program ProtoMol in which we have implemented these methods.

Using simple analysis of a 1-d model problem we show the linear instability present in Verlet-I/r-RESPA at approximately half the period of the fastest motion, and more interestingly, how the mollified methods can be designed to overcome them. The paper also includes an experimental component that shows how these methods overcome instability barriers in practice.

We also present evidence that more complicated instabilities are present in Verlet-I/r-RESPA than linear analysis reveals. In particular, we postulate nonlinear resonance mechanisms hereto ignored, although these mechanisms are known for leapfrog. This means that Verlet-I/r-RESPA is no better than leapfrog if one wants a simulation with no drift. Currently, we use mild Langevin damping to overcome these nonlinear instabilities, but it is possible to design symplectic MOLLY integrators that are nonlinearly stable as well.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, Indiana, 46556-0309, USA

    Jesús A. Izaguirre, Qun Ma, Jeremiah Willcock, Thomas Slabach, Branden Moore & George Viamontes

  2. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    Thierry Matthey

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  1. Jesús A. Izaguirre
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Editors and Affiliations

  1. Department of Chemistry, Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012, USA

    Tamar Schlick  & Hin Hark Gan  & 

  2. Howard Hughes Medical Institute, 251 Mercer Street, New York, NY, 10012, USA

    Tamar Schlick  & Hin Hark Gan  & 

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Izaguirre, J.A. et al. (2002). Overcoming Instabilities in Verlet-I/r-RESPA with the Mollified Impulse Method. In: Schlick, T., Gan, H.H. (eds) Computational Methods for Macromolecules: Challenges and Applications. Lecture Notes in Computational Science and Engineering, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56080-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-56080-4_7

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