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

Izaguirre, Jesús A.; Ma, Qun; Matthey, Thierry; Willcock, Jeremiah; Slabach, Thomas; Moore, Branden J.; Viamontes, George F.

doi:10.1007/978-3-642-56080-4_7

Cited by 15 publications

(13 citation statements)

References 34 publications

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“…[11] Second, one can integrate the vibrations more accurately using multiple time-steps [12] : a large time-step for the slowly varying intermolecular forces, and a smaller time-step for the quickly varying intramolecular forces (including the most critical bond and angle vibrations). The stability of this approach can be improved in various ways, for example, with the mollified impulse method [13] used in NAMD. [14] Third, one can totally remove bond vibrations by constraining the bond lengths using algorithms like LINCS [15] or SHAKE.…”

Section: Introductionmentioning

confidence: 99%

New ways to boost molecular dynamics simulations

2015

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We describe a set of algorithms that allow to simulate dihydrofolate reductase (DHFR, a common benchmark) with the AMBER all‐atom force field at 160 nanoseconds/day on a single Intel Core i7 5960X CPU (no graphics processing unit (GPU), 23,786 atoms, particle mesh Ewald (PME), 8.0 Å cutoff, correct atom masses, reproducible trajectory, CPU with 3.6 GHz, no turbo boost, 8 AVX registers). The new features include a mixed multiple time‐step algorithm (reaching 5 fs), a tuned version of LINCS to constrain bond angles, the fusion of pair list creation and force calculation, pressure coupling with a “densostat,” and exploitation of new CPU instruction sets like AVX2. The impact of Intel's new transactional memory, atomic instructions, and sloppy pair lists is also analyzed. The algorithms map well to GPUs and can automatically handle most Protein Data Bank (PDB) files including ligands. An implementation is available as part of the YASARA molecular modeling and simulation program from www.YASARA.org . © 2015 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

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Section: Introductionmentioning

confidence: 99%

New ways to boost molecular dynamics simulations

2015

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“…In an effort to overcome the linear instability of Verlet-I/r-RESPA/Impulse, we and other researchers have developed the mollified Impulse method (MOLLY) [9,10,16,17,18,20]. MOLLY defines the slow part of the potential energy at time-averaged positions, and the force is made a gradient of the potential energy.…”

Section: Linear Instabilities Of Multiple Time Stepping Integratorsmentioning

confidence: 99%

Verlet-I/R-RESPA/Impulse is Limited by Nonlinear Instabilities

Ma¹,

Izaguirre²,

Skeel³

2003

SIAM J. Sci. Comput.

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This paper shows that in molecular dynamics (MD) when constant-energy (NVE) simulations of Newton's equations of motion are attempted using the multiple time stepping (MTS) integrator Verlet-I/r-RESPA/Impulse, there are nonlinear instabilities when the longest step size is a third or possibly a fourth of the period(s) of the fastest motion(s) in the system. This is demonstrated both through a thorough set of computer experiments and through the analysis of a nonlinear model problem. The numerical experiments include not only the unconstrained dynamics simulation of a droplet of flexible water and a flexible protein, but also the constrained dynamics simulation of a solvated protein, representing a range of simulation protocols commonly in use by biomolecular modelers. The observed and predicted instabilities match exactly. Previous work has identified and explained a linear instability for Verlet-I/r-RESPA/Impulse at around half the period of the fastest motion. Mandziuk and Schlick discovered nonlinear resonances in single time stepping MD integrators, but unstable nonlinear resonances for MTS integrators are reported here for the first time. This paper also offers an explanation on the instability of MTS constrained molecular dynamics simulations of explicitly solvated proteins. More aggressive multiple step sizes are possible with mild Langevin coupling or targeted Langevin coupling, and its combination with the mollified Impulse method permits step sizes 3 to 4 times larger than Verlet-I/r-RESPA/Impulse while still retaining some accuracy.1. Introduction. This paper uncovers additional stability limitations of multiple time stepping (MTS) integrators for molecular dynamics (MD) that attempt to bridge time scales. In particular, it is shown that when constant-energy (NVE) simulations of Newton's equations of motion are attempted using the MTS integrator Verlet-I [12]/r-RESPA [42]/Impulse, there are nonlinear instabilities when the longest step size is a third or possibly a fourth of the period(s) of the fastest motion(s) in the system. This is demonstrated both through a thorough set of computer experiments and through the analysis of a nonlinear model problem. The observed and predicted instabilities match exactly.A linear instability for Verlet-I/r-RESPA/Impulse at around half the period of the fastest motion has been identified and explained by previous work [9,40]. Mandziuk and Schlick [29] discovered nonlinear resonances in single time stepping MD integrators, but unstable nonlinear resonances for MTS integrators are reported here for the first time.

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“…It has been long recognized that this method can display resonance instabilities, especially in the context of molecular dynamics simulations [22,1,41,43,31,6]. These resonances severely limit the relative size of the time steps.…”

Section: Introductionmentioning

confidence: 99%