Rapid sampling of stochastic displacements in Brownian dynamics simulations

Andrew M. Fiore, Florencio Balboa Usabiaga, Aleksandar Donev, James W. Swan

Research output: Contribution to journalArticle

Abstract

We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform fast Fourier transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. For geometrically dense microstructures (fractal dimension equal three), the performance is independent of volume fraction, while for tenuous microstructures (fractal dimension less than three), such as gels and polymer solutions, the performance improves with decreasing volume fraction. This is in stark contrast with other related linear-scaling methods such as the force coupling method and the fluctuating immersed boundary method, for which performance degrades with decreasing volume fraction. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4×106 particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable to the cost of computing deterministic displacements in BD simulations. A high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.

Original languageEnglish (US)
Article number124116
JournalJournal of Chemical Physics
Volume146
Issue number12
DOIs
StatePublished - Mar 28 2017

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Tensors
sampling
Sampling
Volume fraction
tensors
Computer simulation
Fractal dimension
Fast Fourier transforms
Microstructure
scaling
simulation
Gels
microstructure
fractals
gels
costs
Benchmarking
Polymer solutions
Iterative methods
Dispersions

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Rapid sampling of stochastic displacements in Brownian dynamics simulations. / Fiore, Andrew M.; Balboa Usabiaga, Florencio; Donev, Aleksandar; Swan, James W.

In: Journal of Chemical Physics, Vol. 146, No. 12, 124116, 28.03.2017.

Research output: Contribution to journalArticle

Fiore, Andrew M. ; Balboa Usabiaga, Florencio ; Donev, Aleksandar ; Swan, James W. / Rapid sampling of stochastic displacements in Brownian dynamics simulations. In: Journal of Chemical Physics. 2017 ; Vol. 146, No. 12.
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