Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

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Title: Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations
Author: Ando, Tadashi ; Chow, Edmond ; Saad, Yousef ; Skolnick, Jeffrey
Abstract: Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N²) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the “block” version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing largescale Brownian dynamics simulations with hydrodynamic interactions.
Description: © 2012 American Institute of Physics The electronic version of this article is the complete one and can be found online at: DOI: 10.1063/1.4742347
Type: Article
ISSN: 0021-9606
Citation: Tadashi Ando, Edmond Chow, Yousef Saad, and Jeffrey Skolnick, "Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations," Journal of Chemical Physics, 137, 064106 (2012)
Date: 2012-08
Contributor: Georgia Institute of Technology. Center for the Study of Systems Biology
Georgia Institute of Technology. School of Biology
Georgia Institute of Technology. School of Computational Science and Engineering
University of Minnesota. Dept. of Computer Science and Engineering
Publisher: Georgia Institute of Technology
American Institute of Physics
Subject: Brownian motion
Chebyshev approximation
Linear algebra

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