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Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

机译:布朗动力学仿真中计算水动力相互作用的Krylov子空间方法

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摘要

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 large-scale Brownian dynamics simulations with hydrodynamic interactions.
机译:流体动力学相互作用在大分子动力学中起重要作用。在分子模拟中考虑流体动力学效应的最常见方法是在布朗动力学模拟的背景下。然而,在这些模拟中,相关布朗噪声矢量的计算在计算上要求很高,并且需要替代方法。本文研究了基于Krylov子空间的布朗噪声矢量的计算方法。这些方法与Chebyshev多项式逼近有关,但不需要特征值估计。我们表明,布朗噪声矢量只需要低精度即可准确计算聚合物和单分散悬浮液模型的动态和静态特性值。以这种水平的精度,Krylov子空间方法的计算时间几乎可以缩放为O(N 2 ),最多可测试10 000个粒子N。 Krylov子空间方法的性能,特别是“块”方法,比Chebyshev方法的性能稍好,即使不考虑后者所需的特征值估计的额外成本。此外,在N = 10000时,Krylov子空间方法比精确的Cholesky方法快13倍。因此,建议使用Krylov子空间方法进行具有水动力相互作用的大规模布朗动力学模拟。

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