Center for the Study of Systems Biology, School of Biology, Georgia Institute of Technology, 250 14th Street NW, Atlanta, Georgia 30318-5304, USA.
J Chem Phys. 2012 Aug 14;137(6):064106. doi: 10.1063/1.4742347.
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(N(2)) 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.
流体动力相互作用在大分子动力学中起着重要作用。在分子模拟中考虑流体动力效应的最常见方法是在布朗动力学模拟的背景下。然而，在这些模拟中计算相关的布朗噪声向量在计算上非常耗费，因此需要替代方法。本文研究了基于 Krylov 子空间的计算布朗噪声向量的方法。这些方法与切比雪夫多项式逼近有关，但不需要特征值估计。我们表明，仅需要在布朗噪声向量中具有低精度，就可以准确计算聚合物和单分散悬浮模型的动态和静态特性的值。在这种精度水平下，Krylov 子空间方法的计算时间对于粒子数 N 高达 10000 的情况，几乎呈 O(N^2)的比例缩放，这是测试的极限。Krylov 子空间方法的性能，特别是“块”版本，甚至比切比雪夫方法略好，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，建议在具有流体动力相互作用的大规模布朗动力学模拟中使用 Krylov 子空间方法。
