An O(N~2) approximation for hydrodynamic interactionsin Brownian dynamics simulations

摘要

In the Ermak-McCammon algorithm for Brownian dynamics, the hydrodynamic interactions (HIs)between N spherical particles are described by a 3N X 3N diffusion tensor. This tensor has to befactorized at each time step with a runtime of 0(N3), making the calculation of the correlatedrandom displacements the bottleneck for many-particle simulations. Here we present a fasteralgorithm for this step, which is based on a truncated expansion of the hydrodynamic multiparticlecorrelations as two-body contributions. The comparison to the exact algorithm and to the Chebyshevapproximation of Fixman verifies that for bead-spring polymers this approximation yields about95% of the hydrodynamic correlations at an improved runtime scaling of O(N~2) and a reducedmemory footprint. The approximation is independent of the actual form of the hydrodynamic tensorand can be applied to arbitrary particle configurations. This now allows to include HI into largemany-particle Brownian dynamics simulations, where until now the runtime scaling of thecorrelated random motion was prohibitive.