  In the Ermak-McCammon algorithm for Brownian Dynamics, the hydrodynamic
interactions (HI) between N spherical particles are described by a 3N x 3N
diffusion tensor. This tensor has to be factorized at each timestep with a
runtime of O(N^3), making the calculation of the correlated random
displacements the bottleneck for many-particle simulations. Here we present a
faster algorithm for this step, which is based on a truncated expansion of the
hydrodynamic multi-particle correlations as two-body contributions. The
comparison to the exact algorithm and to the Chebyshev approximation of Fixman
verifies that for bead-spring polymers this approximation yields about 95% of
the hydrodynamic correlations at an improved runtime scaling of O(N^2) and a
reduced memory footprint. The approximation is independent of the actual form
of the hydrodynamic tensor and can be applied to arbitrary particle
configurations. This now allows to include HI into large many-particle Brownian
dynamics simulations, where until now the runtime scaling of the correlated
random motion was prohibitive.
