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We develop a new algorithm for the Brownian dynamics of soft matter systemsthat evolves time by spatially correlated Monte Carlo moves. The algorithm usesvector wavelets as its basic moves and produces hydrodynamics in the lowReynolds number regime propagated according to the Oseen tensor. When smallmoves are removed the correlations closely approximate the Rotne-Prager tensor,itself widely used to correct for deficiencies in Oseen. We also include planewave moves to provide the longest range correlations, which we detail for bothinfinite and periodic systems. The computational cost of the algorithm scalescompetitively with the number of particles simulated, $N$, scaling as $N\ln N$in homogeneous systems and as $N$ in dilute systems. In comparisons toestablished lattice Boltzmann and Brownian dynamics algorithms the waveletmethod was found to be only a factor of order 1 times more expensive than thecheaper lattice Boltzmann algorithm in marginally semi-dilute simulations,while it is significantly faster than both algorithms at large $N$ in dilutesimulations. We also validate the algorithm by checking it reproduces thecorrect dynamics and equilibrium properties of simple single polymer systems,as well as verifying the effect of periodicity on the mobility tensor.

Wavelet Monte Carlo dynamics: a new algorithm for simulating the hydrodynamics of interacting Brownian particles