Adaptive Brownian Dynamics

A framework for performant Brownian Dynamics (BD) many-body simulations with adaptive timestepping is presented. Contrary to the Euler-Maruyama scheme in common non-adaptive BD, we employ an embedded Heun-Euler integrator propagation of overdamped coupled Langevin equations motion. This enables derivation a local error estimate and formulation criteria acceptance or rejection trial steps control optimal stepsize. Introducing erroneous bias random forces avoided by Rejection Sampling Memory (RSwM) due Rackauckas Nie, which makes use bridge theorem guarantees correct generation specified process even when rejecting steps. For test cases Lennard-Jones fluids bulk confinement, it shown that BD solves performance stability issues conventional already outperforming latter standard situations. We expect this novel computational approach be especially helpful long-time complex systems, e.g. non-equilibrium, where concurrent slow fast processes occur.