Collective mode Brownian dynamics: A method for fast relaxation of statistical ensembles

Sampling equilibrium configurations of correlated systems of particles with long relaxation times (e.g., polymeric solutions) using conventional molecular dynamics and Monte Carlo methods can be challenging. This is especially true for systems with complicated, extended bond network topologies and other interactions that make the use and design of specialized relaxation protocols infeasible. We introduce a method based on Brownian dynamics simulations that can reduce the computational time it takes to reach equilibrium and draw decorrelated samples. Importantly, the method is completely agnostic to the particle configuration and the specifics of interparticle forces. In particular, we develop a mobility matrix that excites non-local, collective motion of N particles and can be computed efficiently in O(N) time. Particle motion in this scheme is computed by integrating the overdamped Langevin equation with an Euler-Maruyama scheme, in which Brownian displacements are drawn efficiently using a low-rank representation of the mobility matrix in position and wave space. We demonstrate the efficacy of the method with various examples from the realm of soft condensed matter and release a massively parallel implementation of the code as a plugin for the open-source package HOOMD-blue [J. A. Anderson et al., J. Comput. Phys. 227, 5342 (2008) and J. Glaser et al., Comput. Phys. Commun. 192, 97 (2015)] which runs on graphics processing units.