Fast neighbor lists for adaptive-resolution particle simulations

Particle methods provide a simple yet powerful framework for simulating both discrete and continuous systems either deterministically or stochastically. The inherent adaptivity of particle methods is particularly appealing when simulating multiscale models or systems that develop a wide spectrum of length scales. Evaluating particle–particle interactions using neighbor-finding algorithms such as cell lists or Verlet lists, however, quickly becomes inefficient in adaptive-resolution simulations where the interaction cutoff radius is a function of space. We present a novel adaptive-resolution cell list algorithm and the associated data structures that provide efficient access to the interaction partners of a particle, independent of the (potentially continuous) spectrum of cutoff radii present in a simulation. We characterize the computational cost of the proposed algorithm for a wide range of resolution spans and particle numbers, showing that the present algorithm outperforms conventional uniform-resolution cell lists in most adaptive-resolution settings.