Accelerated force-coupling method and applications

Microscale fluid-structure interactions are present in many biological and industrial processes. To accelerate the computation of these interactions, we develop a fast implementation of the force-coupling method (FCM) in which the action of the mobility matrix is split between a global, grid-based computation involving a modified FCM kernel, and a local pairwise correction. The approach is constructed to yield a sparse, local-correction matrix to limit the need for pairwise corrections and to ensure the positive definiteness of the global and local-correction matrices. In most physical configurations, we have observed that fast FCM surpasses regular FCM by a factor of 10 to 100. Moreover, it has the advantage of being more memory-efficient, enabling larger simulations to be conducted. We demonstrate the effectiveness of fast FCM in simulating rod sedimentation and active filament synchronisation, where we find that the hydrodynamic solve constitutes a small fraction of the total computation costs.