Large-Scale Hydrodynamic Brownian Simulations on Multicore and Manycore Architectures

Conventional Brownian dynamics (BD) simulations with hydrodynamic interactions utilize 3n×3n dense mobility matrices, where n is the number of simulated particles. This limits the size of BD simulations, particularly on accelerators with low memory capacities. In this paper, we formulate a matrix-free algorithm for BD simulations, allowing us to scale to very large numbers of particles while also being efficient for small numbers of particles. We discuss the implementation of this method for multicore and many core architectures, as well as a hybrid implementation that splits the workload between CPUs and Intel Xeon Phi coprocessors. For 10,000 particles, the limit of the conventional algorithm on a 32 GB system, the matrix-free algorithm is 35 times faster than the conventional matrix based algorithm. We show numerical tests for the matrix-free algorithm up to 500,000 particles. For large systems, our hybrid implementation using two Intel Xeon Phi coprocessors achieves a speedup of over 3.5x compared to the CPU-only case. Our optimizations also make the matrix-free algorithm faster than the conventional dense matrix algorithm on as few as 1000 particles.