GPU parallel simulation algorithm of Brownian particles with excluded volume using Delaunay triangulations

A novel parallel simulation algorithm on the GPU, implemented in CUDA and C++, is presented for the simulation of Brownian particles that display excluded volume repulsion and interact with long and short range forces. When an explicit Euler-Maruyama integration step is performed to take into account the pairwise forces and Brownian motion, particle overlaps can appear. The excluded volume property brings up the need for correcting these overlaps as they happen, since predicting them is not feasible due to the random displacement of Brownian particles. The proposed solution handles, at each time step, a Delaunay triangulation of the particle positions because it allows us to efficiently solve overlaps between particles by checking just their neighborhood. The algorithm starts by generating a periodic Delaunay triangulation of the particle initial positions on CPU, but after that the triangulation is always kept on GPU memory. We used a parallel edge-flip implementation to keep the triangulation updated during each time step, checking previously that the triangulation was not rendered invalid due to the particle displacements. We designed and implemented an exact long range force simulation with an all-pairs N-body simulation, tiling the particle interaction computations based on the warp size of the target device architecture. The resulting implementation was validated with two models of active colloidal particles, also showing a speedup of up to two orders of magnitude when compared to a sequential implementation. A short range forces simulation using Verlet lists for neighborhood handling was also developed and validated, showing similar performance improvements.