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

## TL;DR

This paper introduces a GPU-based parallel algorithm for simulating Brownian particles with excluded volume, utilizing Delaunay triangulations to efficiently handle overlaps and achieve significant performance improvements.

## Contribution

The paper presents a novel GPU parallel simulation method using Delaunay triangulations to manage particle overlaps in Brownian motion simulations, enhancing efficiency.

## Key findings

- Achieved up to 100x speedup over sequential methods.
- Validated the algorithm with active colloidal particle models.
- Maintained triangulation validity during particle displacements.

## Abstract

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 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. The algorithm is validated with two models of active colloidal particles. Upon testing the parallel implementation of a long range forces simulation, the results show a performance improvement of up to two orders of magnitude when compared to the previously existing sequential solution.