Langevin dynamics simulation with dipole–dipole interactions: Massive performance improvements and advanced analytical integrator

Abstract

The required computation duration is a crucial element for the computer simulation of both molecular and suspended nanoparticle dynamics. The latter one is already highly-optimized on a theoretical level by the implicit solvent notion within the Langevin and Brownian Dynamics techniques which still requires a more clear theoretical connection though. Also, the calculation performance issue becomes much more serious in case of the long-range interaction within the magnetostatics and/or electrostatics problems. Hence, both conceptual aspects and a technical challenge require a resolution for the real experimental applications. In order to do so, the analytical fluctuative–dissipative integrator has been derived from basic theoretical foundation. A numerical simulation complexity is partly reduced by the analytical solution. The method is reinforced by the Barnes–Hut general-purpose graphics processing unit (GPU) based dipole–dipole interaction algorithm. As a real application close to an experiment, the Langevin dynamics simulation of up to 1 million ferrofluid nanoparticles evolution have been performed at the all-with-all dipole–dipole long-range interactions without any cutoff radius and with real coefficients of translational and rotational viscous friction. Computational time scales comparisons of different methods have been made: 100 ns in silico could take between minutes till years of a computation Unix epoch time depending on a method. The 850000 times calculation duration speed up from slowest (well-known) towards fastest (suggested here) simulation method has been achieved. Due to a GPU parallel computation the required calculation time scales up proportionally to a number of nanoparticles N which is much better compared to N*N or N*log(N) in case of a direct dipole summation or Barnes–Hut on the single processor method, respectively. The overall implementation is available and ready to be used within the wider open-source software package.