Supervised parallelintime algorithm for longtime Lagrangian simulations of stochastic dynamics: Application to hydrodynamics
Abstract
Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation period of the fastest atomic motion, rendering longtime simulations very expensive. To resolve this bottleneck, we propose a supervised parallelintime algorithm for stochastic dynamics (SPASD) to accelerate longtime Lagrangian particle simulations. Our method is inspired by bottomup coarsegraining projections that yield meanfield hydrodynamic behavior in the continuum limit. Here as an example, we use the dissipative particle dynamics (DPD) as the Lagrangian particle simulator that is supervised by its macroscopic counterpart, i.e., the NavierStokes simulator. The lowdimensional macroscopic system (here, the NavierStokes solver) serves as a predictor to supervise the highdimensional Lagrangian simulator, in a predictorcorrector type algorithm. The results of the Lagrangian simulation then correct the meanfield prediction and provide the proper microscopic details (e.g., consistent fluctuations, correlations, etc.). The unique feature that sets SPASD apart from other multiscale methods is the use of a lowfidelity macroscopic model as a predictor. The macromodel can be approximate and even inconsistent with the microscale description, but SPASD anticipates the deviation and corrects it internally to recover the true dynamics. We first present the algorithm and analyze its theoretical speedup, and subsequently we present the accuracy and convergence of the algorithm for the timedependent plane Poiseuille flow, demonstrating that SPASD converges exponentially fast over iterations, irrespective of the accuracy of the predictor. Moreover, the fluctuating characteristics of the stochastic dynamics are identical to the unsupervised (serial in time) DPD simulation. We also compare the performance of SPASD to the conventional spatial decomposition method, which is one of the most parallelefficient methods for particle simulations. We find that the parallel efficiency of SPASD and the conventional spatial decomposition method are similar for a small number of computing cores, but for a large number of cores the performance of SPASD is superior. Furthermore, SPASD can be used in conjunction with spatial decomposition for enhanced performance. Lastly, we simulate a twodimensional cavity flow that requires more iterations to converge compared to the Poiseuille flow, and we observe that SPASD converges to the correct solution. Although a DPD solver is used to demonstrate the results, SPASD is a general framework and can be readily applied to other Lagrangian approaches including molecular dynamics and Langevin dynamics.
 Publication:

Journal of Computational Physics
 Pub Date:
 September 2019
 DOI:
 10.1016/j.jcp.2019.05.016
 arXiv:
 arXiv:1904.02137
 Bibcode:
 2019JCoPh.393..214B
 Keywords:

 Multiscale modeling;
 Lagrangian method;
 Parallelintime;
 Particle simulations;
 Dissipative particle dynamics;
 Physics  Computational Physics
 EPrint:
 17 pages, 19 figures