2019/02/21 by Hannes Vandecasteele, Vandecasteele, Hannes, Przemysław Zieliński +3
Engineering · Physics and Astronomy · Economics, Econometrics and Finance · #Fluid Dynamics and Turbulent Flows #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1902.08045
We discuss through multiple numerical examples the accuracy and efficiency of\na micro-macro acceleration method for stiff stochastic differential equations\n(SDEs) with a time-scale separation between the fast microscopic dynamics and\nthe evolution of some slow macroscopic state variables. The algorithm\ninterleaves a short simulation of the stiff SDE with extrapolation of the\nmacroscopic state variables over a longer time interval. After extrapolation,\nwe obtain the reconstructed microscopic state via a matching procedure: we\ncompute the probability distribution that is consistent with the extrapolated\nstate variables, while minimally altering the microscopic distribution that was\navailable just before the extrapolation. In this work, we numerically study the\naccuracy and efficiency of micro-macro acceleration as a function of the\nextrapolation time step and as a function of the chosen macroscopic state\nvariables. Additionally, we compare the effect of different hierarchies of\nmacroscopic state variables. We illustrate that the method can take\nsignificantly larger time steps than the inner microscopic integrator, while\nsimultaneously being more accurate than approximate macroscopic models.\n