Multiscale Modeling &Simulation, Volume 18, Issue 3, Page 1272-1298, January 2020.
We discuss through multiple numerical examples the accuracy and efficiency of a micro-macro acceleration method for stiff stochastic differential equations (SDEs) with a time-scale separation between the fast microscopic dynamics and the evolution of some slow macroscopic state variables. The algorithm interleaves a short simulation of the stiff SDE with extrapolation of the macroscopic state variables over a longer time interval. After extrapolation, we obtain the reconstructed microscopic state via a matching procedure: we compute the probability distribution that is consistent with the extrapolated state variables, while minimally altering the microscopic distribution that was available just before the extrapolation. In this work, we numerically study the accuracy and efficiency of micro-macro acceleration as a function of the extrapolation time step and as a function of the chosen macroscopic state variables. Additionally, we compare the effect of different hierarchies of macroscopic state variables. We illustrate that the method can take significantly larger time steps than the inner microscopic integrator, while simultaneously being more accurate than approximate macroscopic models.

中文翻译：

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尺度分离随机微分方程的微宏加速方法的效率

多尺度建模与仿真，第18卷，第3期，第1272-1298页，2020年1月。
我们通过多个数值示例讨论了用于刚性随机微分方程（SDE）的微宏加速方法的精度和效率，该方法在快速微观动力学和一些慢速宏观状态变量的演化之间具有时间尺度的分隔。该算法通过在较长的时间间隔内外推宏观状态变量来对刚性SDE进行简短的模拟。外推后，我们通过匹配过程获得重构的微观状态：我们计算与外推状态变量一致的概率分布，同时最小化更改外推之前可用的微观分布。在这项工作中 我们从数值上研究了微宏加速的精度和效率，该精度和效率是外推时间步长的函数以及所选择的宏观状态变量的函数。此外，我们比较了宏观状态变量的不同层次结构的影响。我们说明，该方法比内部微观积分器可以花费更多的时间，同时比近似宏观模型更准确。