线性尺度分离Ornstein-Uhlenbeck SDE的微宏观Parareal方法的收敛性：扩展版本
Convergence of the micro-macro Parareal Method for a Linear Scale-Separated Ornstein-Uhlenbeck SDE: extended version
AI总结：
本文提出并测试了用于随机微分方程的微宏观Parareal方法，分析了近似模型的模型误差对算法收敛性的影响，并通过数值实验验证了分析。
摘要：
时间并行方法可以通过在时间维度上进行并行化，来减少精确数值求解微分方程所需的实际运行时间。在本文中，我们提出并测试了用于随机微分方程（SDEs）的Parareal方法的一种多尺度、微宏观版本的收敛行为。在我们的方法中，SDE的精细传播子基于高维慢快微观模型；粗传播子基于后者的模型降阶版本，该版本捕获了慢时间尺度上的低维有效动力学。我们研究了近似模型的模型误差如何影响微宏观Parareal算法的收敛性，并通过数值实验支持了我们的分析。这是[Domain Decomposition Methods in Science and Engineering XXVII. DD 2022, vol 149 (2024), pp. 69-76, Bossuyt, I., Vandewalle, S., Samaey, G.]的扩展和修正版本。
英文摘要：
Time-parallel methods can reduce the wall clock time required for the accurate numerical solution of differential equations by parallelizing across the time-dimension. In this paper, we present and test the convergence behavior of a multiscale, micro-macro version of a Parareal method for stochastic differential equations (SDEs). In our method, the fine propagator of the SDE is based on a high-dimensional slow-fast microscopic model; the coarse propagator is based on a model-reduced version of the latter, that captures the low-dimensional, effective dynamics at the slow time scales. We investigate how the model error of the approximate model influences the convergence of the micro-macro Parareal algorithm and we support our analysis with numerical experiments. This is an extended and corrected version of [Domain Decomposition Methods in Science and Engineering XXVII. DD 2022, vol 149 (2024), pp. 69-76, Bossuyt, I., Vandewalle, S., Samaey, G.].
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