论文标题
多层次瘫痪算法，平均振荡问题
Multi-level Parareal algorithm with Averaging for Oscillatory Problems
论文作者
论文摘要
本研究是对振荡PDE所做的工作的扩展，该振荡PDE具有有限的时间尺度分离（2019），A。G. Peddle，T。Haut和B. Wingate，[16]，以及用于高度振荡的PDES（2014）（2014），T。Haut和B. Wingate和B. Wingate，[10]的渐近平行方法，本文提出的方法是一种多级瘫痪方法，其任意级别不限于两级情况。我们给出一个渐近误差估计，该估计值将仅考虑两个级别的情况下减少了两级估计。引入两个以上的级别对平均过程产生了重要的后果，因为我们为每个不同级别选择单独的平均窗口，这是本研究的另一个新功能。不同的平均窗口使所提出的方法特别适合多规模问题，因为我们可以为问题的每个固有规模引入一个级别，并调整平均过程，以便我们在由级别解决的特定规模上重现模型的行为。研究了新方法的计算复杂性，并在几个示例上研究了效率。
The present study is an extension of the work done in Parareal convergence for oscillatory pdes with finite time-scale separation (2019), A. G. Peddle, T. Haut, and B. Wingate, [16], and An asymptotic parallel-in-time method for highly oscillatory pdes (2014), T. Haut and B. Wingate, [10], where a two-level Parareal method with averaging is examined. The method proposed in this paper is a multi-level Parareal method with arbitrarily many levels, which is not restricted to the two-level case. We give an asymptotic error estimate which reduces to the two-level estimate for the case when only two levels are considered. Introducing more than two levels has important consequences for the averaging procedure, as we choose separate averaging windows for each of the different levels, which is an additional new feature of the present study. The different averaging windows make the proposed method especially appropriate for multi-scale problems, because we can introduce a level for each intrinsic scale of the problem and adapt the averaging procedure such that we reproduce the behavior of the model on the particular scale resolved by the level. The computational complexity of the new method is investigated and the efficiency is studied on several examples.
