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arXiv 1503.02094math.NAcs.NA
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并行方法用于高振荡动力系统

Parareal methods for highly oscillatory dynamical systems

Bar-Ilan University（巴伊兰大学）；Georgia Institute of Technology（佐治亚理工学院）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；KTH Royal Institute of Technology（瑞典皇家理工学院）

Gil Ariel, Seong Jun Kim, Richard Tsai

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AI总结：

本文提出一种将并行时间方法与多尺度积分器结合的新策略，用于高振荡动力系统的高效求解。

摘要：

我们介绍了一种将并行时间（parareal）迭代方法与多尺度积分器结合的新策略。按照parareal框架，该算法使用适当的多尺度积分器计算系统中所有慢变量的低成本近似值，然后通过并行细尺度积分进行细化。通过快速相位样变量的对齐算法实现收敛。该方法可用于增强多尺度方法在仅近似慢变量时的精度和适用范围，或用于求解所有状态变量。该数值方案不要求系统被拆分为慢和快坐标。此外，动力学可能包含隐藏的慢变量，例如由于共振。我们提出了一种几乎周期解的对齐算法，此时parareal迭代的收敛性得到证明。该方法的适用性通过数值示例进行了演示。

英文摘要：

We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the system using an appropriate multiscale integrator, which is refined using parallel fine scale integrations. Convergence is obtained using an alignment algorithm for fast phase-like variables. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the state variables. The numerical scheme does not require that the system is split into slow and fast coordinates. Moreover, the dynamics may involve hidden slow variables, for example, due to resonances. We propose an alignment algorithm for almost-periodic solution, in which case convergence of the parareal iterations is proved. The applicability of the method is demonstrated in numerical examples.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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