This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial values at each subinterval as well as the corresponding period iteratively. As in the Parareal method, parallelization in the time domain is performed using discretization on a two-level grid. A special linearization of the time-periodic system on the coarse grid is introduced to speed up the computations. The iterative algorithm is verified via its application to the Colpitt oscillator model.

中文翻译：

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对未知周期的时间周期解进行时间并行计算

本文提出了一种新颖的时间并行算法，能够计算未给定周期的问题的时间周期解。该方法利用多次拍摄方法的思想，迭代计算每个子间隔以及相应周期的初始值。与 Parareal 方法一样，时域中的并行化是在两级网格上使用离散化来执行的。引入了粗网格上时间周期系统的特殊线性化以加快计算速度。通过将迭代算法应用于 Colpitt 振荡器模型来验证迭代算法。