The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to develop and analyze a MGRIT algorithm using FCF-relaxation with time-dependent time-grid propagators to seek the finite element approximations of unsteady fractional Laplacian problems. The multigrid with line smoother proposed in Chen et al. (2016) is chosen to be the spatial solver. Motivated by Southworth (2019), we provide a new temporal eigenvalue approximation property and then deduce a generalized two-level convergence theory which removes the previous unitary diagonalization assumption on the fine and coarse time-grid propagators required in Yue et al. (2019). Numerical computations are included to confirm the theoretical predictions and demonstrate the sharpness of the derived convergence upper bound.

事实证明，通过及时利用并行性，多时间网格缩减（MGRIT）技术成功实现了更高的运行时加速。本文的目的是开发和分析一种使用FCF松弛和时间相关的时间网格传播器的MGRIT算法，以寻求非定常分数拉普拉斯问题的有限元逼近。Chen等人提出的带有线平滑器的多重网格。（2016）被选为空间求解器。受Southworth（2019）的启发，我们提供了一种新的时间特征值逼近性质，然后推导了广义的两级收敛理论，该理论消除了对Yue等人所要求的细粒度和粗粒度网格传播器的先前unit对角化假设。（2019）。