Parallel-in-time multigrid for space-time finite element approximations of two-dimensional space-fractional diffusion equations
Parallel-in-time multigrid for space-time finite element approximations of two-dimensional space-fractional diffusion equations
复制标题
二维空间分数扩散方程的时空有限元近似的时间并行多重网格
DOI：
10.1016/j.camwa.2019.05.017
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发表时间：
2019-12-01
影响因子：
2.9
通讯作者：
Pan, Kejia
中科院分区：
文献类型：
--
作者：
Yue, Xiaoqiang;Shu, Shi;Pan, Kejia
本文研究了二维空间分数阶扩散方程的多重网格非侵入式并行时间积分，并用时空有限元方法对其进行离散以传播解。在时间网格传播子的稳定性和同时对角化的假设下，提出了一种时间网格传播子与时间相关的多重网格时间约简(MGRIT)算法，并给出了算法的两级收敛理论。数值结果表明，该方法具有饱和误差阶，两级变型的理论计算结果对模型问题有较好的预测效果，与两级变型的F-松弛算法(相当于Parareal算法)和序贯时间步长方法相比，MGRIT具有显著的加速比。(C)2019爱思唯尔有限公司。保留所有权利。
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions, which is discretized by the space-time finite element method to propagate solutions. We develop a multigrid-reduction-in-time (MGRIT) algorithm with time-dependent time-grid propagators and provide its two-level convergence theory under the assumptions of the stability and simultaneous diagonalizability on time-grid propagators. Numerical results show that the proposed method possesses the saturation error order, theoretical results of the two-level variant deliver good predictions for our model problems, and significant speedups of the MGRIT can be achieved when compared to the two-level variant with F-relaxation (an equivalent version of the parareal algorithm) and the sequential time-stepping approach. (C) 2019 Elsevier Ltd. All rights reserved.