Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations
Abstract
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to discretize spatial and temporal derivatives to propagate solutions. Next, we present a non-intrusive time-parallelization and its two-level convergence analysis, where we algorithmically and theoretically generalize the MGRIT to time-dependent fine time-grid propagators. Finally, numerical illustrations show that the obtained numerical scheme possesses the saturation error order, theoretical results of the two-level variant deliver good predictions, and significant speedups can be achieved when compared to parareal and the sequential time-stepping approach.
Cite
@article{arxiv.1805.06688,
title = {Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations},
author = {Xiaoqiang Yue and Shi Shu and Xiaowen Xu and Weiping Bu and Kejia Pan},
journal= {arXiv preprint arXiv:1805.06688},
year = {2018}
}
Comments
20 pages, 4 figures, 8 tables