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arXiv · 1805.06688

Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations

Xiaoqiang Yue·Shi Shu·Xiaowen Xu·Weiping Bu·Kejia Pan
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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.

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Xiaoqiang Yue, Shi Shu, Xiaowen Xu, Weiping Bu, Kejia Pan. 2018-05-17. Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations. https://arxiv.org/abs/1805.06688

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