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

2018/05/17 by Xiaoqiang Yue, Yue, Xiaoqiang, Shi Shu +7
Mathematics · #Fractional Differential Equations Solutions #Differential Equations and Numerical Methods #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1805.06688

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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