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The paper investigates a non-intrusive parallel time integration withmultigrid for space-fractional diffusion equations in two spatial dimensions.We firstly obtain a fully discrete scheme via using the linear finite elementmethod to discretize spatial and temporal derivatives to propagate solutions.Next, we present a non-intrusive time-parallelization and its two-levelconvergence analysis, where we algorithmically and theoretically generalize theMGRIT to time-dependent fine time-grid propagators. Finally, numericalillustrations show that the obtained numerical scheme possesses the saturationerror order, theoretical results of the two-level variant deliver goodpredictions, and significant speedups can be achieved when compared to pararealand the sequential time-stepping approach.

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