Parallel-in-Time with Fully Finite Element Multigrid for 2-D Space-fractional Diffusion Equations
It provides a practical parallel-in-time solver for fractional diffusion equations, which are computationally expensive, but the contribution is incremental as it extends existing MGRIT methods to a specific problem class.
The paper develops a non-intrusive parallel time integration method with multigrid for 2-D space-fractional diffusion equations, achieving significant speedups over parareal and sequential time-stepping while maintaining saturation error order.
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.