Asynchronous Truncated Multigrid-reduction-in-time (AT-MGRIT)

TL;DR

The paper introduces AT-MGRIT, an asynchronous multigrid-reduction-in-time algorithm that enhances parallelism for time-dependent problems by using local truncated coarse grids, outperforming traditional methods like Parareal.

Contribution

It proposes a novel asynchronous multigrid-reduction-in-time method utilizing local coarse grids, improving parallel efficiency and convergence over existing approaches.

Findings

AT-MGRIT reduces sequential bottlenecks in time parallelism.

The method outperforms Parareal/MGRIT in convergence speed.

Numerical experiments confirm improved performance on nonlinear problems.

Abstract

In this paper, we present the new "asynchronous truncated multigrid-reduction-in-time" (AT-MGRIT) algorithm for introducing time parallelism to the solution of discretized time-dependent problems. The new algorithm is based on the multigrid-reduction-in-time (MGRIT) approach, which, in certain settings, is equivalent to another common multilevel parallel-in-time method, Parareal. In contrast to Parareal and MGRIT that both consider a global temporal grid over the entire time interval on the coarsest level, the AT-MGRIT algorithm uses truncated local time grids on the coarsest level, each grid covering certain temporal subintervals. These local grids can be solved completely independent from each other, which reduces the sequential part of the algorithm and, thus, increases parallelism in the method. Here, we study the effect of using truncated local coarse grids on the convergence of the algorithm, both theoretically and numerically, and show, using challenging nonlinear problems, that the new algorithm consistently outperforms classical Parareal/MGRIT in terms of time to solution.