Multigrid reduction in time with Richardson extrapolation

Abstract

The advent of exascale computing will leave many users with access to more computational resources than they can simultaneously use, e.g., billion-way parallelism. In particular, this is true for time-dependent simulations that limit parallelism to the spatial domain. One method to add parallelism in time to existing simulation codes and thus take advantage of ever larger compute resources is Multigrid Reduction in Time (MGRIT). The goal is to achieve a smaller time-to-solution through parallelism in time. In this paper, MGRIT is enhanced with Richardson extrapolation in a cost-efficient way to produce a parallel-in-time method with improved accuracy. Overall, this leads to a large improvement in the accuracy per computational cost of MGRIT.

Linear multistep methods and global Richardson extrapolation

“…In [5], global (also known as passive) or local (active) versions of RE are implemented with Runge-Kutta sequences. These combined methods can find applications in air pollution problems [6] or in machine learning [7], for example.…”