Assignment of idle processors to spatial redistributed domains on coarse levels in multigrid reduction in time
Ryo Yoda, Matthias Bolten, Kengo Nakajima, Akihiro Fujii · 2022
Parallel-in-time approaches for time-dependent PDEs have attracted a great deal of attention in the context of massively parallel environments. One such approach, multigrid reduction in time (MGRIT), extracts temporal parallelism by applying the reduction-based multigrid method for the temporal domain. To make efficient use of this parallelism, some processors need to be idle on a temporal coarse level of MGRIT. This paper proposes an optimization of the implementation that uses idle processors by assigning the spatial redistributed domain on coarse levels. It accelerates coarse-level spatial solvers and promotes early switching to parallelization-in-time by reducing its overhead. Although the spatial redistribution is contrary to the motivation of parallel-in-time approaches, it is expected to be effective when we need to balance spatial and temporal parallelism. This is because parallelization-in-time is already usually switched on when parallelization-in-space starts to saturate, so one can still benefit from additional parallelism. Numerical experiments demonstrate an improvement in runtime, at most, about 16.6% compared with pure MGRIT, which assigns best spatial and temporal parallelism at specific parallelism.