Acceleration of Optimized Coarse-Grid Operators by Spatial Redistribution for Multigrid Reduction in Time

The multigrid reduction in time (MGRIT) method is one of the parallel-in-time approaches for time-dependent PDEs and typically uses rediscretized coarse-grid operators. As their convergence struggle with hyperbolic problems, an optimization method for coarse-grid operators has been proposed to deal with these problems. This method improves convergence using coarse-grid operators with a slightly increased number of nonzero elements. However, it is more desirable for coarse-grid operators to be cheaper than fine-grid operators, and there is room for improvement in terms of parallel implementation. This work combines the spatial redistribution technique for MGRIT, which accelerates coarse-grid solvers using agglomerated idle processors, with the above optimization method. This combination attempts to achieve better scaling performance while maintaining good convergence. Numerical experiments demonstrate a 23% runtime reduction at most among the various assignments tried with specific amount of parallelism.