The paper presents a combination of the time-parallel parallel full approximation scheme in space and time (PFASST) with a parallel multigrid method (PMG) in space, resulting in a mesh-based solver for the three-dimensional heat equation with a uniquely high degree of efficient concurrency. Parallel scaling tests are reported on the Cray XE6 machine Monte Rosa on up to 16,384 cores and on the IBM Blue Gene/Q system JUQUEEN on up to 65,536 cores. The efficacy of the combined spatial- and temporal parallelization is shown by demonstrating that using PFASST in addition to PMG significantly extends the strong-scaling limit. Implications of using spatial coarsening strategies in PFASSTs multi-level hierarchy in large-scale parallel simulations are discussed.
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