  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 PFASST's multi-level hierarchy in large-scale parallel
simulations are discussed.
