With current trends in computer architectures leading towards systems with more, but not faster, processors, faster time-to-solution must come from greater parallelism. We present a family of truly multilevel approaches to parallel time integration based on multigrid reduction (MGR) principles. The resulting multigrid-reduction-in-time (MGRIT) algorithms are non-intrusive approaches, which directly use an existing time propagator and, thus, can easily exploit substantially more computational resources then standard sequential time-stepping. Furthermore, we demonstrate that MGRIT offers excellent strong and weak parallel scaling up to thousands of processors for solving diffusion equations in two and three space dimensions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]
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