PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method

Schöbel, Ruth; Speck, Robert

doi:10.1007/s00791-020-00330-5

Journal Article

FZJ-2020-03974

PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method

Schöbel, R. (Corresponding author)FZJ* ; Speck, R.FZJ*

2020
Springer Heidelberg

Computing and visualization in science 23(1-4), 12 (2020) [10.1007/s00791-020-00330-5]

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Please use a persistent id in citations: http://hdl.handle.net/2128/25908 doi:10.1007/s00791-020-00330-5

Abstract: To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to space–time multigrid, PFASST is able to compute multiple time-steps simultaneously and is therefore in particular suitable for large-scale applications on high performance computing systems. In this work we couple PFASST with a parallel spectral deferred correction (SDC) method, forming an unprecedented doubly time-parallel integrator. While PFASST provides global, large-scale “parallelization across the step”, the inner parallel SDC method allows integrating each individual time-step “parallel across the method” using a diagonalized local Quasi-Newton solver. This new method, which we call “PFASST with Enhanced concuRrency” (PFASST-ER), therefore exposes even more temporal concurrency. For two challenging nonlinear reaction-diffusion problems, we show that PFASST-ER works more efficiently than the classical variants of PFASST and can use more processors than time-steps.

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