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

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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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APA

Schöbel, R., & Speck, R. (2020). PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method. Computing and Visualization in Science, 23(1–4). https://doi.org/10.1007/s00791-020-00330-5

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