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| Hauptseite > Publikationsdatenbank > Efficient Massively Space-Time-Parallel Simulations with Adaptive Spectral Deferred Correction |
| Hauptseite > Publikationsdatenbank > Efficient Massively Space-Time-Parallel Simulations with Adaptive Spectral Deferred Correction |
| Talk (non-conference) (Other) | FZJ-2025-05338 |
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2025
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Please use a persistent id in citations: doi:10.34734/FZJ-2025-05338
Abstract: Spectral Deferred Correction (SDC) is a method for numerically integrating initialvalue problems. The method iteratively generates solutions to fully implicit Runge-Kuttamethods with forward substitution using low order solves. This allows great flexibility, forinstance in terms of splitting techniques or inexact solves. Furthermore, various parallel-in-time extensions exist that parallelize the solution of a single time-step or solve multiplesteps concurrently.We propose two adaptive step size selection algorithms that tailor the ideas behindembedded Runge-Kutta methods to SDC. Both are completely generic and work only onintermediate values within the time-integration process. We show, with a range of experi-ments, that computational efficiency can be boosted significantly by employing these algo-rithms compared to standard SDC. Furthermore, we show that parallel-in-time adaptiveSDC is competitive with state-of-the-art Runge-Kutta methods for stiff partial differentialequations.We also show that adaptivity increases the resilience against soft faults in SDC. Softfaults are unanticipated alterations of the data stored in memory, brought about, forinstance, by environmental radiation. Iterative or adaptive methods inherently providean elevated level of resilience, which is well known also in the context of the embeddedRunge-Kutta methods that the adaptive step size selection is based on.We then move on to port implementations of partial differential equations within theprototyping library pySDC to GPUs and make extensive space-time-parallel scaling tests.We find that the parallel-in-time extension diagonal SDC can help extend the scalingcapabilities and allowed to run a Gray-Scott example on 3584 GPUs at decent parallelefficiency. Finally, we demonstrate that findings from the previous experiments translateto practical use via space-time-parallel production runs of Gray-Scott and Rayleigh-Benardconvection using adaptive SDC.
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