Ruprecht, DanielDanielRuprecht1429300590000-0003-1904-2473Saupe, ThomasThomasSaupe2026-01-062026-01-062026Technische Universität Hamburg (2026)https://hdl.handle.net/11420/60514Spectral Deferred Correction (SDC) is a method for numerically integrating initial value problems. The method iteratively generates solutions to fully implicit Runge-Kutta methods with forward substitution using low order solves. This allows great flexibility, for instance 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 multiple steps concurrently. We propose two adaptive step size selection algorithms that tailor the ideas behind embedded Runge-Kutta methods to SDC. Both are completely generic and work only on intermediate values within the time-integration process. We show, with a range of experiments, that computational efficiency can be boosted significantly by employing these algorithms compared to standard SDC. Furthermore, we show that parallel-in-time adaptive SDC is competitive with state-of-the-art Runge-Kutta methods for stiff partial differential equations. We also show that adaptivity increases the resilience against soft faults in SDC. Soft faults are unanticipated alterations of the data stored in memory, brought about, for instance, by environmental radiation. Iterative or adaptive methods inherently provide an elevated level of resilience, which is well known also in the context of the embedded Runge-Kutta methods that the adaptive step size selection is based on. We then move on to port implementations of partial differential equations within the prototyping 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 scaling capabilities and allowed to run a Gray-Scott example on 3584 GPUs at decent parallel efficiency. Finally, we demonstrate that findings from the previous experiments translate to practical use via space-time-parallel production runs of Gray-Scott and Rayleigh-Benard convection using adaptive SDC.Spectral deferred correction (SDC) ist ein Zeitschrittverfahren bei dem Lösungen zu voll-impliziten Runge-Kutta (RK) Verfahren iterativ gewonnen werden. Wir entwickeln zwei Methoden zur adaptiven Schrittweitensteuerung und demonstrieren deren Potenzial zur Effizienzsteigerung an vier nichtlinearen Problemen. Dann messen wir Beschleunigung durch Parallelisierung mittels diagonalem SDC und Block Gauß-Seidel SDC, wobei Zeit-paralleles SDC für steife PDEs schneller war als RK Verfahren. Danach bestätigen wir experimentell, dass adaptives SDC gegen spontane Bit-Flips schützen kann, welche auf großen Supercomputern regelmäßig zu erwarten sind. Schließlich entwickeln wir Raum-Zeit-parallele Implementierungen von Spektralverfahren und diagonalem SDC, die für Rayleigh-Benard Konvektion bis tausenden von CPUs und für das Gray-Scott Modell bis tausenden von GPUs skalieren.enhttps://creativecommons.org/licenses/by/4.0/spectral deferred correctionparallel-in-timeadaptivitytime integrationresilienceNatural Sciences and Mathematics::518: Numerical AnalysisDoctoral Thesishttps://doi.org/10.15480/882.1636010.15480/882.16360Bolten, MatthiasMatthiasBolten10.5281/zenodo.15308622Other