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001028863 0247_ $$2datacite_doi$$a10.34734/FZJ-2024-04849
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001028863 1001_ $$0P:(DE-Juel1)190575$$aBaumann, Thomas$$b0$$eCorresponding author$$ufzj
001028863 1112_ $$a13th Parallel-in-Time Workshop$$cBruges$$d2024-02-05 - 2024-02-09$$wBelgium
001028863 245__ $$aAdaptive Step Size in SDC and What’s New With pySDC?
001028863 260__ $$c2024
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001028863 520__ $$aWe are transferring well-known concepts from embedded Runge-Kutta methods to Spectral Deferred Corrections (SDC) to enable adaptive step size selection.This works by estimating the local error and updating the step size such that a set tolerance is matched.The local error is estimated via a secondary lower-order method and the step size is updated according to this method's order.Taking a converged collocation problem, we can generate a secondary solution by interpolation from all but one collocation node to the remaining node.Because there is no dependence on how the collocation problem was solved, advanced SDC approaches such as inexactness and diagonal preconditioners can be used.We show with experiments in pySDC that such schemes can outperform state-of-the-art diagonally implicit Runge-Kutta methods for partial differential equations in wall-time measurements.
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001028863 536__ $$0G:(EU-Grant)955701$$aTIME-X - TIME parallelisation: for eXascale computing and beyond (955701)$$c955701$$fH2020-JTI-EuroHPC-2019-1$$x1
001028863 7001_ $$0P:(DE-Juel1)132268$$aSpeck, Robert$$b1$$ufzj
001028863 7001_ $$0P:(DE-HGF)0$$aLunet, Thibaut$$b2
001028863 7001_ $$0P:(DE-HGF)0$$aRuprecht, Daniel$$b3
001028863 7001_ $$0P:(DE-HGF)0$$aGötschel, Sebastian$$b4
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001028863 9141_ $$y2024
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