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001020591 1001_ $$00000-0001-8450-9223$$aGander, Martin J.$$b0
001020591 245__ $$aA Unified Analysis Framework for Iterative Parallel-in-Time Algorithms
001020591 260__ $$aPhiladelphia, Pa.$$bSIAM$$c2023
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001020591 520__ $$aParallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various iterative parallel-in-time algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notation, and the convergence estimates that are available are difficult to compare. We describe Parareal, PFASST, MGRIT, and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions. This allows us, for the first time, to directly compare their convergence. We prove that all four methods eventually converge superlinearly, and we also compare them numerically. The generating function framework provides further opportunities to explore and analyze existing and new methods.
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001020591 536__ $$0G:(EU-Grant)955701$$aTIME-X - TIME parallelisation: for eXascale computing and beyond (955701)$$c955701$$fH2020-JTI-EuroHPC-2019-1$$x1
001020591 536__ $$0G:(BMBF)16HPC047$$aVerbundprojekt: TIME-X - Parallelisierung zeitabhängiger Simulationen für das zukünftige Supercomputing (16HPC047)$$c16HPC047$$x2
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001020591 7001_ $$0P:(DE-HGF)0$$aLunet, Thibaut$$b1$$eCorresponding author
001020591 7001_ $$00000-0003-1904-2473$$aRuprecht, Daniel$$b2
001020591 7001_ $$0P:(DE-Juel1)132268$$aSpeck, Robert$$b3$$ufzj
001020591 773__ $$0PERI:(DE-600)1468391-X$$a10.1137/22M1487163$$gVol. 45, no. 5, p. A2275 - A2303$$n5$$pA2275 - A2303$$tSIAM journal on scientific computing$$v45$$x1064-8275$$y2023
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