000278997 001__ 278997 000278997 005__ 20230310131354.0 000278997 0247_ $$2doi$$a10.1137/14097536X 000278997 0247_ $$2ISSN$$a0196-5204 000278997 0247_ $$2ISSN$$a1064-8275 000278997 0247_ $$2ISSN$$a1095-7197 000278997 0247_ $$2Handle$$a2128/9528 000278997 0247_ $$2WOS$$aWOS:000364457000031 000278997 0247_ $$2altmetric$$aaltmetric:2537338 000278997 037__ $$aFZJ-2015-07167 000278997 082__ $$a004 000278997 1001_ $$0P:(DE-HGF)0$$aMinion, M. L.$$b0$$eCorresponding author 000278997 245__ $$aInterweaving PFASST and Parallel Multigrid 000278997 260__ $$aPhiladelphia, Pa.$$bSIAM$$c2015 000278997 3367_ $$2DRIVER$$aarticle 000278997 3367_ $$2DataCite$$aOutput Types/Journal article 000278997 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1502263819_32596 000278997 3367_ $$2BibTeX$$aARTICLE 000278997 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000278997 3367_ $$00$$2EndNote$$aJournal Article 000278997 520__ $$aThe parallel full approximation scheme in space and time (PFASST) introduced by Emmett and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and discretized PDEs. As the name suggests, PFASST is similar in spirit to a space-time full approximation scheme multigrid method performed over multiple time steps in parallel. However, since the original focus of PFASST was on the performance of the method in terms of time parallelism, the solution of any spatial system arising from the use of implicit or semi-implicit temporal methods within PFASST have simply been assumed to be solved to some desired accuracy completely at each substep and each iteration by some unspecified procedure. It hence is natural to investigate how iterative solvers in the spatial dimensions can be interwoven with the PFASST iterations and whether this strategy leads to a more efficient overall approach. This paper presents an initial investigation on the relative performance of different strategies for coupling PFASST iterations with multigrid methods for the implicit treatment of diffusion terms in PDEs. In particular, we compare full accuracy multigrid solves at each substep with a small fixed number of multigrid V-cycles. This reduces the cost of each PFASST iteration at the possible expense of a corresponding increase in the number of PFASST iterations needed for convergence. Parallel efficiency of the resulting methods is explored through numerical examples. 000278997 536__ $$0G:(DE-HGF)POF3-511$$a511 - Computational Science and Mathematical Methods (POF3-511)$$cPOF3-511$$fPOF III$$x0 000278997 536__ $$0G:(GEPRIS)450829162$$aDFG project 450829162 - Raum-Zeit-parallele Simulation multimodale Energiesystemen (450829162)$$c450829162$$x1 000278997 536__ $$0G:(DE-Juel1)hwu12_20141101$$aScalable solvers for linear systems and time-dependent problems (hwu12_20141101)$$chwu12_20141101$$fScalable solvers for linear systems and time-dependent problems$$x2 000278997 588__ $$aDataset connected to CrossRef 000278997 7001_ $$0P:(DE-Juel1)132268$$aSpeck, R.$$b1$$ufzj 000278997 7001_ $$0P:(DE-HGF)0$$aBolten, M.$$b2 000278997 7001_ $$0P:(DE-HGF)0$$aEmmett, M.$$b3 000278997 7001_ $$0P:(DE-HGF)0$$aRuprecht, D.$$b4 000278997 773__ $$0PERI:(DE-600)1468391-x$$a10.1137/14097536X$$gVol. 37, no. 5, p. 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