000154819 001__ 154819
000154819 005__ 20230310131346.0
000154819 037__ $$aFZJ-2014-04087
000154819 041__ $$aEnglish
000154819 1001_ $$0P:(DE-HGF)0$$aMinion, Michael$$b0$$eCorresponding Author
000154819 245__ $$aInterweaving PFASST and Parallel Multigrid
000154819 260__ $$c2014
000154819 3367_ $$0PUB:(DE-HGF)25$$2PUB:(DE-HGF)$$aPreprint$$bpreprint$$mpreprint$$s1407312392_13621
000154819 3367_ $$2ORCID$$aWORKING_PAPER
000154819 3367_ $$2DRIVER$$apreprint
000154819 3367_ $$2DataCite$$aOutput Types/Working Paper
000154819 3367_ $$028$$2EndNote$$aElectronic Article
000154819 3367_ $$2BibTeX$$aARTICLE
000154819 520__ $$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 FAS multigrid method performed over multiple time-steps in parallel. However, since the original focus of PFASST has been 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 sub-step 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 sub-step 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.
000154819 536__ $$0G:(DE-HGF)POF2-411$$a411 - Computational Science and Mathematical Methods (POF2-411)$$cPOF2-411$$fPOF II$$x0
000154819 536__ $$0G:(GEPRIS)450829162$$aDFG project 450829162 - Raum-Zeit-parallele Simulation multimodale Energiesystemen (450829162)$$c450829162$$x1
000154819 7001_ $$0P:(DE-Juel1)132268$$aSpeck, Robert$$b1$$ufzj
000154819 7001_ $$0P:(DE-HGF)0$$aBolten, Matthias$$b2
000154819 7001_ $$0P:(DE-HGF)0$$aEmmett, Matthew$$b3
000154819 7001_ $$0P:(DE-HGF)0$$aRuprecht, Daniel$$b4
000154819 8564_ $$uhttp://arxiv.org/abs/1407.6486
000154819 909CO $$ooai:juser.fz-juelich.de:154819$$pVDB
000154819 9101_ $$0I:(DE-588b)5008462-8$$6P:(DE-Juel1)132268$$aForschungszentrum Jülich GmbH$$b1$$kFZJ
000154819 9132_ $$0G:(DE-HGF)POF3-511$$1G:(DE-HGF)POF3-510$$2G:(DE-HGF)POF3-500$$aDE-HGF$$bKey Technologies$$lSupercomputing & Big Data $$vComputational Science and Mathematical Methods$$x0
000154819 9131_ $$0G:(DE-HGF)POF2-411$$1G:(DE-HGF)POF2-410$$2G:(DE-HGF)POF2-400$$3G:(DE-HGF)POF2$$4G:(DE-HGF)POF$$aDE-HGF$$bSchlüsseltechnologien$$lSupercomputing$$vComputational Science and Mathematical Methods$$x0
000154819 9141_ $$y2014
000154819 920__ $$lyes
000154819 9201_ $$0I:(DE-Juel1)JSC-20090406$$kJSC$$lJülich Supercomputing Center$$x0
000154819 980__ $$apreprint
000154819 980__ $$aVDB
000154819 980__ $$aI:(DE-Juel1)JSC-20090406
000154819 980__ $$aUNRESTRICTED