Minion, ML, Speck, R, Bolten, M et al. (2 more authors) (2015) Interweaving PFASST and Parallel Multigrid. SIAM Journal on Scientific Computing, 37 (5). 5. S244-S263. ISSN 1064-8275
Abstract
The 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, SIAM. Reproduced in accordance with the publisher's self-archiving policy |
Keywords: | parallel in time, PFASST, multigrid |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mechanical Engineering (Leeds) > Institute of Engineering Thermofluids, Surfaces & Interfaces (iETSI) (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Jun 2016 14:50 |
Last Modified: | 09 Jun 2016 14:50 |
Published Version: | http://dx.doi.org/10.1137/14097536X |
Status: | Published |
Publisher: | Society for Industrial and Applied Mathematics |
Identification Number: | 10.1137/14097536X |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:91962 |