Publisher DOI: 10.1137/14097536X
arXiv ID: 1407.6486v2
Title: Interweaving PFASST and Parallel Multigrid
Authors: Minion, Michael 
Speck, Robert 
Bolten, Matthias 
Emmett, Matthew 
Ruprecht, Daniel  
Keywords: Multigrid;Parallel in time;PFASST;Mathematics - Numerical Analysis;Mathematics - Numerical Analysis;Computer Science - Distributed; Parallel; and Cluster Computing;Computer Science - Numerical Analysis
Issue Date: 2015
Source: SIAM Journal on Scientific Computing 37(5), S244-S263 (2015)
Journal: SIAM Journal on Scientific Computing 37(5), pp. S244-S263, 2015 
Abstract (english): 
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 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.
ISSN: 10648275
Document Type: Chapter/Article (Proceedings)
Peer Reviewed: Yes
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