PFASST

PFASST has been proposed by [1]. It is based on spectral deferred corrections (SDC) and contains multi-level spectral deferred corrections (missing reference) as special case when running on a single processor in time. PFASST’s performance has been studied in massively parallel simulation using tens and hundreds of thousands of cores [2], [3].

A C++ library implementing SDC, MLSDC and PFASST is available under a BSD license.

M. Emmett and M. L. Minion, “Toward an Efficient Parallel in Time Method for Partial Differential Equations,” Communications in Applied Mathematics and Computational Science, vol. 7, pp. 105–132, 2012, doi: 10.2140/camcos.2012.7.105. [Online]. Available at: http://dx.doi.org/10.2140/camcos.2012.7.105

SpeckEtAl2012

R. Speck et al., “A massively space-time parallel N-body solver,” in Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, Los Alamitos, CA, USA, 2012, pp. 92:1–92:11, doi: 10.1109/SC.2012.6 [Online]. Available at: http://dx.doi.org/10.1109/SC.2012.6
BibTeX entry SpeckEtAl2012

@inproceedings{SpeckEtAl2012, address = {Los Alamitos, CA, USA}, articleno = {92}, author = {Speck, Robert and Ruprecht, Daniel and Krause, Rolf and Emmett, Matthew and Minion, Michael L. and Winkel, Mathias and Gibbon, Paul}, booktitle = {Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis}, doi = {10.1109/SC.2012.6}, location = {Salt Lake City, Utah}, numpages = {11}, pages = {92:1--92:11}, publisher = {IEEE Computer Society Press}, series = {{SC '12}}, title = {{A massively space-time parallel {N}-body solver}}, url = {http://dx.doi.org/10.1109/SC.2012.6}, year = {2012} }
Abstract for BibTeX entry SpeckEtAl2012

We present a novel space-time parallel version of the Barnes-Hut tree code PEPC using PFASST, the Parallel Full Approximation Scheme in Space and Time. The naive use of increasingly more processors for a fixed-size N-body problem is prone to saturate as soon as the number of unknowns per core becomes too small. To overcome this intrinsic strong-scaling limit, we introduce temporal parallelism on top of pepc’s existing hybrid MPI/PThreads spatial decomposition. Here, we use PFASST which is based on a combination of the iterations of the parallel-in-time algorithm parareal with the sweeps of spectral deferred correction (SDC) schemes. By combining these sweeps with multiple space-time discretization levels, PFASST relaxes the theoretical bound on parallel efficiency in parareal. We present results from runs on up to 262,144 cores on the IBM Blue Gene/P installation JUGENE, demonstrating that the space-time parallel code provides speedup beyond the saturation of the purely space-parallel approach.

D. Ruprecht, R. Speck, M. Emmett, M. Bolten, and R. Krause, “Poster: Extreme-scale space-time parallelism,” in Proceedings of the 2013 Conference on High Performance Computing Networking, Storage and Analysis Companion, 2013 [Online]. Available at: http://sc13.supercomputing.org/sites/default/files/PostersArchive/tech_posters/post148s2-file3.pdf