Abstract
We compare the performance of pipelined and s-step GMRES, respectively referred to as l-GMRES and s-GMRES, on distributed multicore CPUs. Compared to standard GMRES, s-GMRES requires fewer all-reduces, while l-GMRES overlaps the all-reduces with computation. To combine the best features of two algorithms, we propose another variant, (l, t)-GMRES, that not only does fewer global all-reduces than standard GMRES, but also overlaps those all-reduces with other work. We implemented the thread-parallelism and communication-overlap in two different ways. The first uses nonblocking MPI collectives with thread-parallel computational kernels. The second relies on a shared-memory task scheduler. In our experiments, (l, t)-GMRES performed better than l-GMRES by factors of up to 1.67×. In addition, though we only used 50 nodes, when the latency cost became significant, our variant performed up to 1.22× better than s-GMRES by hiding all-reduces.
| Original language | English |
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| Title of host publication | Proceedings - 2017 IEEE 31st International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2017 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 1118-1127 |
| Number of pages | 10 |
| ISBN (Electronic) | 9781538634080 |
| DOIs | |
| State | Published - Jun 30 2017 |
| Externally published | Yes |
| Event | 31st IEEE International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2017 - Orlando, United States Duration: May 29 2017 → Jun 2 2017 |
Publication series
| Name | Proceedings - 2017 IEEE 31st International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2017 |
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Conference
| Conference | 31st IEEE International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2017 |
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| Country/Territory | United States |
| City | Orlando |
| Period | 05/29/17 → 06/2/17 |
Funding
We thank Xi Luo at the University of Tennessee for helpful discussions on the non-blocking all-reduce communication. This research was supported in part by the U.S. Department of Energy Office of Science under Award Numbers DE-FG0213ER26137 and DE-SC0010042, and the U.S. National Science Foundation under Award Number 1339822. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energys National Nuclear Security Administration under contract DE-AC04-94AL85000.