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The impact of global communication latency at extreme scales on Krylov methods

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Abstract
Krylov Subspace Methods (KSMs) are popular numerical tools for solving large linear systems of equations. We consider their role in solving sparse systems on future massively parallel distributed memory machines, by estimating future performance of their constituent operations. To this end we construct a model that is simple, but which takes topology and network acceleration into account as they are important considerations. We show that, as the number of nodes of a parallel machine increases to very large numbers, the increasing latency cost of reductions may well become a problematic bottleneck for traditional formulations of these methods. Finally, we discuss how pipelined KSMs can be used to tackle the potential problem, and appropriate pipeline depths.

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Chicago
Ashby, Thomas J, Pieter Ghysels, Wim Heirman, and Wim Vanroose. 2012. “The Impact of Global Communication Latency at Extreme Scales on Krylov Methods.” In Lecture Notes in Computer Science, ed. Yang Xiang, I Stojmenovic, BO Apduhan, Guojun Wang, K Nakano, and A Zomaya, 7439:428–442. Berlin, Germany: Springer.
APA
Ashby, T. J., Ghysels, P., Heirman, W., & Vanroose, W. (2012). The impact of global communication latency at extreme scales on Krylov methods. In Y. Xiang, I. Stojmenovic, B. Apduhan, G. Wang, K. Nakano, & A. Zomaya (Eds.), Lecture Notes in Computer Science (Vol. 7439, pp. 428–442). Presented at the 12th International conference on Algorithms and Architectures for Parallel Processing (ICA3PP-12), Berlin, Germany: Springer.
Vancouver
1.
Ashby TJ, Ghysels P, Heirman W, Vanroose W. The impact of global communication latency at extreme scales on Krylov methods. In: Xiang Y, Stojmenovic I, Apduhan B, Wang G, Nakano K, Zomaya A, editors. Lecture Notes in Computer Science. Berlin, Germany: Springer; 2012. p. 428–42.
MLA
Ashby, Thomas J, Pieter Ghysels, Wim Heirman, et al. “The Impact of Global Communication Latency at Extreme Scales on Krylov Methods.” Lecture Notes in Computer Science. Ed. Yang Xiang et al. Vol. 7439. Berlin, Germany: Springer, 2012. 428–442. Print.
@inproceedings{3003890,
  abstract     = {Krylov Subspace Methods (KSMs) are popular numerical tools for solving large linear systems of equations. We consider their role in solving sparse systems on future massively parallel distributed memory machines, by estimating future performance of their constituent operations. To this end we construct a model that is simple, but which takes topology and network acceleration into account as they are important considerations. We show that, as the number of nodes of a parallel machine increases to very large numbers, the increasing latency cost of reductions may well become a problematic bottleneck for traditional formulations of these methods. Finally, we discuss how pipelined KSMs can be used to tackle the potential problem, and appropriate pipeline depths.},
  author       = {Ashby, Thomas J and Ghysels, Pieter and Heirman, Wim and Vanroose, Wim},
  booktitle    = {Lecture Notes in Computer Science},
  editor       = {Xiang, Yang and Stojmenovic, I and Apduhan, BO and Wang, Guojun and Nakano, K and Zomaya, A},
  isbn         = {9783642330773},
  issn         = {0302-9743},
  language     = {eng},
  location     = {Fukuoka, Japan},
  pages        = {428--442},
  publisher    = {Springer},
  title        = {The impact of global communication latency at extreme scales on Krylov methods},
  url          = {http://dx.doi.org/10.1007/978-3-642-33078-0\_31},
  volume       = {7439},
  year         = {2012},
}

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