Eliminating synchronizations is one of the important techniques related to minimizing communications for modern high performance computing. This paper discusses principles of reducing communications due to global synchronizations in sparse iterative solvers on distributed supercomputers. We demonstrate how to minimize global synchronizations by rescheduling a typical Krylov subspace method. The benefit of minimizing synchronizations is shown in theoretical analysis and verified by numerical experiments. The experiments also show the local communications for some structured sparse matrix-vector multiplications and global communications in the underlying supercomputers increase in the order P1/2.5 and P4/5 respectively, where P is the number of processors. © 2013 Elsevier Ltd. All rights reserved.
Bibliographical noteKAUST Repository Item: Exported on 2021-03-31
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: Thanks to the referees for valuable suggestions which improved the manuscript. Thanks also to technicians from Dawning Company for technical support.
The first authors’ research is supported by Award No. KUK-C1-013-04, from King Abdullah University of Science of Technology. The second and third authors’ research is partly supported by the NSF of China (No. 61170309, 91130024 and 60973151) and the key project of scientific and technical development of China Academy of Engineering Physics (2012A0202008 and 2011A0202012).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics