Abstract
Some scientific and engineering applications need to compute a large number of eigenpairs of a large Hermitian matrix. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenpairs (e.g., in terms of computation and communication). To improve the performance of the method, in this paper, we study an s-step variant of thick-restart Lanczos (TRLan) combined with an explicit external deflation (EED). The s-step method generates a set of s basis vectors at a time and reduces the communication costs of generating the basis vectors. We then design a specialized matrix powers kernel (MPK) that reduces both the communication and computational costs by taking advantage of the special properties of the deflation matrix. We conducted numerical experiments of the new TRLan eigensolver using synthetic matrices and matrices from electronic structure calculations. The performance results on the Cori supercomputer at the National Energy Research Scientific Computing Center (NERSC) demonstrate the potential of the specialized MPK to significantly reduce the execution time of the TRLan eigensolver. The speedups of up to 3.1× and 5.3× were obtained in our sequential and parallel runs, respectively.
| Original language | English |
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| Title of host publication | Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019 |
| Pages | 472-481 |
| Number of pages | 10 |
| ISBN (Electronic) | 9781728112466 |
| DOIs | |
| State | Published - May 2019 |
| Event | 33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019 - Rio de Janeiro, Brazil Duration: May 20 2019 → May 24 2019 |
Publication series
| Name | Proceedings - 2019 IEEE 33rd International Parallel and Distributed Processing Symposium, IPDPS 2019 |
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Conference
| Conference | 33rd IEEE International Parallel and Distributed Processing Symposium, IPDPS 2019 |
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| Country/Territory | Brazil |
| City | Rio de Janeiro |
| Period | 5/20/19 → 5/24/19 |
Bibliographical note
Publisher Copyright:© 2019 IEEE
Funding
ACKNOWLEDGMENTS This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration, 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 Awards 1339822, DMS-1522697, and CCF-1527091. This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration, 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 Awards 1339822, DMS-1522697, and CCF-1527091.
| Funders | Funder number |
|---|---|
| Exascale Computing Project | 17-SC-20-SC |
| U.S. Department of Energy Office of Science Visiting Faculty Program | |
| U.S. National Science Foundation (NSF) | |
| National Science Foundation Arctic Social Science Program | 1339822, CCF-1527091, DMS-1522697 |
| National Nuclear Security Administration | DE-FG0213ER26137, DE-SC0010042 |
| Savannah River Operations Office, U.S. Department of Energy |
ASJC Scopus subject areas
- Computer Networks and Communications
- Hardware and Architecture
- Information Systems and Management