Using performance models to understand scalable Krylov solver performance at scale for structured grid problems

Paul R. Eller, Torsten Hoefler, William Gropp

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Krylov solvers are key kernels in many large-scale science and engineering applications for solving sparse linear systems. Applications running at scale can experience significant slowdown due to factors such as network congestion, off-node congestion, network distance, and performance variation across processes. Performance models can help us better understand factors limiting performance, however simple models fail to capture slowdowns often occurring at scale and performance variation across multiple runs of the same code. This work develops performance models that capture behavior found at scale and uses these models to guide optimizations for Krylov solvers and related kernels using both blocking and non-blocking communication for structured grid problems at scale. We use detailed performance analysis with network performance counters to show how network behavior relates to observed performance and guide the development of performance models that capture the runtime impact of network congestion, network distance, communication and computation overlap, and process mappings. These models guide us to optimize kernels using MPI protocol changes, node-aware communication, and topology-aware communication. The resulting tools and analysis provide us with a better understanding of how to improve performance at scale that can benefit a wider range of applications.

Original languageEnglish (US)
Title of host publicationICS 2019 - International Conference on Supercomputing
PublisherAssociation for Computing Machinery
Pages138-149
Number of pages12
ISBN (Electronic)9781450360791
DOIs
StatePublished - Jun 26 2019
Event33rd ACM International Conference on Supercomputing, ICS 2019, held in conjunction with the Federated Computing Research Conference, FCRC 2019 - Phoenix, United States
Duration: Jun 26 2019 → …

Publication series

NameProceedings of the International Conference on Supercomputing

Conference

Conference33rd ACM International Conference on Supercomputing, ICS 2019, held in conjunction with the Federated Computing Research Conference, FCRC 2019
CountryUnited States
CityPhoenix
Period6/26/19 → …

Keywords

  • Krylov solvers
  • Performance analysis
  • Performance modeling

ASJC Scopus subject areas

  • Computer Science(all)

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  • Cite this

    Eller, P. R., Hoefler, T., & Gropp, W. (2019). Using performance models to understand scalable Krylov solver performance at scale for structured grid problems. In ICS 2019 - International Conference on Supercomputing (pp. 138-149). (Proceedings of the International Conference on Supercomputing). Association for Computing Machinery. https://doi.org/10.1145/3330345.3330358