Scalability of High-Performance PDE Solvers

Paul Fischer, Misun Min, Thilina Rathnayake, Som Dutta, Tzanio Kolev, Veselin Dobrev, Jean-Sylvain Camier, Martin Kronbichler, Tim Warburton, Kasia Swirydowicz, Jed Brown

Research output: Contribution to journalArticlepeer-review

48 Scopus Citations


Performance tests and analyses are critical to effective high-performance computing software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing architectures for large-scale application problems. In this article, we explore performance and space-time trade-offs for important compute-intensive kernels of large-scale numerical solvers for partial differential equations (PDEs) that govern a wide range of physical applications. We consider a sequence of PDE-motivated bake-off problems designed to establish best practices for efficient high-order simulations across a variety of codes and platforms. We measure peak performance (degrees of freedom per second) on a fixed number of nodes and identify effective code optimization strategies for each architecture. In addition to peak performance, we identify the minimum time to solution at 80% parallel efficiency. The performance analysis is based on spectral and p-type finite elements but is equally applicable to a broad spectrum of numerical PDE discretizations, including finite difference, finite volume, and h-type finite elements.
Original languageAmerican English
Pages (from-to)562-586
Number of pages25
JournalInternational Journal of High Performance Computing Applications
Issue number5
StatePublished - 2020

NREL Publication Number

  • NREL/JA-2C00-77682


  • high-order discretizations
  • high-performance computing
  • PDEs
  • strong-scale limit


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