FFT, FMM, and multigrid methods are widely used fast and highly scalable solvers for elliptic PDEs. However, emerging large-scale computing systems are introducing challenges in comparison to current petascale computers. Recent efforts (Dongarra et al. 2011) have identified several constraints in the design of exascale software that include massive concurrency, resilience management, exploiting the high performance of heterogeneous systems, energy efficiency, and utilizing the deeper and more complex memory hierarchy expected at exascale. In this paper, we perform a model-based comparison of the FFT, FMM, and multigrid methods in the context of these projected constraints. In addition we use performance models to offer predictions about the expected performance on upcoming exascale system configurations based on current technology trends.

Original languageEnglish (US)
Pages (from-to)63-74
Number of pages12
JournalJournal of Parallel and Distributed Computing
StatePublished - Feb 2020


  • Exascale
  • Fast Fourier transform
  • Fast multipole method
  • Multigrid
  • Performance modeling

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computer Networks and Communications
  • Artificial Intelligence


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