SUNDIALS time integrators for exascale applications with many independent systems of ordinary differential equations

Cody J. Balos*, Marcus Day, Lucas Esclapez, Anne M. Felden, David J. Gardner, Malik Hassanaly, Daniel R. Reynolds, Jon S. Rood, Jean M. Sexton, Nicholas T. Wimer, Carol S. Woodward

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Many complex systems can be accurately modeled as a set of coupled time-dependent partial differential equations (PDEs). However, solving such equations can be prohibitively expensive, easily taxing the world’s largest supercomputers. One pragmatic strategy for attacking such problems is to split the PDEs into components that can more easily be solved in isolation. This operator splitting approach is used ubiquitously across scientific domains, and in many cases leads to a set of ordinary differential equations (ODEs) that need to be solved as part of a larger “outer-loop” time-stepping approach. The SUNDIALS library provides a plethora of robust time integration algorithms for solving ODEs, and the U.S. Department of Energy Exascale Computing Project (ECP) has supported its extension to applications on exascale-capable computing hardware. In this paper, we highlight some SUNDIALS capabilities and its deployment in combustion and cosmology application codes (Pele and Nyx, respectively) where operator splitting gives rise to numerous, small ODE systems that must be solved concurrently.

Original languageEnglish
Pages (from-to)123-146
Number of pages24
JournalInternational Journal of High Performance Computing Applications
Volume39
Issue number1
DOIs
Publication statusPublished - 2024

Bibliographical note

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Keywords

  • chemical kinetics
  • combustion
  • computational fluid dynamics
  • cosmology
  • exascale
  • GPUs
  • initial value problems
  • operator splitting
  • Ordinary differential equations
  • partial differential equations

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