SUNDIALS Time Integrators for Exascale Applications with Many Independent Systems of Ordinary Differential Equations

Cody Balos, Marcus Day, Lucas Esclapez, Anne Felden, David Gardner, Malik Hassanaly, Daniel Reynolds, Jon Rood, Jean Sexton, Nicholas Wimer, Carol Woodward

Research output: Contribution to journalArticlepeer-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.

NREL Publication Number

  • NREL/JA-2C00-92340

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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