SUNDIALS Time Integrators for Exascale Applications with Many Independent ODE Systems
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.
Cite
@article{arxiv.2405.01713,
title = {SUNDIALS Time Integrators for Exascale Applications with Many Independent ODE Systems},
author = {Cody J. Balos and Marc Day and Lucas Esclapez and Anne M. Felden and David J. Gardner and Malik Hassanaly and Daniel R. Reynolds and Jon Rood and Jean M. Sexton and Nicholas T. Wimer and Carol S. Woodward},
journal= {arXiv preprint arXiv:2405.01713},
year = {2024}
}