SUNDIALS Time Integrators for Exascale Applications with Many Independent ODE Systems

TL;DR

This paper discusses the extension of the SUNDIALS library for solving many small ODE systems efficiently on exascale supercomputers, demonstrated through applications in combustion and cosmology.

Contribution

It introduces enhancements to SUNDIALS for handling numerous independent ODE systems in exascale applications, supported by the DOE ECP.

Findings

Effective parallel solution of many small ODEs demonstrated in combustion and cosmology codes.

SUNDIALS extensions enable scalable exascale computations with operator splitting.

Improved performance and robustness in large-scale scientific simulations.

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.