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New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0

Steven B. Roberts, Mustafa Ağgül, Daniel R. Reynolds, Cody J. Balos, David J. Gardner, Carol S. Woodward

TL;DR

SUNDIALS 6.2.0–7.4.0 delivers major extensions to ARKODE, including low storage and symplectic one-step integrators, flexible operator splitting, advanced multirate adaptivity, discrete adjoint sensitivity for explicit RK, and enhanced Anderson acceleration alongside improved error handling and logging. The work demonstrates concrete algorithmic advancements and performance gains on HPC-relevant problems, validating convergence orders and efficiency improvements in multiphysics and optimization contexts. These developments expand SUNDIALS’ applicability to large-scale, differentiable simulations and complex coupled systems, enabling more robust integration, sensitivity analysis, and debugging capabilities on modern architectures.

Abstract

SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This paper overviews several significant improvements and new features added over the last three years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge-Kutta, symplectic partitioned Runge-Kutta, and operator splitting. In addition, we describe new time step adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge-Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.

New Time Integrators and Capabilities in SUNDIALS Versions 6.2.0-7.4.0

TL;DR

SUNDIALS 6.2.0–7.4.0 delivers major extensions to ARKODE, including low storage and symplectic one-step integrators, flexible operator splitting, advanced multirate adaptivity, discrete adjoint sensitivity for explicit RK, and enhanced Anderson acceleration alongside improved error handling and logging. The work demonstrates concrete algorithmic advancements and performance gains on HPC-relevant problems, validating convergence orders and efficiency improvements in multiphysics and optimization contexts. These developments expand SUNDIALS’ applicability to large-scale, differentiable simulations and complex coupled systems, enabling more robust integration, sensitivity analysis, and debugging capabilities on modern architectures.

Abstract

SUNDIALS is a well-established numerical library that provides robust and efficient time integrators and nonlinear solvers. This paper overviews several significant improvements and new features added over the last three years to support scientific simulations run on high-performance computing systems. Notably, three new classes of one-step methods have been implemented: low storage Runge-Kutta, symplectic partitioned Runge-Kutta, and operator splitting. In addition, we describe new time step adaptivity support for multirate methods, adjoint sensitivity analysis capabilities for explicit Runge-Kutta methods, additional options for Anderson acceleration in nonlinear solvers, and improved error handling and logging.

Paper Structure

This paper contains 15 sections, 15 equations, 2 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. New Features
  3. Low Storage Runge--Kutta (LSRK) Methods
  4. Symplectic Partitioned Runge--Kutta (SPRK) Methods
  5. Operator Splitting Methods
  6. Standard Operator Splitting
  7. The Forcing Method
  8. Multirate Adaptivity
  9. Discrete Adjoint Sensitivity Analysis for Explicit Runge--Kutta Methods
  10. Extensions to Anderson Acceleration
  11. Error Handling and Logging
  12. Numerical Experiments
  13. Gray--Scott Diffusion Reaction PDE
  14. Adjoint Sensitivity Analysis Applied to a Predator-Prey Model
  15. Conclusions

Figures (2)

  • Figure 1: Results from applying the operator splitting methods (left) and a low storage Runge--Kutta method (right) to the Gray--Scott problem in \ref{['eq:Gray-Scott_discretized']}.
  • Figure 2: Results from the new discrete adjoint sensitivity analysis capability in ARKODE. The methods converge at the expected order for the forward solution as well as the adjoint solution.