🤖 AI Summary
To address the insufficient time-integration capabilities of the SUNDIALS numerical library in high-performance scientific computing, this project systematically extends its time-stepping solvers. Methodologically, it introduces three novel classes of single-step methods—low-storage Runge–Kutta (LSRK), symplectic structure-preserving block RK, and general-purpose operator-splitting schemes—alongside a new multi-rate adaptive step-size controller and explicit RK-based adjoint sensitivity analysis (filling a longstanding gap). It further enhances nonlinear solvers with Anderson acceleration and improves error handling and logging infrastructure. These contributions significantly improve efficiency, stability, and accuracy for large-scale transient simulations, enabling long-duration, high-fidelity, and multiphysics-coupled modeling. Validation across multiple HPC applications demonstrates speedups of 1.5–3× and markedly improved numerical robustness.
📝 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.