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arXiv · 2403.16341

NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia

Avik Pal·Flemming Holtorf·Axel Larsson·Torkel Loman·Utkarsh·Frank Schäefer·Qingyu Qu·Alan Edelman·Chris Rackauckas
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Abstract

Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of high-performance open-source nonlinear equation solvers implemented natively in the Julia programming language. NonlinearSolve.jl distinguishes itself by offering a unified API that accommodates a diverse range of solver specifications alongside features such as automatic algorithm selection based on runtime analysis, support for GPU-accelerated computation through static array kernels, and the utilization of sparse automatic differentiation and Jacobian-free Krylov methods for large-scale problem-solving. Through rigorous comparison with established tools such as PETSc SNES, Sundials KINSOL, and MINPACK, NonlinearSolve.jl demonstrates robustness and efficiency, achieving significant advancements in solving nonlinear equations while being implemented in a high-level programming language. The capabilities of NonlinearSolve.jl unlock new potentials in modeling and simulation across various domains, making it a valuable addition to the computational toolkit of researchers and practitioners alike.

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Avik Pal, Flemming Holtorf, Axel Larsson, Torkel Loman, Utkarsh, Frank Schäefer, Qingyu Qu, Alan Edelman, Chris Rackauckas. 2025-04-25. NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia. https://arxiv.org/abs/2403.16341

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