%0 Generic %1 pal2024nonlinearsolvejl %A Pal, Avik %A Holtorf, Flemming %A Larsson, Axel %A Loman, Torkel %A Utkarsh, %A Schaefer, Frank %A Qu, Qingyu %A Edelman, Alan %A Rackauckas, Chris %D 2024 %K 65-04-numerical-analysis-software-source-code 65h10-systems-of-nonlinear-algebraic-equations %T NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia %U https://arxiv.org/abs/2403.16341 %X Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for complex 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 Sundials and MINPACK, NonlinearSolve.jl demonstrates unparalleled robustness and efficiency, achieving significant advancements in solving benchmark problems and challenging real-world applications. 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.

@misc{pal2024nonlinearsolvejl, abstract = {Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for complex 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 Sundials and MINPACK, NonlinearSolve.jl demonstrates unparalleled robustness and efficiency, achieving significant advancements in solving benchmark problems and challenging real-world applications. 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.}, added-at = {2024-03-27T00:06:48.000+0100}, archiveprefix = {arXiv}, author = {Pal, Avik and Holtorf, Flemming and Larsson, Axel and Loman, Torkel and Utkarsh and Schaefer, Frank and Qu, Qingyu and Edelman, Alan and Rackauckas, Chris}, biburl = {https://www.bibsonomy.org/bibtex/2ab277d1bf5a48ba49abddcd816b6092c/gdmcbain}, eprint = {2403.16341}, interhash = {e1422490665e83e9f2a4029b9ecd8a6e}, intrahash = {ab277d1bf5a48ba49abddcd816b6092c}, keywords = {65-04-numerical-analysis-software-source-code 65h10-systems-of-nonlinear-algebraic-equations}, primaryclass = {math.NA}, timestamp = {2024-03-27T00:06:48.000+0100}, title = {NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia}, url = {https://arxiv.org/abs/2403.16341}, year = 2024 }