Nonlinearsolve.jl: Fast and Robust Solvers for Nonlinear Equations in Julia

Jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia, by Avik Pal and 8 other authors. View PDF HTML. Abstract:Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for complex system models remains a challenge. Jl - a suite of high-performance open-source nonlinear equation solvers implemented natively in the Julia programming language. 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. 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.