NonlinearSolve.jl: High-Performance and Robust Solvers for Systems of Nonlinear Equations in Julia
CoRR(2024)
摘要
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.
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