The article discusses the capabilities and efficiencies of NonlinearSolve.jl, a nonlinear solver framework that excels by using sparsity detection and advanced algorithms for Jacobian construction. Notably, it compares various methods, showcasing its numerical algorithms, globalization strategies, and robustness across multiple test problems, including battery models and nonlinear systems. Findings indicate that while traditional solvers struggle with performance due to lack of sparsity support, NonlinearSolve.jl maintains competitive speed and accuracy, illustrated through performance graphs and failures of other frameworks to converge effectively.
Our comparison of different frameworks reveals that NonlinearSolve.jl, by leveraging sparsity detection and colored sparse matrix algorithms, significantly outperforms existing solvers, notably with Jacobian construction.
Jacobian-free Krylov Methods with Preconditioning implemented in NonlinearSolve.jl allow for solving linear systems efficiently, demonstrating that explicit Jacobian construction is often not feasible in advanced discretizations.
Collection
[
|
...
]