NonlinearSolve.jl: High-Performance Unified Nonlinear Solvers

NonlinearSolve.jl is a unified interface for the nonlinear solving packages of Julia. The package includes its own high-performance nonlinear solvers which include the ability to swap out to fast direct and iterative linear solvers, along with the ability to use sparse automatic differentiation for Jacobian construction and Jacobian-vector products. NonlinearSolve.jl interfaces with other packages of the Julia ecosystem to make it easy to test alternative solver packages and pass small types to control algorithm swapping. It also interfaces with the ModelingToolkit.jl world of symbolic modeling to allow for automatically generating high-performance code.

Performance is key: the current methods are made to be highly performant on scalar and statically sized small problems, with options for large-scale systems. If you run into any performance issues, please file an issue. Consult the NonlinearSystemSolvers page for information on how to import solvers from different packages.

Installation

To install NonlinearSolve.jl, use the Julia package manager:

using Pkg
Pkg.add("NonlinearSolve")

Contributing

Please refer to the SciML ColPrac: Contributor's Guide on Collaborative Practices for Community Packages for guidance on PRs, issues, and other matters relating to contributing to SciML.
See the SciML Style Guide for common coding practices and other style decisions.
There are a few community forums:
- The #diffeq-bridged and #sciml-bridged channels in the Julia Slack
- The #diffeq-bridged and #sciml-bridged channels in the Julia Zulip
- On the Julia Discourse forums
- See also SciML Community page

Reproducibility

The documentation of this SciML package was built using these direct dependencies,

Status `~/.julia/packages/NonlinearSolve/P1qJg/docs/Project.toml`
  [2169fc97] AlgebraicMultigrid v0.6.0
  [4fba245c] ArrayInterface v7.7.1
  [6e4b80f9] BenchmarkTools v1.4.0
  [2b5f629d] DiffEqBase v6.147.0
  [e30172f5] Documenter v1.2.1
  [daee34ce] DocumenterCitations v1.3.2
  [40713840] IncompleteLU v0.2.1
  [7ed4a6bd] LinearSolve v2.23.4
  [961ee093] ModelingToolkit v8.75.0
  [8913a72c] NonlinearSolve v3.6.0 `~/.julia/packages/NonlinearSolve/P1qJg`
  [1dea7af3] OrdinaryDiffEq v6.71.0
  [91a5bcdd] Plots v1.40.1
  [0bca4576] SciMLBase v2.26.1
  [727e6d20] SimpleNonlinearSolve v1.5.0
  [47a9eef4] SparseDiffTools v2.17.0
  [90137ffa] StaticArrays v1.9.2
  [9672c7b4] SteadyStateDiffEq v2.0.1
  [c3572dad] Sundials v4.24.0
  [0c5d862f] Symbolics v5.18.0
  [b77e0a4c] InteractiveUtils
  [9a3f8284] Random

and using this machine and Julia version.

Julia Version 1.10.0
Commit 3120989f39b (2023-12-25 18:01 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 8 × Intel(R) Xeon(R) Platinum 8375C CPU @ 2.90GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, icelake-server)
  Threads: 1 on 8 virtual cores
Environment:
  JULIA_CPU_TARGET = generic;sandybridge,-xsaveopt,clone_all;haswell,-rdrnd,base(1)
  JULIA_GPG = 3673DF529D9049477F76B37566E3C7DC03D6E495
  JULIA_PKG_UNPACK_REGISTRY = true
  JULIA_VERSION = 1.10.0
  JULIA_PATH = /usr/local/julia
  JULIA_PKG_SERVER =

A more complete overview of all dependencies and their versions is also provided.

Status `~/.julia/packages/NonlinearSolve/P1qJg/docs/Manifest.toml`
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  [21216c6a] Preferences v1.4.1
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Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

You can also download the manifest file and the project file.