[ANN] SIAMFANLEquations.jl: Nonlinear solvers and book project

[linwaytin]

Thank you for the great packages. I needed to solve a PDE a few year ago but at that time I couldn’t find these packages. The NLsolve.jl did not work on my large problem. I’m glad to see there is more than one package now which can provide Newton-Krylov method. This is big progress.

[ctkelley]

I’ve just tagged v0.4.3 of SIAMFANLEquations.jl. This is a suite of nonlinear solvers, test problems, and examples. Chapter 4 is Anderson acceleration, which is the new material since v0.3.3.

This package supports my book project

Solving Nonlinear Equations with Iterative Methods:
Solvers and Examples in Julia

which will be published by SIAM in 2022.

The solvers are documented with Documenter.jl on the github repo and with a collection of IJulia notebooks at

GitHub - ctkelley/NotebookSIAMFANL: Notebook for my new solver book

The notebooks are a faithful reproduction of the entire book.

This version includes the draft of Chapter 4: Fixed Point Problems and Anderson Acceleration

I have decided to take my own advice from the middle of the discussion in

Quasi-newton nonlinear solver for sparse jacobian

BFGS is not a nonlinear solver method. It seeks to maintain a SPD Hessian for optimization. The thing to remember is that optimization and nonlinear solvers are not the same thing. Using an algorithm desinged for one of them to solve the other is a bad, bad, bad idea. Broyden looks for a general low-rank change to an approximate Jacobian and is designed for nonlinear solver applications. Broyden needs a good preconditioner to perform well and has fallen out of favor in the last few decades. New…

and leave Broyden’s method out. So, the solvers are done.

The last chapter will be Chapter 5: Case Studies.

[ctkelley]

I’ve just tagged v0.5.3 of SIAMFANLEquations.jl.

This is a suite of nonlinear solvers, test problems, and examples. Chapter 5 is Case Studies, which is the new material since v0.4.3. Chapter 5 is the last chapter.

The case studies are more elaborate examples than those in the rest of the
text.

1. Conductive-Radiative heat transfer is a multiphysics coupling problem.

2. Pseudo-arclength continuation for the H-equation

This package supports my book project

Solving Nonlinear Equations with Iterative Methods:
Solvers and Examples in Julia

which will be published by SIAM in 2022 (I hope).

The solvers are documented with Documenter.jl on the github repo and with a collection of IJulia notebooks

The notebooks are a more-or-less faithful reproduction of the entire book.

This version includes Chapter 5: Case Studies

I will not be announcing new versions on Discourse until 1.0 unless I find a significant bug.

Future versions will focus on updating the written material for publication, fixing bugs, and improving the internal documentation for the codes.

0.6.0: announcement to NA-Digest
0.7.0: print book to publisher for copy editing
0.8.0: fix problems the copy editor finds. Print book is done at this point.
0.9.x: last shot at getting the notebooks and codes where I want them
1.0: Fin