Generic Elliptical Terms

[jejjohnson]

Some generic Hyperbolic functions that we may need to solve, e.g. Laplacian, Poisson. It's 2023 so we'll stick with iterative solvers that scale, e.g., the steepest descent methods, the conjugate gradient methods and the discrete sine transform methods.

$$ \begin{aligned} \boldsymbol{\nabla}^2\boldsymbol{u}&= 0 \ \boldsymbol{\nabla}^2\boldsymbol{u}&= \boldsymbol{b} \end{aligned} $$

Methods From Scratch

I have don't a few methods from scratch but they are not well tested...

• [ ] Steepest Descent
• [ ] Conjugate Gradient
• [ ] Discrete Sine Transformation

External Packages

There are many external packages that can be used with general linear solvers

• [ ] Jaxopt
• [ ] Lineax (New)

This showcases some of the ways we can do linear solvers using the package.

• Exact Linear Solver
• Iterative Linear Solvers w/ jaxopt (Steepest Descent, Conjugate Gradient)
• Discrete Sine Transform
• Staggered Discrete Sine Transform
• Spectral