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[WIP] Update Hyperbolic Solvers API #25

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[WIP] Update Hyperbolic Solvers API #25

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@jejjohnson jejjohnson commented Jul 4, 2023

This pull request will implement and test 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
    • Clean Tutorial
  • Conjugate Gradient
    • Clean Tutorial
  • Discrete Sine Transformation
    • Clean Tutorial

External Packages

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

This will close #24

@jejjohnson jejjohnson self-assigned this Jul 4, 2023
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Generic Elliptical Terms
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