termoshtt/eom

Configurable ODE/PDE solver

Equation of Motions

Configurable ODE/PDE solver

Contents

• Algorithms
  • explicit schemes
    • Euler
    • Heun
    • classical 4th order Runge-Kutta
  • semi-implicit schemes
    • stiff RK4
• ODE
  • Lorenz three-variables system
  • Lorenz 96 system
  • Roessler system
  • GOY shell model
    • notebook
• PDE
  • Kuramoto-Sivashinsky equation
    • notebook
  • Swift-Hohenberg equation
    • notebook

Lyapunov analysis

• Lyapunov expoents of Lorenz 63 model
  • example
• Covarient Lyapunov vector (CLV)
  • example
  • notebook

Gallery

Lorenz '63 model

Kuramoto-Sivashinsky equation

Swift-Hohenberg equation

License

MIT-License, see LICENSE file.

eom's Issues

Document with MathJax or KaTeX

Numerical Continuation

Re-implementation of Jacobian-Free Newton-Krylov method based continuation library
https://github.com/termoshtt/continuate

Kuramoto–Sivashinsky Fails to Compile

すみません、私は日本語を勉強するが始める。私は英語な通信文を送得ります、けど丁寧語練習すろ。蔵本ースイワシヌスキPDE範をコンパイルするがしくじります。

カルゴはndarray-linalgをもはや認めりません。私はCargo.tomlにversion="0.12"を除く、けど
コンパイルしません。

ありがとうございます。
GitHubはアップロードをとして.txt求めりますだから私はCargo.toml.txtアップロードする。
Cargo.toml.txt

Split lyapunov module into another crate

Lyapunov analysis is not a part of ode solver/

Remove num-extra dependence

Requirements about basic operation (Add, AddAssign etc.) should be revised.

Add DOI using Zenodo

https://zenodo.org/

RandomInit trait for models

Most model should have a moderate random initial state, which is placed on the attractor.
However, we cannot choose good initial point for all parameters. Thus, this should be return Result value, and assured to return value for default setting.

trait RandomInit {
  fn random_init(&self) -> Result<ArrayBase<S, D>, DivergenceError>
}

TimeSeries iterator is slow

let ts = TimeSeries { teo: teo, state: x };
let v = ts.take(time).last().unwrap();

is 20-30% slower than

for 0..time {
   x = teo(x)
}

I think it is because that next() implementation creates two clones while one iteration step.

Test Coverage

Remove A type-parameter in RK<EOM, A>

EOM should have Scalar: ndarray_linalg::Scalar associated type

Merge rust-spectral as PDE module

https://github.com/termoshtt/rust-spectral

Array size from TimeEvolution

Every struct of TimeEvolution should have its size.

trait TimeEvolution<S, D> {
  ...
  fn size(&self) -> D;
}

Lyapunov Analysis for complex dynamical systems

Current code has A: RealScalar bound, but it will be not necessary.

Test of Jupyter notebooks

Adapter utilities

Currently, the user code uses itertools to create time series.
This crate should serve typical functions.

Code usage in fluid dynamics software

Hello!

I found your library after searching about odes and solvers and it looks very promising :) (I'm the one from twitter).

Are you open to contribution? Because the fluid equation will be massively used in this new code and I want to help improve it! :)

Lyapunov Analysis

Implement the followings:

• Lyapunov exponent
• Covariant Lyapunov Vector

Implicit Schemes

• implicit Euler (ieuler)
• diagonally implicit runge-kutta (dirk)

fftw 0.4

Switch to fftw 0.4 which drops Pair interface.
https://github.com/termoshtt/rust-fftw3

PDEs to be implemented

• Kuramoto-Sivashinsky (1D) #45
• Swift-Hohenberg (1D) #74
• Complex Ginzburg-Landau (1D)
• KdV (1D)
• Gray-Scott (2D)
• Navier-Stokes (2D, 3D)

Buffer for Explicit and SemiImplicit

Simplify TimeEvolution

self-consuming trait technique is too complicated. This should be removed with version up to 0.6

Lyapunov Analysis of KSE

Confirm the current implementation of CLV reproduces the past studies.

[Ginelli et al.]

• arxiv: https://arxiv.org/abs/1212.3961
• title: Covariant Lyapunov vectors

TODOs

• Henon Map

[Takeuchi et al.]

• URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.84.046214
• title: Hyperbolic decoupling of tangent space and effective dimension of dissipative systems

TODOs

• Kuramoto-Sivashinsky equation

Schemes for Hamilton systems

Explicit Schemes

• Euler (euler)
• Heun (heun)
• refined Euler (reuler)
• classical 4th-order Runge-Kutta (rk4)

Simplify TimeEvolution trait

pub trait TimeEvolution<S, D> {
  ...
  fn iterate<'a>(&self, &'a mut ArrayBase<S, D>) -> &'a mut ArrayBase<S, D>;
}

will be enough.