Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

Awesome Lists | Featured Topics | Projects

https://github.com/JuliaSmoothOptimizers/PDENLPModels.jl

A NLPModel API for optimization problems with PDE-constraints
https://github.com/JuliaSmoothOptimizers/PDENLPModels.jl

Last synced: 3 months ago
JSON representation

A NLPModel API for optimization problems with PDE-constraints

Awesome Lists containing this project

README 

        
# PDENLPModels



| **Documentation** | **CI** | **Coverage** | **Release** | **DOI** |

|:-----------------:|:------:|:------------:|:-----------:|:-------:|

| [![docs-stable][docs-stable-img]][docs-stable-url] [![docs-dev][docs-dev-img]][docs-dev-url] | [![build-ci][build-ci-img]][build-ci-url] | [![codecov][codecov-img]][codecov-url] | [![release][release-img]][release-url] | [![doi][doi-img]][doi-url] |



[docs-stable-img]: https://img.shields.io/badge/docs-stable-blue.svg

[docs-stable-url]: https://JuliaSmoothOptimizers.github.io/PDENLPModels.jl/stable

[docs-dev-img]: https://img.shields.io/badge/docs-dev-purple.svg

[docs-dev-url]: https://JuliaSmoothOptimizers.github.io/PDENLPModels.jl/dev

[build-ci-img]: https://github.com/JuliaSmoothOptimizers/PDENLPModels.jl/workflows/CI/badge.svg?branch=main

[build-ci-url]: https://github.com/JuliaSmoothOptimizers/PDENLPModels.jl/actions

[codecov-img]: https://codecov.io/gh/JuliaSmoothOptimizers/PDENLPModels.jl/branch/main/graph/badge.svg

[codecov-url]: https://codecov.io/gh/JuliaSmoothOptimizers/PDENLPModels.jl

[release-img]: https://img.shields.io/github/v/release/JuliaSmoothOptimizers/PDENLPModels.jl.svg?style=flat-square

[release-url]: https://github.com/JuliaSmoothOptimizers/PDENLPModels.jl/releases

[doi-img]: https://joss.theoj.org/papers/10.21105/joss.04736/status.svg

[doi-url]: https://doi.org/10.21105/joss.04736



PDENLPModels specializes the [NLPModel API](https://github.com/JuliaSmoothOptimizers/NLPModels.jl) to optimization problems with partial differential equations in the constraints. The package relies on [Gridap.jl](https://github.com/gridap/Gridap.jl) for the modeling and the computation of the derivatives. Find tutorials for using Gridap [here](https://github.com/gridap/Tutorials).



We consider optimization problems of the form: Find functions $(y,u): Y \times U \rightarrow ℜⁿ \times ℜⁿ$ and $κ \in ℜⁿ$ satisfying



$$

\begin{equation}

   \begin{array}{cl} 

   \min_{\kappa,y,u} & \int_\Omega f(\kappa,y,u) d\Omega \\ 

   \text{ s.t. } & y \text{ solution of a } PDE(\kappa,u)=0, \\

   & lcon \leq c(\kappa,y,u) \leq ucon, \\

   & lvar \leq (\kappa,y,u) \leq uvar,\\

   \end{array} 

\end{equation}

$$



We refer to the the repository [PDEOptimizationProblems](https://github.com/tmigot/PDEOptimizationProblems) for examples of problems of different types: calculus of variations, optimal control problem, PDE-constrained problems, and mixed PDE-contrained problems with both function and algebraic unknowns.



## Installation



```

] add PDENLPModels

```

The current version of PDENLPModels relies on Gridap v0.15.5.



## Example



$$

\begin{equation}

   \min_{y \in H^1_0,u \in H^1} \frac{1}{2} \int_{\Omega} |y(x) - y_d(x)|^2dx + \frac{\alpha}{2} \int_{\Omega} |u|^2 \quad \text{ s.t. } -\Delta y = u + h,   \text{ for }    x \in \Omega, y = 0 \text{ for } x \in \partial \Omega,

\end{equation}

$$



where $y_d(x) = -x_1^2$, $h(x) = 1$ and $\alpha = 10^{-2}$.



```julia

using Gridap, PDENLPModels



  # Definition of the domain

  n = 100

  domain = (-1, 1, -1, 1)

  partition = (n, n)

  model = CartesianDiscreteModel(domain, partition)



  # Definition of the spaces:

  valuetype = Float64

  reffe = ReferenceFE(lagrangian, valuetype, 2)

  Xpde = TestFESpace(model, reffe; conformity = :H1, dirichlet_tags = "boundary")

  y0(x) = 0.0

  Ypde = TrialFESpace(Xpde, y0)



  reffe_con = ReferenceFE(lagrangian, valuetype, 1)

  Xcon = TestFESpace(model, reffe_con; conformity = :H1)

  Ycon = TrialFESpace(Xcon)



  # Integration machinery

  trian = Triangulation(model)

  degree = 1

  dΩ = Measure(trian, degree)



  # Objective function:

  yd(x) = -x[1]^2

  α = 1e-2

  function f(y, u)

    ∫(0.5 * (yd - y) * (yd - y) + 0.5 * α * u * u) * dΩ

  end



  # Definition of the constraint operator

  ω = π - 1 / 8

  h(x) = -sin(ω * x[1]) * sin(ω * x[2])

  function res(y, u, v)

    ∫(∇(v) ⊙ ∇(y) - v * u - v * h) * dΩ

  end



  # initial guess

  npde = num_free_dofs(Ypde)

  ncon = num_free_dofs(Ycon)

  xin = zeros(npde + ncon)



  nlp = GridapPDENLPModel(xin, f, trian, Ypde, Ycon, Xpde, Xcon, res, name = "Control elastic membrane")

```



## References



> Migot, T., Orban D., & Siqueira A. S.

> PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints

> Journal of Open Source Software 7(80), 4736 (2022).

> [10.21105/joss.04736](https://doi.org/10.21105/joss.04736)

>

> Badia, S., & Verdugo, F.

> Gridap: An extensible Finite Element toolbox in Julia.

> Journal of Open Source Software, 5(52), 2520 (2020).

> [10.21105/joss.02520](https://doi.org/10.21105/joss.02520)



## How to Cite



If you use PDENLPModels.jl in your work, please cite using the format given in [CITATION.cff](https://github.com/JuliaSmoothOptimizers/PDENLPModels.jl/blob/main/CITATION.cff).



# Bug reports and discussions



If you think you found a bug, feel free to open an [issue](https://github.com/JuliaSmoothOptimizers/PDENLPModels.jl/issues).

Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.



If you want to ask a question not suited for a bug report, feel free to start a discussion [here](https://github.com/JuliaSmoothOptimizers/Organization/discussions). This forum is for general discussion about this repository and the [JuliaSmoothOptimizers](https://github.com/JuliaSmoothOptimizers), so questions about any of our packages are welcome.