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https://github.com/galerkintoolkit/galerkintoolkit.jl

FEM toolbox with automatic code generation, HPC support, and more.
https://github.com/galerkintoolkit/galerkintoolkit.jl

code-generation computational-science finite-element-methods hpc julia metaprogramming mpi pdes scientific-computing

Last synced: about 2 months ago
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FEM toolbox with automatic code generation, HPC support, and more.

Host: GitHub
URL: https://github.com/galerkintoolkit/galerkintoolkit.jl
Owner: GalerkinToolkit
License: mit
Created: 2022-05-28T08:35:38.000Z (over 2 years ago)
Default Branch: main
Last Pushed: 2024-10-24T12:14:08.000Z (about 2 months ago)
Last Synced: 2024-10-25T07:32:32.140Z (about 2 months ago)
Topics: code-generation, computational-science, finite-element-methods, hpc, julia, metaprogramming, mpi, pdes, scientific-computing
Language: Julia
Homepage:
Size: 6 MB
Stars: 22
Watchers: 2
Forks: 0
Open Issues: 19
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
- Code of conduct: CODE_OF_CONDUCT.md
- Citation: CITATION.cff

Awesome Lists containing this project

README

        # GalerkinToolkit

[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://GalerkinToolkit.github.io/GalerkinToolkit.jl/stable/)

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://GalerkinToolkit.github.io/GalerkinToolkit.jl/dev/)

[![Build Status](https://github.com/GalerkinToolkit/GalerkinToolkit.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/GalerkinToolkit/GalerkinToolkit.jl/actions/workflows/CI.yml?query=branch%3Amain)

[![Coverage](https://codecov.io/gh/GalerkinToolkit/GalerkinToolkit.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/GalerkinToolkit/GalerkinToolkit.jl)

[![DOI](https://zenodo.org/badge/497260571.svg)](https://doi.org/10.5281/zenodo.13938389)

## What

This package aims at providing a fully-fledged finite-element toolbox in pure Julia, with support for different computing systems from laptops to supercomputers and GPUs.  

NB. This package is work in progress; a proof-of-concept API is already available (for CPUs). The package is not production ready at this point. Planned performance and documentation improvements are needed.

## Why

This package follows a new approach to implement finite-element methods based on the lessons learned in the [Gridap](https://github.com/gridap/Gridap.jl) project.

## Acknowledgments

Since July 2024, this package is being developed with support from the [Netherlands eScience Center](https://www.esciencecenter.nl/) under grant ID [NLESC.SS.2023.008](https://research-software-directory.org/projects/hp2sim).

## Documentation

- [**STABLE**](https://GalerkinToolkit.github.io/GalerkinToolkit.jl/stable) — **Documentation for the most recently tagged version.**

- [**LATEST**](https://GalerkinToolkit.github.io/GalerkinToolkit.jl/dev) — *Documentation for the in-development version.*

## Help and discussion

- You can open a new discussion to ask questions [here](https://github.com/GalerkinToolkit/GalerkinToolkit.jl/discussions).

- If you have found a bug, open an issue [here](https://github.com/GalerkinToolkit/GalerkinToolkit.jl/issues). Do not forget to include a (minimal) reproducer.

## Contributing

This package is under active development and there are several ways to contribute:

- by enhancing the documentation (e.g., fixing typos, enhancing doc strings, adding examples).

- by addressing one of the [issues waiting for help](https://github.com/GalerkinToolkit/GalerkinToolkit.jl/labels/help%20wanted).

- by adding more tests to increase the code coverage.

- by extending the current functionality. In this case, open a discussion [here](https://github.com/GalerkinToolkit/GalerkinToolkit.jl/discussions) to coordinate with the package maintainers before proposing significant changes.

Discuss with the package authors before working on any non-trivial contribution.

## Examples

### "Hello world" Laplace PDE

The following code solves a Laplace PDE with Dirichlet boundary conditions.

```julia

import GalerkinToolkit as GT

import ForwardDiff

using LinearAlgebra

mesh = GT.mesh_from_gmsh("assets/demo.msh")

GT.label_boundary_faces!(mesh;physical_name="boundary")

Ω = GT.interior(mesh)

Γd = GT.boundary(mesh;physical_names=["boundary"])

k = 2

V = GT.lagrange_space(Ω,k;dirichlet_boundary=Γd)

uhd = GT.dirichlet_field(Float64,V)

u = GT.analytical_field(sum,Ω)

GT.interpolate_dirichlet!(u,uhd)

dΩ = GT.measure(Ω,2*k)

gradient(u) = x->ForwardDiff.gradient(u,x)

∇(u,x) = GT.call(gradient,u)(x)

a(u,v) = GT.∫( x->∇(u,x)⋅∇(v,x), dΩ)

l(v) = 0

x,A,b = GT.linear_problem(uhd,a,l)

x .= A\b

uh = GT.solution_field(uhd,x)

GT.vtk_plot("results",Ω) do plt

    GT.plot!(plt,u;label="u")

    GT.plot!(plt,uh;label="uh")

end

```

### Multi-field example

This code solves the same boundary value problem, but using an auxiliary field of Lagrange

multipliers to impose Dirichlet boundary conditions.

```julia

import GalerkinToolkit as GT

import ForwardDiff

using LinearAlgebra

mesh = GT.mesh_from_gmsh("assets/demo.msh")

GT.label_boundary_faces!(mesh;physical_name="boundary")

Ω = GT.interior(mesh)

Γd = GT.boundary(mesh;physical_names=["boundary"])

k = 2

V = GT.lagrange_space(Ω,k)

Q = GT.lagrange_space(Γd,k-1; conformity=:L2)

VxQ = V × Q

dΓd = GT.measure(Γd,2*k)

gradient(u) = x->ForwardDiff.gradient(u,x)

∇(u,x) = GT.call(gradient,u)(x)

a((u,p),(v,q)) =

    GT.∫( x->∇(u,x)⋅∇(v,x), dΩ) +

    GT.∫(x->

        (u(x)+p(x))*(v(x)+q(x))

        -u(x)*v(x)-p(x)*q(x), dΓd)

l((v,q)) = GT.∫(x->u(x)*q(x), dΓd)

x,A,b = GT.linear_problem(Float64,VxQ,a,l)

x .= A\b

uh,qh = GT.solution_field(VxQ,x)

GT.vtk_plot("results",Ω) do plt

    GT.plot!(plt,u;label="u")

    GT.plot!(plt,uh;label="uh")

end

```