https://github.com/juliafem/femquad.jl

FEMQuad.jl package contains various of integration schemes for cartesian and tetrahedral domains. The most common integration rules are tabulated and focus is on speed. Each rule has own "label" so we can easily implement several rules with same degree. API is very simple making is easy to utilize package in different FEM projects.
https://github.com/juliafem/femquad.jl

fem integral integration numerical-integration quadrature tetrahedron

Last synced: 29 days ago
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FEMQuad.jl package contains various of integration schemes for cartesian and tetrahedral domains. The most common integration rules are tabulated and focus is on speed. Each rule has own "label" so we can easily implement several rules with same degree. API is very simple making is easy to utilize package in different FEM projects.

• Host: GitHub
• URL: https://github.com/juliafem/femquad.jl
• Owner: JuliaFEM
• License: mit
• Created: 2017-07-18T20:25:10.000Z (over 7 years ago)
• Default Branch: master
• Last Pushed: 2021-01-24T14:57:51.000Z (almost 4 years ago)
• Last Synced: 2024-09-09T06:28:56.744Z (3 months ago)
• Topics: fem, integral, integration, numerical-integration, quadrature, tetrahedron
• Language: Julia
• Homepage: https://juliafem.github.io/FEMQuad.jl/latest
• Size: 183 KB
• Stars: 7
• Watchers: 3
• Forks: 7
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# FEMQuad.jl

[![ci][ci-img]][ci-url]

[![docs-stable][docs-stable-img]][docs-stable-url]

[![docs-latest][docs-latest-img]][docs-latest-url]

FEMQuad.jl contains various of integration schemes for cartesian and tetrahedron

domains. The most common integration rules are tabulated and focus is on speed.

Usage is straightforward. For example, to integrate function

`f(x) = 1 + x[1] + x[2] + x[1]*x[2]` in a standard rectangular domain `[-1,1]^2`,

4 point Gauss-Legendre integration rule is needed:

```julia

using FEMQuad

f(x) = 1 + x[1] + x[2] + x[1]*x[2]

I = 0.0

for (w, gp) in get_quadrature_points(Val{:GLQUAD4})

    I += w*f(gp)

end

```

Result can be verified to be 4. `w` is integration weight, `gp` is integration

point location and `GLQUAD4` is the integration rule used. In the same principle

we have integration rules for tetrahedrons, hexahedrons and so on. For example,

`GLTET15` is a 15-point tetrahedron rule.

## References

- Wikipedia contributors. "Gaussian quadrature." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 24 Jul. 2017. Web. 29 Jul. 2017.

[ci-img]: https://github.com/JuliaFEM/FEMQuad.jl/workflows/CI/badge.svg

[ci-url]: https://github.com/JuliaFEM/FEMQuad.jl/actions?query=workflow%3ACI+branch%3Amaster

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

[docs-stable-url]: https://juliafem.github.io/FEMQuad.jl/stable

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

[docs-latest-url]: https://juliafem.github.io/FEMQuad.jl/latest