https://github.com/WolframResearch/FEMAddOns

Finite Element Method addons for Wolfram Language
https://github.com/WolframResearch/FEMAddOns

distmesh domaindecomposition finite-element-analysis finite-element-methods finite-elements mathematica wolfram wolfram-language wolfram-mathematica wolframlanguage

Last synced: about 1 month ago
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Finite Element Method addons for Wolfram Language

• Host: GitHub
• URL: https://github.com/WolframResearch/FEMAddOns
• Owner: WolframResearch
• License: other
• Created: 2018-04-24T14:14:11.000Z (over 6 years ago)
• Default Branch: master
• Last Pushed: 2024-01-08T08:10:15.000Z (12 months ago)
• Last Synced: 2024-08-05T09:11:35.552Z (5 months ago)
• Topics: distmesh, domaindecomposition, finite-element-analysis, finite-element-methods, finite-elements, mathematica, wolfram, wolfram-language, wolfram-mathematica, wolframlanguage
• Language: Mathematica
• Size: 18.4 MB
• Stars: 57
• Watchers: 24
• Forks: 14
• Open Issues: 0
• Metadata Files:
  • Readme: Readme.md
  • Contributing: Contributing.md
  • License: License.md

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• awesome-wolfram-language - FEMAddOns

README

        

# FEMAddOns for the Wolfram Language

[![View notebooks](https://wolfr.am/lA6mO5hv)](https://wolfr.am/Dzga9EH4)

The [Wolfram Language has build in support for the Finite Element Method](https://www.wolfram.com/language/core-areas/fem/). FEMAddOns is a package that provides additional Finite Element Method functionality. FEMAddOns supports 11.3 and later versions of Wolfram Language deployments for the desktop, including [Wolfram Desktop](https://www.wolfram.com/desktop/) and [Mathematica](https://www.wolfram.com/mathematica/).

### Installing and Updating the FEMAddOns release

The easiest way to install or update the FEMAddOns is to evaluate the following:

    ResourceFunction["FEMAddOnsInstall"][]

The use of the ResourceFunction requires you to log into your wolfram account. If you can not or do not want to do that then you can install the latest release of the FEMAddOns-X.Y.Z.paclet from the [Github repo's releases page](https://github.com/WolframResearch/FEMAddOns/releases). To install, run the following command in the Wolfram Language:

    PacletInstall["/full/path/to/FEMAddOnsX.Y.Z.paclet"]

Either installation will permanently install the latest version of the FEMAddOns paclet. Installed versions can be enumerated using the command:

    PacletFind["FEMAddOns"]

And all versions can be uninstalled using the command:

    PacletUninstall["FEMAddOns"]

To make use of the documentation it may be necessary to restart.

### Using FEMAddOns

To access the documentation, open the notebook interface help viewer, and search for FEMAddOns. The first hit will be a summary page enumerating the most commonly used functions in FEMAddOns. From there you can also follow the link to *contributed FEM Applications*.

For example generate structured meshes with `StructuredMesh`:

	raster = Table[#, {fi, 0, 2 Pi, 2 Pi/360}] & /@ {{Cos[fi], Sin[fi]}, 0.8*{Cos[fi], Sin[fi]}};

	mesh = StructuredMesh[raster, {90, 5}];

	mesh["Wireframe"]

![StructuredMesh](Images/structuredMesh.png)

With `ToQuadMesh` convert triangle meshes into quadrilateral meshes:

	region = ImplicitRegion[And @@ (# <= 0 & /@ {-y, 1/25 - (-3/2 + x)^2 - y^2, 

       1 - x^2 - y^2, -4 + x^2 + y^2, y - x*Tan[Pi/8]}), {x, y}];

	ToQuadMesh[ToElementMesh[region]]["Wireframe"]

![triMeshToQuadMesh](Images/triMeshToQuadMesh.png)

Use the `DistMesh` mesh generator to create smooth meshes:

	mesh = DistMesh[RegionDifference[Rectangle[{-1, -1}, {1, 1}], Disk[{0, 0}, 1/2]], 

	   "DistMeshRefinementFunction" -> 

	    Function[{x, y}, Min[4*Sqrt[Plus @@ ({x, y}^2)] - 1, 2]], 

	   "MaxCellMeasure" -> {"Length" -> 0.05}, 

	   "IncludePoints" -> {{-1, -1}, {-1, 1}, {1, -1}, {1, 1}}]; 

	mesh["Wireframe"]

![DistMesh](Images/distMesh.png)

 With `ImportMesh` load meshes from Abaqus, Comsol, Elfen and Gmsh  

	mesh = ImportMesh[ "filePath", "mesh.mphtxt"];

	mesh["Wireframe"]

![screenshot](https://imgur.com/aq92uqA.gif "Geometry source: https://grabcad.com/    library/goose-2")

Use `DomainDecomposition` to solve stationary PDEs on a cluster:

	kernels = LaunchKernels[24];

	DecompositionNDSolveValue[{Laplacian[u[x, y], {x, y}] == 1, 

	  DirichletCondition[u[x, y] == 0, 

	   x == 0 || x == 5 || y == 0 || y == 1]}, u, Element[{x, y}, 

	  Rectangle[{0, 0}, {5, 1}]], "Kernels" -> kernels]

### More...

See the following files for more information:

* [License.md](License.md) - FEMAddOns license

* [Contributing.md](Contributing.md) - Guidelines for contributing to FEMAddOns

* [HowToBuild.md](HowToBuild.md) - Instructions for building and debugging FEMAddOns

* [AlternativeInstallation.md](AlternativeInstallation.md) - Alternative instructions for installing the  FEMAddOns paclet