TuringPatternsOn2DSurfaces

WORK IN PROGRESS

Table of Contents

1. About The Project
   • Built With
2. Progress so far
3. Roadmap
4. License
5. Contact
6. Acknowledgments

About The Project

An investigation of turing patterns on (no-boundary, smooth) 2D manifolds (in 3D space) using numerical (FEM) and analytical methods.

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Built With

• 
  • Ferrite.jl
  • Symbolics.jl
• []

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Progress so far

• Solved stationary heat equation on Dziuk surface. (See 02_heateq_on_dziuksurf)
• Created refined meshes, using a manually initial mesh (4nodes-8triangles).
  • function to generate meshes
  • .msh files
• Created custom linear function interpolation, geometric interpolation, and CellValues (in accordance with Ferrite.jl devdocs) for 2d triangular surface meshes embedded in 3D space. (needs to be tested)

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Next Steps

• Test custom interpolation and CellValues. Possibly calculate the matrix and RHS vector manually for 6 node mesh to verify.
• Update documentation on simulating heat equation on Dziuk surface.

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License

Distributed under the GNU AFFERO GENERAL PUBLIC LICENSE Version 3. See LICENSE.txt for more information.

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Contact

Author name: Avina Kalle LinkedIn

Project Link: https://github.com/Avina-cK/TuringPatternsOn2DSurfaces

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Reference(s)

Gerhard Dziuk. Finite Elements for the Beltrami operator on arbitrary surfaces, pages 142–155. Springer Berlin Heidelberg, Berlin, Heidelberg, 1988.

Acknowledgments

• Choose an Open Source License
• Img Shields
• Alan Turing
• othneildrew. README Template.

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