https://github.com/perinim/vem_grids

MATLAB Implementation of Polygonal Grids for VEM Applications
https://github.com/perinim/vem_grids

analysis fea fem grid mechanical-engineering polygons vem voronoi

Last synced: 2 months ago
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MATLAB Implementation of Polygonal Grids for VEM Applications

• Host: GitHub
• URL: https://github.com/perinim/vem_grids
• Owner: PeriniM
• License: mit
• Created: 2022-09-23T13:31:03.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2022-10-11T10:30:22.000Z (over 2 years ago)
• Last Synced: 2025-02-14T12:18:06.246Z (4 months ago)
• Topics: analysis, fea, fem, grid, mechanical-engineering, polygons, vem, voronoi
• Language: MATLAB
• Homepage:
• Size: 1.92 MB
• Stars: 2
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Polygonal grids for Virtual Elements Method (VEM) 

## Abstract

Virtual Elements Method, unlike FEM, works with any kind of grid elements, from regular to non-regular shapes. Since it is a research field, there are not many resources and experimental grids need to be created to test this new algorithm. This method can be used to mesh very rough surfaces (like a rock with many irregular spikes and holes) and, from initial tests, faster than FEM on solving systems of partial differential equations.

## Github repo

List of Matlab scripts that generates polygonal (regular and irregular) grids with particular requirements to be used in VEM solvers.

## Presentation Slides

![Slide1](presentation_slides/Slide1.JPG?raw=true "Slide1")

![Slide2](presentation_slides/Slide2.JPG?raw=true "Slide2")

![Slide3](presentation_slides/Slide3.JPG?raw=true "Slide3")

![Slide4](presentation_slides/Slide4.JPG?raw=true "Slide4")

![Slide5](presentation_slides/Slide5.JPG?raw=true "Slide5")

![Slide1](presentation_slides/Slide6.JPG?raw=true "Slide6")

![Slide2](presentation_slides/Slide7.JPG?raw=true "Slide7")

![Slide3](presentation_slides/Slide8.JPG?raw=true "Slide8")

![Slide4](presentation_slides/Slide9.JPG?raw=true "Slide9")

![Slide5](presentation_slides/Slide10.JPG?raw=true "Slide10")

![Slide1](presentation_slides/Slide11.JPG?raw=true "Slide11")

![Slide2](presentation_slides/Slide12.JPG?raw=true "Slide12")

![Slide3](presentation_slides/Slide13.JPG?raw=true "Slide13")

![Slide4](presentation_slides/Slide14.JPG?raw=true "Slide14")

![Slide5](presentation_slides/Slide15.JPG?raw=true "Slide15")

![Slide1](presentation_slides/Slide16.JPG?raw=true "Slide16")

![Slide2](presentation_slides/Slide17.JPG?raw=true "Slide17")

## Fast way to create custom grids

I have created a simple online platform to build custom shape to be arrange into a grid. You can then export the new shapes in a CSV file for further manipulation. In the matlab folder in the following repo you can find a script that takes as input the CSV shape and outputs a NxM grid. 

[createGrid() repo](https://github.com/PeriniM/createGrid)

## Useful Links

[Hexagons Explanation](https://www.redblobgames.com/grids/hexagons/) 

[Pentagonal Tilings](https://commons.wikimedia.org/wiki/Category:Pentagonal_tilings) 

[An Introduction to Virtual Elements Method](https://www.maths.dur.ac.uk/lms/101/talks/0493daveiga.pdf) 

[Matlab Documentation](https://it.mathworks.com/help/matlab/index.html?s_tid=CRUX_topnav) 

[Mesh Refinement](https://www.comsol.it/multiphysics/mesh-refinement)