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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

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MATLAB Implementation of Polygonal Grids for VEM Applications

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# 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)