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Diffusion localised on the map of France

POSTED BY: André Dauphiné
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Thanks very much A. Dauphiné
POSTED BY: André Dauphiné

I hope it helps, I am new to using finite element mesh. Is there a source I could look at for the diffusion equation you are modeling? Probably there is a better way to model a single source in Paris than the Gaussian used in the second plot.
POSTED BY: Jason Biggs

Yes, I would also be interested in what kind of general problem @André Dauphiné is trying to approach. André, could you please share?
POSTED BY: Sam Carrettie
POSTED BY: Jason Biggs

@Jason which version of Mathematica did you use to make these. I tried 10.4 and 11.1 with fresh kernel and i am not able to run your code. it is giving an error. Can you please clarify?

POSTED BY: Ali Hashmi

Ali - I don't know what happened here, I was most certainly using version 10.xx - not sure which, but when I evaluate this now it doesn't work. The problem is the one mentioned by the OP here: http://community.wolfram.com/groups/-/m/t/1023182

There is a bug with DiscretizeGraphics where it isn't working on multi-polygons. Make this change in the definition of carto in either of the code blocks above and it should work

carto = DiscretizeGraphics[
   CountryData["France", {"Polygon", "Mercator"}] /. 
    Polygon[x : {{{_, _} ..} ..}] :> Polygon /@ x];
POSTED BY: Jason Biggs

Thanks this works !

On a different note, I do also wish that people at Wolfram can incorporate some ways to repair broken meshes/or self intersections in mesh
POSTED BY: Ali Hashmi
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