How to Apply a Nodal Transformation to Densify Mesh in Gridap?

[JCHostos]

Hi everyone,

I am working with Gridap.jl and generated a simple structured mesh using the following code:

domain = (0,1,0,1)
partition = (20,20)
model = CartesianDiscreteModel(domain, partition)

This creates a structured 20x20 quadrilateral mesh in the domain [0,1]×[0,1]. Now, I would like to modify the structure "model" to densify the mesh towards the edges using the following transformation:

(xn,yn)= 0.5 + 0.5 * tanh(eps * (2 * (x,y) - 1)) / tanh(eps)

where (xn,yn) are the new nodal coordinates after applying the transformation to the original coordinates (x,y), epsilon is the densification parameter.

​My Question:

How can I modify the model structure in Gridap to change only the nodal coordinates according to this transformation, while keeping the connectivity and other aspects of the mesh unchanged?. I adding pictures of what I want for clarity:

I want to past from this:

to this:

[JordiManyer]

f(X) = .... where X = (x,y)
model = CartesianDiscreteModel(domain,partition;map=f)

[JCHostos]

Thank you for your answer, Jordi.

I try something like this:
function Clustering(X)
alpha=2.0
x, y = X
xn = 0.5 + 0.5 * tanh(alpha * (2 * x - 1)) / tanh(alpha)
yn = 0.5 + 0.5 * tanh(alpha * (2 * y - 1)) / tanh(alpha)
return (xn, yn)
end
model = CartesianDiscreteModel(domain,partition;map=Clustering)

but it did not work. It is maybe too basic, but I am not a programmer so I will need a little more guidance. I am very new working on this powerfull Gridap enviroment.

Beforehand, thank you very much

[JordiManyer]

Our Point type, used for coordinates, is not iterable. I.e you cannot do this x, y = X.
Instead, do this:

x, y = X[1], X[2]

Also, you need to return the same type, i.e instead of (xn,yn), return Point(xn,yn).

For future reference, saying something "doesn't work" is quite useless to anyone trying to help. Posting the terminal output of the error usually makes this kind of interaction go quicker. :)

[JCHostos]

Thank you very much, Jordi.

I will show the terminal output of the error for futuer opportunities. But now, thanks to you, it worked. So, this is that I have to show:

Muchas gracias!!!