Getting node positions in higher-order elements

[ethrelfall]

Dear community,

I want to interpolate a function onto a higher-order mesh. I'm calling the function from the mpmath library and this doesn't work with the interpolate() method, so I thought I'd write the function values onto the node positions.

Can I do this and how i.e. access the spatial positions of nodes on e.g. a CG(2) function space?

Currently I only know how to do this at first order using mesh.coordinates.dat.data[i] to get the node positions on the lowest-order elements (CG(1)).

Did search for matching discussions - nada.

Thanks!

[colinjcotter]

Dear Ed, The basis coefficients of any Lagrange element of any degree are the values of the function at those points. So the steps are: 1. Get x,y,z = SpatialCoordinate(mesh) [or x,y in 2d] 2. Interpolate x, y, z separately to Functions from CG2, call them X, Y, Z 3. Create a new CG2 function, and write to its .dat.data[:] from X.dat.data[:]. Y.dat.data[:] using mpmath. However, what is the function? It might be best just to get it added to UFL and support in TSFC. All the best --cjc

[dham]

Extracting higher order coordinate node locations is covered in the manual here: https://www.firedrakeproject.org/interpolation.html#interpolation-from-external-data

There is no need to treat separate components separately.

[ethrelfall]

Thanks for both of these, I'm gonna mark this one as the answer but both would have worked. I did find that page but somehow I didn't twig that it was what I needed (dur).
The function is the JacobiSn elliptic function BTW ...