Managing data interpolation onto extruded meshes

[icepack]

Managing data interpolation onto extruded meshes

[dlilien]

Not sure if it does what you need, but I did write a quick fix to go directly from raster data to an extruded 3d mesh, but I never put in a pull request: 824655f

[nholschuh]

This is perfect! Thanks David -- the part of the code that I felt like I understood the least was the following, which obviously was integral to this issue:

V_new = firedrake.VectorFunctionSpace(mesh, element)
X = firedrake.interpolate(mesh.coordinates, V_new)

Daniel mentioned that he had already made the interpolate function xarray compatible, but I've written an interpolate_xr function (that now incorporates your change) if anyone things it might be useful for icepack. It handles some edge cases that we kept running into, which may or may not be helpful.

[nholschuh]

I may have spoken too soon -- this works for a 1-layer extruded mesh fine, but still fails for multi-layered meshes in a way that I find baffling... I'm going to see if I can implement the lift function that Daniel suggested to me, and get back to you.