[firedrake] Interpolating data to Function

[Tuomas Karna]

Hi Firedrake-people,

I'm working with simple 2D ocean model and I'd like to load bathymetric 
data to a Function, interpolating to the correct coordinates of the 
nodes. Currently I get the x/y coordinates from specialized x/y function 
and then just write the data directly to Function.dat.data array. So 
something like this:

P1 = FunctionSpace(mesh, "CG", 1)
bath = Function(P1,name='bathymetry')
x_func = Function(P1).interpolate(Expression('x[0]'))
y_func = Function(P1).interpolate(Expression('x[1]'))
def interpolateBath(x,y):
     # interpolate here
     return 3.0
bath.dat.data[:] = interpolateBath(x_func.dat.data, y_func.dat.data)

Is there a cleaner way of doing this?

I have a similar question for the boundaries. I have external data 
defined on a line which I'd like to interpolate to the nodes of a 
certain boundary. I could use a Function for this too, if I knew the 
indices of the boundary nodes. I've hacked something together using 
mesh.exterior_facets and FunctionSpace.exterior_facet_boundary_node_map, 
just wondering if there is an easier way?

Regs,

Tuomas Karna
Post-Doctoral Fellow
Oregon Health & Science University