Line Integral of Vector Field

General
8

Hopefully a final followup question. Seems that the 3d version of the previous code is not as easy as I thought. Let me consider the line integral of the scalar function u=1+x^2+2y^2+3z^2 across a trivial straight line starting from (0.5,0.5,0) to (0.5,0.5,1). I changed the dimensions accordingly and also the _integral_types to dx but if I print the facets seems that no facet is found, therfore obviously the integral is zero, which is not correct. Minimal code follows:

import dolfinx
from mpi4py import MPI
import numpy as np
import ufl

domain = dolfinx.mesh.create_unit_cube(MPI.COMM_WORLD, 10, 10, 10, dolfinx.mesh.CellType.tetrahedron)

V = dolfinx.fem.FunctionSpace(domain, ("Lagrange", 1))
u_test = dolfinx.fem.Function(V)
u_test.interpolate(lambda x: 1 + x[0]**2 + 2*x[1]**2 + 3*x[2]**2)

def facet_eq(x):
 return np.logical_and(np.isclose(x[0], 0,5), np.isclose(x[1], 0,5))

facets = dolfinx.mesh.locate_entities(domain, domain.topology.dim, facet_eq)
facet_tags = dolfinx.mesh.meshtags(domain, domain.topology.dim, facets, np.full_like(facets, 5))

# Define the measure
ds = ufl.Measure("dx", subdomain_data=facet_tags, subdomain_id=5)

intergal = dolfinx.fem.form(u_test * ds)
print(facets,dolfinx.fem.assemble_scalar(intergal))