Custom integrals and source terms

[dokken]

@belmont

How can I define the proper measure? Since this is a integration of the same spatial dimension as the problem I tried (full MWE in the end)

def facet_eq_2D(x):
   tol=1e-6
   less1 =  x[0] < 0.5 + tol
   less2 = x[1] < 0.5 + tol
   return np.logical_and(less1, less2)
cells = dolfinx.mesh.locate_entities(domain, domain.topology.dim, facet_eq_2D)
tags = np.full_like(cells, 1)
cell_tags = dolfinx.mesh.meshtags(domain, domain.topology.dim, cells, tags)
dx1 = ufl.Measure('dx', domain, subdomain_data=cell_tags, subdomain_id=1 )
print(dolfinx.fem.assemble_scalar(dolfinx.fem.form(uh * dx1(1))))
L1 = source * v * ufl.dx + v * dx1(1)
problem = dolfinx.fem.petsc.LinearProblem(a, L1, bcs=[bc], petsc_options={"ksp_type": "preonly", "pc_type": "lu"})
uh1 = problem. Solve()

but it doesn’t work.
Still though the line print(dolfinx.fem.assemble_scalar(dolfinx.fem.form(uh * dx1(1)))) very accurately calculates the integral.

I don’t understand what you mean by measure here.
As far as I can tell, you want to integrate the function \theta(0.5-x)\theta(0.5-y) over the whole domain \Omega. This does not require a new measure.

Your definition of dx1 generates an integral measure over all cells whose vertices satisfies

@belmont

def facet_eq_2D(x):
   tol=1e-6
   less1 =  x[0] < 0.5 + tol
   less2 = x[1] < 0.5 + tol
   return np.logical_and(less1, less2)

which would be an integral over all cells where x<0.5+tol and y<0.5+tol in your domain.

@belmont

def facet_eq_1D(x):
    tol=1e-6
    close =  np.isclose(x[0], 0.5)
    less = x[1] < 0.5 + tol
    return np.logical_and(close, less)
cells = dolfinx.mesh.locate_entities(domain, domain.topology.dim-1, facet_eq_1D)
tags = np.full_like(cells, 1)
cell_tags = dolfinx.mesh.meshtags(domain, domain.topology.dim-1, cells, tags)

As you are stating that this is a 3D problem, you are now searching for all facets where both vertices has an x coordinate close to 0.5 (which cannot be satisfied). If you want to implement the point-source at a given degree of freedom, you should locate that degree of freedom and add to the correct position in the rhs. If you want to use a smoothed version of delta, see for instance; Dirac delta distribution (dolfinx) - #3 by dokken