Unable to specify BC at a point in FEniCSx

dolfinx
1

Hello,
I am trying t solve a diffusion problem (Please find the image) in which I want to apply a boundary condition at a point. I have found the discussion regarding this, but it was implemented in FEniCS, I want the solution in FEniCSx.
I have tried something like this but it doesn’t work out.

mesh = dolfinx.UnitSquareMesh(MPI.COMM_WORLD, 2, 2)
boundaries_2 = [(5, lambda x: np.isclose([x[0], x[1]], [0, 0]))]

facet_indices_2, facet_markers_2 = [], []
fdim_2 = mesh.topology.dim - 2
for (marker, locator) in boundaries_2:
    facets_2 = dolfinx.mesh.locate_entities(mesh, fdim_2, locator)
    facet_indices_2.append(facets_2)
    facet_markers_2.append(np.full(len(facets_2), marker))
facet_tag_2 = dolfinx.MeshTags(mesh, fdim_2, np.array(np.hstack(facet_indices_2),dtype=np.int32), np.array(np.hstack(facet_markers_2),dtype=np.int32))

It threw this error.


---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
/tmp/ipykernel_65/458078783.py in <module>
      2 fdim_2 = mesh.topology.dim - 2
      3 for (marker, locator) in boundaries_2:
----> 4     facets_2 = dolfinx.mesh.locate_entities(mesh, fdim_2, locator)
      5     facet_indices_2.append(facets_2)
      6     facet_markers_2.append(np.full(len(facets_2), marker))

/usr/local/dolfinx-real/lib/python3.8/dist-packages/dolfinx/mesh.py in locate_entities(mesh, dim, marker)
     41     """
     42 
---> 43     return cpp.mesh.locate_entities(mesh, dim, marker)
     44 
     45 

/tmp/ipykernel_65/2253244396.py in <lambda>(x)
----> 1 boundaries_2 = [(5, lambda x: np.isclose([x[0], x[1]], [0, 0]))]

<__array_function__ internals> in isclose(*args, **kwargs)

/usr/local/lib/python3.8/dist-packages/numpy/core/numeric.py in isclose(a, b, rtol, atol, equal_nan)
   2356     yfin = isfinite(y)
   2357     if all(xfin) and all(yfin):
-> 2358         return within_tol(x, y, atol, rtol)
   2359     else:
   2360         finite = xfin & yfin

/usr/local/lib/python3.8/dist-packages/numpy/core/numeric.py in within_tol(x, y, atol, rtol)
   2337     def within_tol(x, y, atol, rtol):
   2338         with errstate(invalid='ignore'):
-> 2339             return less_equal(abs(x-y), atol + rtol * abs(y))
   2340 
   2341     x = asanyarray(a)

ValueError: operands could not be broadcast together with shapes (2,9) (2,)

Please tell, how can I implement this.
Thank you

Capture
Capture1200×591 32.9 KB

2

This is for instance illustrated in: dolfinx/demo_stokes-taylor-hood.py at main · FEniCS/dolfinx · GitHub
Thus, you can use the syntax:

boundaries_2 = [(5, lambda x: np.isclose(x.T, [0, 0, 0]).all(axis=1))]

or the numpy.logical_and operator:

boundaries_2 = [(5, lambda x: np.logical_and(np.isclose(x[0], 0), np.isclose(x[1], 0)))]
2 Likes
3

Thanks. It worked for me.
I have one more doubt.

dofs_L = dolfinx.fem.locate_dofs_geometrical(V, lambda x: np.logical_and(np.isclose(x[0], 0), np.isclose(x[1], 0)))
u_L = dolfinx.Function(V)
x = ufl.SpatialCoordinate(mesh)
u_L.interpolate(lambda x: x[0]+3)
u_L.x.scatter_forward()
#u_L = dolfinx.Constant(mesh, 0)
#u_L.x.scatter_forward()
bc_L = dolfinx.DirichletBC(u_L, dofs_L)

In this code, I am specifying the boundary value to 3 at x=0 and y=0.
Why can’t I directly specify the value 3 to this boundary, in this way

u_L = dolfinx.Constant(mesh, 3)
bc_L = dolfinx.DirichletBC(u_L, dofs_L)

This gives NotImplementedError: to me.
Instead of doing this in an indirect way like

u_L.interpolate(lambda x: x[0]+3)
u_L.x.scatter_forward()
bc_L = dolfinx.DirichletBC(u_L, dofs_L)

Is there any simple way to do this, as we have it in FEniCS?

Thanks

4

As clearly stated by the error message, this has not yet been implemented in DOLFINx, and thus you have to use the indirect method

5

Understood. Thank you very much.