How can I find the closest node to an arbitrary coordinates?

2

Dirichlet BCs are applied on the DOFs of the FunctionSpace. These coincide with the mesh vertices for P1 elements.

Why not something simple such as the following (not for parallel):

from dolfin import *
import numpy as np

mesh = UnitSquareMesh(16, 16)
V = FunctionSpace(mesh, 'P', 2)  # because P1 would be boring
# get coordinates of DOFs
dof_coords = V.tabulate_dof_coordinates()

# random location
x0 = np.array([0.51241, 0.56245])

# find nearest DOF:
dof = np.argmin(np.linalg.norm(dof_coords - x0, axis=1))

print('dof {}, x = {}'.format(dof, dof_coords[dof]))

# now define a DirichletBC at that point
bc = DirichletBC(V, Constant(123),
                 'near(x[0], {x}) && near(x[1], {y})'.format(x=dof_coords[dof][0], y=dof_coords[dof][1]),
                 'pointwise')

PS: Regarding your linked question, the docstring of the function near is: near(x0: float, x1: float, eps: float = 3e-16). It doesn’t give you the nearest dof but all dofs within abs(x1-x2) < eps.

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