Hi, I solved a Dirichlet problem associated to a Laplace equation with FEniCSx, in a square.
After that, I computed the normal derivatives in the cells of the mesh adjacent to the boundary of the square.
Then I want to map these derivatives on the dofs of the inner boundary of a domain made up by a rectangle with a hole in the centre, where the hole is the square in which I solved the problem. I managed to do this when the two meshes are conforming, but when the two meshes are not conforming how can I do this? Is there a specific function that I can use?
I paste the code that works with conforming meshes
def map_normal_derivatives_on_dof(V, msh, inner_facets, normal_derivatives_dict):
"""
Map the normal derivatives (from dict di interpolate_derivatives_near_boundary)
to the DOF of the inner boundary of the rectangle with hole
"""
import numpy as np
import matplotlib.pyplot as plt
from dolfinx import fem, mesh
g_neumann = fem.Function(V)
g_neumann.x.array[:] = 0.0
dof_vals = np.zeros_like(g_neumann.x.array)
dof_count = np.zeros_like(g_neumann.x.array)
# Connettività: faccets → vertices
msh.topology.create_connectivity(1, 0)
edge_to_vertex = msh.topology.connectivity(1, 0)
for facet in inner_facets:
if facet not in normal_derivatives_dict:
continue
normal_derivative = normal_derivatives_dict[facet]["normal_derivative"]
# Find the vertices (nodes) of the faccet
nodes = edge_to_vertex.links(facet)
for node in nodes:
dofs = fem.locate_dofs_topological(V, 0, [node])
for dof in dofs:
dof_vals[dof] += normal_derivative
dof_count[dof] += 1
# Normalize
mask = dof_count > 0
g_neumann.x.array[mask] = dof_vals[mask] / dof_count[mask]
for facet in inner_facets:
if facet in normal_derivatives_dict:
val = normal_derivatives_dict[facet]["normal_derivative"]
print(f" Facet {facet}: normal_derivative = {val:.6e}")
return g_neumann
This is the case that I’ studying now:
