### Assign Function to subdomain of another Function

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4 months ago by
After solving on a SubMesh, how do I assign the resulting solution Function to a Function defined on the full mesh?

As an example, see the MWE below. We split the the full mesh into two SubMeshes, solve our functions on them, but how can we apply the solutions to the full mesh, then solve on that?

full_mesh = UnitSquareMesh(20,20)

# Setup submeshes
subdomain = CompiledSubDomain('(x[0] > 0.3 && x[0] < 0.6) && (x[1] > 0.3 && x[0] < 0.6)')
subdomain_data = MeshFunction('size_t', mesh, mesh.topology().dim())
subdomain_data.set_all(2)
subdomain.mark(subdomain_data, 1)
sub_mesh = SubMesh(mesh, subdomain_data, 1)
border_mesh = SubMesh(mesh, subdomain_data, 2)

# Solve for "sub_solution" on inner square submesh marked by "1"
sub_V = FunctionSpace(sub_mesh, 'CG', 1)
sub_v = TestFunction(sub_V)
sub_u = TrialFunction(sub_V)
sub_f = interpolate(Expression('x[0]+x[1]', degree=1), sub_V)
sub_L = sub_f*sub_v*dx
sub_bc = DirichletBC(sub_V, 0.0, 'on_boundary')
sub_solution = Function(sub_V)
solve(sub_a == sub_L, sub_solution, sub_bc)

# Solve for "border_solution" on the surrounding border submesh marked by "2"
# This uses the "sub_solution"
border_V = FunctionSpace(sub_mesh, 'CG', 1)
border_coeff = assemble(sub_solution*dx)
border_solution = interpolate(Constant(border_coeff), border_V)

# Solve on the full mesh using both sub_solution and  border_solution
full_V = FunctionSpace(full_mesh, 'CG', 1)
full_v = TestFunction(full_V)
full_u = TrialFunction(full_V)
full_f = interpolate(Expression('10.0*(x[0]+x[1])', degree=1), full_V)
full_q = Function(full_V)
################################
################################
# How do I do this assignment? #
################################
################################
full_q.assign(sub_solution)
full_q.assign(border_solution)
#################################
#################################
#################################
full_L = full_f*full_v*dx
full_bc = DirichletBC(full_V, -1.0, 'on_boundary')
full_solution = Function(full_V)
solve(full_a == full_L, full_solution, full_bc)
​
Community: FEniCS Project

0
4 months ago by
I am not sure if this is what you are looking for .. but you may try

https://github.com/mikaem/fenicstools/wiki/Interpolation-nonmatching-mesh-in-parallel

I have used this with latest FEniCS version.
Thanks for the suggestion. That seems like a nice tool, but I'm using dolfin-adjoint, so I'm limited to using only FEniCS methods. Hopefully others who stumble on this thread find it useful.
written 4 months ago by Matt