# Unstructured Mesh - Topological Optimization

Hello everyone, I am new to using Python FEniCS/DOLFIN and IPOPT.
I am working on topological optimization with a thermofluid problem.
The geometry used has a T shape and can basically be separated into three rectangles of different heights, with the central rectangle being the design domain undergoing optimization.
In this case, an unstructured mesh was initially generated using the mshr library (generate_mesh).
Unfortunately, with this mesh, the following problem arose:

AttributeError: ‘dolfin.cpp.mesh.Mesh’ object has no attribute ‘block_variable’

My code is relatively extensive due to the thermofluid problem, but I later tested a short example considering Stokes, provided on the DOLFIN page (Topology optimisation of fluids in Stokes flow), changed to an unstructured mesh, and the same problem arose.

Could you provide how you modified the code in:

as, you most likely need to use the Mesh wrapper around the object returned by generate_mesh from mshr. See for instance: Adjoint solution with PointSource as source term (f) for Poisson equation - #6 by dokken

from dolfin import *
from mshr import *

try:
import cyipopt
except ImportError:
print("""This example depends on IPOPT and pyipopt. \
When compiling IPOPT, make sure to link against HSL, as it \
is a necessity for practical problems.""")
raise

parameters["std_out_all_processes"] = False

mu = Constant(1.0)
alphaunderbar = 2.5 * mu / (100**2)
alphabar = 2.5 * mu / (0.01**2)
q = Constant(0.01)

def alpha(rho):
"""Inverse permeability as a function of rho, equation (40)"""
return alphabar + (alphaunderbar - alphabar) * rho * (1 + q) / (rho + q)

N = 100
delta = 1.5  # The aspect ratio of the domain, 1 high and \delta wide
V = Constant(1.0/3) * delta  # want the fluid to occupy 1/3 of the domain

# mesh = Mesh(RectangleMesh(MPI.comm_world, Point(0.0, 0.0), Point(delta, 1.0), N, N))
shape = Rectangle(Point(0.0, 0.0), Point(delta, 1.0))
mesh = generate_mesh(shape, N)

A = FunctionSpace(mesh, "CG", 1)        # control function space

U_h = VectorElement("CG", mesh.ufl_cell(), 2)
P_h = FiniteElement("CG", mesh.ufl_cell(), 1)
W = FunctionSpace(mesh, U_h*P_h)          # mixed Taylor-Hood function space

class InflowOutflow(UserExpression):
def eval(self, values, x):
values[1] = 0.0
values[0] = 0.0
l = 1.0/6.0
gbar = 1.0

if x[0] == 0.0 or x[0] == delta:
if (1.0/4 - l/2) < x[1] < (1.0/4 + l/2):
t = x[1] - 1.0/4
values[0] = gbar*(1 - (2*t/l)**2)
if (3.0/4 - l/2) < x[1] < (3.0/4 + l/2):
t = x[1] - 3.0/4
values[0] = gbar*(1 - (2*t/l)**2)

def value_shape(self):
return (2,)

def forward(rho):
"""Solve the forward problem for a given fluid distribution rho(x)."""
w = Function(W)
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)

F = (alpha(rho) * inner(u, v) * dx + inner(grad(u), grad(v)) * dx +
inner(grad(p), v) * dx  + inner(div(u), q) * dx)
bc = DirichletBC(W.sub(0), InflowOutflow(degree=1), "on_boundary")
solve(lhs(F) == rhs(F), w, bcs=bc)

return w

if __name__ == "__main__":
rho = interpolate(Constant(float(V)/delta), A)
w   = forward(rho)
(u, p) = split(w)

controls = File("output/control_iterations_guess.pvd")
allctrls = File("output/allcontrols.pvd")
rho_viz = Function(A, name="ControlVisualisation")
def eval_cb(j, rho):
rho_viz.assign(rho)
controls << rho_viz
allctrls << rho_viz

J = assemble(0.5 * inner(alpha(rho) * u, u) * dx + mu * inner(grad(u), grad(u)) * dx)
m = Control(rho)
Jhat = ReducedFunctional(J, m, eval_cb_post=eval_cb)

lb = 0.0
ub = 1.0

volume_constraint = UFLInequalityConstraint((V/delta - rho)*dx, m)

problem = MinimizationProblem(Jhat, bounds=(lb, ub), constraints=volume_constraint)
parameters = {'maximum_iterations': 20}

solver = IPOPTSolver(problem, parameters=parameters)
rho_opt = solver.solve()

rho_opt_xdmf = XDMFFile(MPI.comm_world, "output/control_solution_guess.xdmf")
rho_opt_xdmf.write(rho_opt)

q.assign(0.1)
rho.assign(rho_opt)
set_working_tape(Tape())

rho_intrm = XDMFFile(MPI.comm_world, "intermediate-guess-%s.xdmf" % N)
rho_intrm.write(rho)

w = forward(rho)
(u, p) = split(w)

controls = File("output/control_iterations_final.pvd")
rho_viz = Function(A, name="ControlVisualisation")
def eval_cb(j, rho):
rho_viz.assign(rho)
controls << rho_viz
allctrls << rho_viz

J = assemble(0.5 * inner(alpha(rho) * u, u) * dx + mu * inner(grad(u), grad(u)) * dx)
m = Control(rho)
Jhat = ReducedFunctional(J, m, eval_cb_post=eval_cb)

problem = MinimizationProblem(Jhat, bounds=(lb, ub), constraints=volume_constraint)
parameters = {'maximum_iterations': 100}

solver = IPOPTSolver(problem, parameters=parameters)
rho_opt = solver.solve()

rho_opt_final = XDMFFile(MPI.comm_world, "output/control_solution_final.xdmf")
rho_opt_final.write(rho_opt)


First of all, please format your code with 3x encapsulation.
Secondly, you would need to change

to
mesh = Mesh(generate_mesh(shape, N))`
as I already mentioned in my previous post