def run_L2tracking_optimization(write_output=False):
""" Test template for fsz.LevelsetFunctional."""
# tool for developing new tests, allows storing shape iterates
if write_output:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# setup problem
mesh = fd.UnitSquareMesh(30, 30)
Q = fs.FeControlSpace(mesh)
inner = fs.ElasticityInnerProduct(Q)
q = fs.ControlVector(Q, inner)
# setup PDE constraint
mesh_m = Q.mesh_m
e = PoissonSolver(mesh_m)
# create PDEconstrained objective functional
J_ = L2trackingObjective(e, Q, cb=cb)
J = fs.ReducedObjective(J_, e)
# ROL parameters
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 10
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
},
},
'Status Test': {
'Gradient Tolerance': 1e-4,
'Step Tolerance': 1e-5,
'Iteration Limit': 15
}
}
# assemble and solve ROL optimization problem
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
state = solver.getAlgorithmState()
assert (state.gnorm < 1e-4)
# import sys; sys.exit()
directory = f"./output/stokes/base_{base_inner}_cr_{use_cr}/"
if not os.path.exists(directory):
os.makedirs(directory, exist_ok=True)
out = fd.File(directory + "u.pvd")
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q)
baryx = fsz.LevelsetFunctional(x, Q)
baryy = fsz.LevelsetFunctional(y, Q)
econ = fs.EqualityConstraint([vol, baryx, baryy])
emul = ROL.StdVector(3)
econ_val = ROL.StdVector(3)
Je = fsz.EnergyObjective(e, Q, cb=None)
Jr = fs.ReducedObjective(Je, e)
# J = 2e-4 * Jr
J = 1e-2 * Jr
q = fs.ControlVector(Q, inner)
params_dict = {
"General": {
"Secant": {
"Type": "Limited-Memory BFGS",
"Maximum Storage": 5
}
},
"Step": {
"Type": "Augmented Lagrangian",
"Line Search": {
"Descent Method": {
e = NavierStokesSolver(Q.mesh_m, viscosity)
# save state variable evolution in file u2.pvd or u3.pvd
if mesh.topological_dimension() == 2: # in 2D
out = fd.File("solution/u2D.pvd")
elif mesh.topological_dimension() == 3: # in 3D
out = fd.File("solution/u3D.pvd")
def cb():
return out.write(e.solution.split()[0])
# create PDEconstrained objective functional
J_ = PipeObjective(e, Q, cb=cb)
J = fs.ReducedObjective(J_, e)
# add regularization to improve mesh quality
Jq = fsz.MoYoSpectralConstraint(10, fd.Constant(0.5), Q)
J = J + Jq
# Set up volume constraint
vol = fsz.VolumeFunctional(Q)
initial_vol = vol.value(q, None)
econ = fs.EqualityConstraint([vol], target_value=[initial_vol])
emul = ROL.StdVector(1)
# ROL parameters
params_dict = {
'General': {'Print Verbosity': 0, # set to 1 to understand output
'Secant': {'Type': 'Limited-Memory BFGS',
e = fsz.StokesSolver(mesh_m,
inflow_bids=[1, 2],
inflow_expr=inflow_expr,
noslip_bids=[4])
e.solve()
out = fd.File("u.pvd")
def cb(*args):
out.write(e.solution.split()[0])
cb()
Je = fsz.EnergyObjective(e, Q, cb=cb)
Jr = 1e-2 * fs.ReducedObjective(Je, e)
Js = fsz.MoYoSpectralConstraint(10., fd.Constant(0.7), Q)
Jd = 1e-3 * fsz.DeformationRegularization(
Q, l2_reg=1e-2, sym_grad_reg=1e0, skew_grad_reg=1e-2)
J = Jr + Jd + Js
q = fs.ControlVector(Q, inner)
g = q.clone()
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q)
baryx = fsz.LevelsetFunctional(x, Q)
baryy = fsz.LevelsetFunctional(y, Q)
econ = fs.EqualityConstraint([vol, baryx, baryy])
emul = ROL.StdVector(3)
params_dict = {
'General': {