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)
def test_equality_constraint(pytestconfig):
mesh = fs.DiskMesh(0.05, radius=2.)
Q = fs.FeControlSpace(mesh)
inner = fs.ElasticityInnerProduct(Q, direct_solve=True)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
q = fs.ControlVector(Q, inner)
if pytestconfig.getoption("verbose"):
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
else:
cb = None
f = (pow(2 * x, 2)) + pow(y - 0.1, 2) - 1.2
J = fsz.LevelsetFunctional(f, Q, cb=cb)
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q)
e = fs.EqualityConstraint([vol])
emul = ROL.StdVector(1)
params_dict = {
'Step': {
'Type': 'Augmented Lagrangian',
'Augmented Lagrangian': {
'Subproblem Step Type': 'Line Search',
'Penalty Parameter Growth Factor': 2.,
'Initial Penalty Parameter': 1.,
'Subproblem Iteration Limit': 20,
},
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
},
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 5
}
},
'Status Test': {
'Gradient Tolerance': 1e-4,
'Step Tolerance': 1e-10,
'Iteration Limit': 10
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q, econ=e, emul=emul)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
state = solver.getAlgorithmState()
assert (state.gnorm < 1e-4)
assert (state.cnorm < 1e-6)
R = 1.0
r = 0.5
print("Harmonic map exists for r^*/R^* = %.2f" % ((0.5 * (R / r + r / R))**-1))
Rs = 1.0
rs = args.rstar
Q = fs.FeControlSpace(mesh)
d = distance_function(Q.get_space_for_inner()[0].mesh(), boundary_ids=[1, 2])
if args.weighted:
mu_base = 0.01 / (0.01 + d)
else:
mu_base = fd.Constant(1.)
# mu_base = fd.Constant(1.0)
if args.base_inner == "elasticity":
inner = fs.ElasticityInnerProduct(Q, mu=mu_base, direct_solve=True)
elif args.base_inner == "laplace":
inner = fs.LaplaceInnerProduct(Q, mu=mu_base, direct_solve=True)
else:
raise NotImplementedError
if args.alpha is not None:
mu_cr = mu_base / args.alpha
inner = CauchyRiemannAugmentation(mu_cr, inner)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
r = fd.sqrt(x**2 + y**2)
expr = (r - fd.Constant(rs)) * (r - fd.Constant(Rs))
J = 0.1 * fsz.LevelsetFunctional(expr, Q, quadrature_degree=5)
import firedrake as fd
import fireshape as fs
import fireshape.zoo as fsz
import ROL
dim = 2
mesh = fs.DiskMesh(0.4)
Q = fs.FeMultiGridControlSpace(mesh, refinements=4, order=2)
# Q = fs.FeControlSpace(mesh)
# inner = fs.SurfaceInnerProduct(Q)
inner = fs.ElasticityInnerProduct(Q)
extension = fs.ElasticityExtension(Q.V_r, direct_solve=True)
mesh_m = Q.mesh_m
if dim == 2:
(x, y) = fd.SpatialCoordinate(mesh_m)
f = (pow(x, 2)) + pow(0.5 * y, 2) - 1.
else:
(x, y, z) = fd.SpatialCoordinate(mesh_m)
f = (pow(x - 0.5, 2)) + pow(y - 0.5, 2) + pow(z - 0.5, 2) - 2.
q = fs.ControlVector(Q, inner, boundary_extension=extension)
out = fd.File("domain.pvd")
J = fsz.LevelsetFunctional(f, Q, cb=lambda: out.write(mesh_m.coordinates))
J.cb()
g = q.clone()
J.update(q, None, 1)
J.gradient(g, q, None)
g.scale(-0.3)
J.update(g, None, 1)
parser.add_argument("--base-inner",
type=str,
default="elasticity",
choices=["elasticity", "laplace"])
parser.add_argument("--alpha", type=float, default=None)
parser.add_argument("--clscale", type=float, default=0.1)
parser.add_argument("--maxiter", type=int, default=50)
args = parser.parse_args()
mesh = fs.DiskMesh(args.clscale, radius=3, smooth=10)
Q = fs.FeControlSpace(mesh)
mu_base = fd.Constant(1.0)
if args.base_inner == "elasticity":
inner = fs.ElasticityInnerProduct(Q, mu=mu_base, direct_solve=True)
elif args.base_inner == "laplace":
inner = fs.LaplaceInnerProduct(Q, mu=mu_base, direct_solve=True)
else:
raise NotImplementedError
if args.alpha is not None:
mu_cr = mu_base / args.alpha
inner = CauchyRiemannAugmentation(mu_cr, inner)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
a = 0.8
b = 2.0
parser = argparse.ArgumentParser()
parser.add_argument("--use_cr", type=int, default=0)
parser.add_argument("--base_inner", type=str, default="elasticity")
args = parser.parse_args()
use_cr = bool(args.use_cr)
base_inner = args.base_inner
mesh = fd.Mesh("Sphere2D.msh")
Q = fs.FeControlSpace(mesh)
d = distance_function(Q.get_space_for_inner()[0].mesh(), eps=fd.Constant(0.1))
mu_base = 0.01 / (0.01 + d)
if base_inner == "elasticity":
inner = fs.ElasticityInnerProduct(Q,
fixed_bids=[1, 2, 3],
mu=mu_base,
direct_solve=True)
elif base_inner == "laplace":
inner = fs.LaplaceInnerProduct(Q,
fixed_bids=[1, 2, 3],
mu=mu_base,
direct_solve=True)
else:
raise NotImplementedError
if use_cr:
mu_cr = 100.0 * mu_base
inner = CauchyRiemannAugmentation(mu_cr, inner)
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
import firedrake as fd
import fireshape as fs
import fireshape.zoo as fsz
import ROL
mesh = fd.Mesh("Sphere2D.msh")
# Q = fs.FeControlSpace(mesh)
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=1)
inner = fs.ElasticityInnerProduct(Q, fixed_bids=[1, 2, 3])
mesh_m = Q.mesh_m
(x, y) = fd.SpatialCoordinate(mesh_m)
inflow_expr = fd.Constant((1.0, 0.0))
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)