def solve_something(mesh):
V = fd.FunctionSpace(mesh, "CG", 1)
u = fd.Function(V)
v = fd.TestFunction(V)
x, y = fd.SpatialCoordinate(mesh)
# f = fd.sin(x) * fd.sin(y) + x**2 + y**2
# uex = x**4 * y**4
uex = fd.sin(x) * fd.sin(y) #*(x*y)**3
# def source(xs, ys):
# return 1/((x-xs)**2+(y-ys)**2 + 0.1)
# uex = source(0, 0)
uex = uex - fd.assemble(uex * fd.dx) / fd.assemble(1 * fd.dx(domain=mesh))
# f = fd.conditional(fd.ge(abs(x)-abs(y), 0), 1, 0)
from firedrake import inner, grad, dx, ds, div, sym
eps = fd.Constant(0.0)
f = uex - div(grad(uex)) + eps * div(grad(div(grad(uex))))
n = fd.FacetNormal(mesh)
g = inner(grad(uex), n)
g1 = inner(grad(div(grad(uex))), n)
g2 = div(grad(uex))
# F = 0.1 * inner(u, v) * dx + inner(grad(u), grad(v)) * dx + inner(grad(grad(u)), grad(grad(v))) * dx - f * v * dx - g * v * ds
F = inner(u, v) * dx + inner(grad(u),
grad(v)) * dx - f * v * dx - g * v * ds
F += eps * inner(div(grad(u)), div(grad(v))) * dx
F += eps * g1 * v * ds
F -= eps * g2 * inner(grad(v), n) * ds
# f = -div(grad(uex))
# F = inner(grad(u), grad(v)) * dx - f * v * dx
# bc = fd.DirichletBC(V, uex, "on_boundary")
bc = None
fd.solve(F == 0,
u,
bcs=bc,
solver_parameters={
"ksp_type": "cg",
"ksp_atol": 1e-13,
"ksp_rtol": 1e-13,
"ksp_dtol": 1e-13,
"ksp_stol": 1e-13,
"pc_type": "jacobi",
"pc_factor_mat_solver_type": "mumps",
"snes_type": "ksponly",
"ksp_converged_reason": None
})
print("||u-uex|| =", fd.norm(u - uex))
print("||grad(u-uex)|| =", fd.norm(grad(u - uex)))
print("||grad(grad(u-uex))|| =", fd.norm(grad(grad(u - uex))))
err = fd.Function(
fd.TensorFunctionSpace(mesh, "DG",
V.ufl_element().degree() - 2)).interpolate(
grad(grad(u - uex)))
# err = fd.Function(fd.FunctionSpace(mesh, "DG", V.ufl_element().degree())).interpolate(u-uex)
fd.File(outdir + "sln.pvd").write(u)
fd.File(outdir + "err.pvd").write(err)
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 retract(self, input_phi, delta_x, scaling=1):
"""input_phi is not modified,
output_phi refers to problem.phi
Args:
input_phi ([type]): [description]
delta_x ([type]): [description]
scaling (int, optional): [description]. Defaults to 1.
Returns:
[type]: [description]
"""
self.current_max_distance_at_t0 = self.current_max_distance
self.hj_solver.ts.setMaxTime(scaling)
try:
output_phi = self.hj_solver.solve(input_phi)
except:
reason = self.hj_solver.ts.getConvergedReason()
print(f"Time stepping of Hamilton Jacobi failed. Reason: {reason}")
if self.output_dir:
print(f"Printing last solution to {self.output_dir}")
fd.File(f"{self.output_dir}/failed_hj.pvd").write(input_phi)
max_vel = calculate_max_vel(delta_x)
self.last_distance = max_vel * scaling
conv = self.hj_solver.ts.getConvergedReason()
rtol, atol = (
self.hj_solver.parameters["ts_rtol"],
self.hj_solver.parameters["ts_atol"],
)
max_steps = self.hj_solver.parameters.get("ts_max_steps", 800)
current_time = self.hj_solver.ts.getTime()
total_time = self.hj_solver.ts.getMaxTime()
if conv == 2:
warning = (
f"Maximum number of time steps {self.hj_solver.ts.getStepNumber()} reached."
f"Current time is only: {current_time} for total time: {total_time}."
"Consider making the optimization time step dt shorter."
"Restarting this step with more time steps and tighter tolerances if applicable."
)
fd.warning(warning)
# Tighten tolerances if we are really far
if current_time / total_time < 0.2:
current_rtol, current_atol = self.hj_solver.ts.getTolerances()
new_rtol, new_atol = max(rtol / 200, current_rtol / 10), max(
atol / 200, current_atol / 10)
self.hj_solver.ts.setTolerances(rtol=new_rtol, atol=new_atol)
# Relax max time steps
current_max_steps = self.hj_solver.ts.getMaxSteps()
new_max_steps = min(current_max_steps * 1.5, max_steps * 3)
self.hj_solver.ts.setMaxSteps(new_max_steps)
output_phi.assign(input_phi)
elif conv == 1:
self.hj_solver.ts.setTolerances(rtol=rtol, atol=atol)
return output_phi
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)
def load_inputs(self, in_dir):
# Bed
B = firedrake.Function(self.V_cg)
firedrake.File(in_dir + "B.pvd") >> B
# Ice thickness
H = firedrake.Function(self.V_cg)
firedrake.File(in_dir + "H.pvd") >> H
# Melt
m = firedrake.Function(self.V_cg)
firedrake.File(in_dir + "m.pvd") >> m
# Sliding speed
u_b = firedrake.Function(self.V_cg)
firedrake.File(in_dir + "u_b.pvd") >> u_b
# Potential at 0 pressure
phi_m = firedrake.Function(self.V_cg)
firedrake.File(in_dir + "phi_m.pvd") >> phi_m
# Potential at overburden pressure
phi_0 = firedrake.Function(self.V_cg)
firedrake.File(in_dir + "phi_0.pvd") >> phi_0
# Ice overburden pressure
p_i = firedrake.Function(self.V_cg)
firedrake.File(in_dir + "p_i.pvd") >> p_i
self.model_inputs["B"] = B
self.model_inputs["H"] = H
self.model_inputs["m"] = m
self.model_inputs["u_b"] = u_b
self.model_inputs["phi_m"] = phi_m
self.model_inputs["phi_0"] = phi_0
self.model_inputs["p_i"] = p_i
def write_outputs(self,
headers: bool,
checkpoint: bool = True,
vtk: bool = False,
plots: bool = False):
"""Write all outputs.
This creates or appends the CSV report,
writes the latest solution, and plots (in 1D/2D case).
Redefine this to control outputs.
Args:
write_headers (bool): Write header line to report if True.
You may want to set this to False, for example, if the
header has already been written.
checkpoint (bool): Write checkpoint if True.
vtk (bool): Write solution to VTK if True.
plots (bool): Write plots if True.
"""
self = self.postprocess()
sapphire.output.report(sim=self, write_header=headers)
if checkpoint:
self.write_checkpoint()
if vtk:
if self.vtk_solution_file is None:
vtk_solution_filepath = self.output_directory_path.joinpath(
"solution").with_suffix(".pvd")
self.vtk_solution_file = fe.File(str(vtk_solution_filepath))
sapphire.output.write_solution_to_vtk(sim=self,
file=self.vtk_solution_file)
if plots:
if self.mesh.geometric_dimension() < 3:
sapphire.output.writeplots(
**self.kwargs_for_writeplots(),
time=self.time.__float__(),
time_index=self.state["index"],
outdir_path=self.output_directory_path)
elif self.mesh.geometric_dimension() == 3:
# This could be done with VTK and PyVista, but VTK can be a
# difficult dependency. It may be best to run a separate
# program for generating 3D plots from the solution files.
raise NotImplementedError()
def mh_cb(mh_r):
fd.File("output/fine_init.pvd").write(mh_r[-1].coordinates)
fd.File("output/coarse_init.pvd").write(mh_r[0].coordinates)
# sys.exit()
d = distance_function(mh_r[0])
mu = 0.01 / (d + 0.01)
extension[0] = fs.ElasticityForm(mu=mu)
if args.cr > 0:
mu_cr = args.cr * mu
extension[0] = fs.CauchyRiemannAugmentation(extension[0], mu=mu_cr)
if args.htwo > 0:
mu_c1 = fd.Constant(args.htwo)
extension[0] = C1Regulariser(extension[0], mu=mu_c1)
if args.surf:
Q[0] = fs.ScalarFeMultiGridControlSpace(mh_r,
extension[0],
order=args.order,
fixed_bids=fixed_bids)
else:
Q[0] = fs.FeMultiGridControlSpace(mh_r, order=args.order)
return Q[0].mh_m
def test_read_and_write_segy():
vp_name = "velocity_models/test"
segy_file = vp_name + ".segy"
hdf5_file = vp_name + ".hdf5"
mesh = fire.UnitSquareMesh(10, 10)
mesh.coordinates.dat.data[:, 0] *= -1
V = fire.FunctionSpace(mesh, 'CG', 3)
x, y = fire.SpatialCoordinate(mesh)
r = 0.2
xc = -0.5
yc = 0.5
vp = fire.Function(V)
c = fire.conditional((x - xc)**2 + (y - yc)**2 < r**2, 3.0, 1.5)
vp.interpolate(c)
xi, yi, zi = spyro.io.write_function_to_grid(vp, V, 10.0 / 1000.0)
spyro.io.create_segy(zi, segy_file)
write_velocity_model(segy_file, vp_name)
model = {}
model["opts"] = {
"method": "CG", # either CG or KMV
"quadrature": "CG", # Equi or KMV
"degree": 3, # p order
"dimension": 2, # dimension
}
model["mesh"] = {
"Lz": 1.0, # depth in km - always positive
"Lx": 1.0, # width in km - always positive
"Ly": 0.0, # thickness in km - always positive
"meshfile": None,
"initmodel": None,
"truemodel": hdf5_file,
}
model["BCs"] = {
"status": False,
}
vp_read = spyro.io.interpolate(model, mesh, V, guess=False)
fire.File("velocity_models/test.pvd").write(vp_read)
value_at_center = vp_read.at(xc, yc)
test1 = math.isclose(value_at_center, 3.0)
value_outside_circle = vp_read.at(xc + r + 0.1, yc)
test2 = math.isclose(value_outside_circle, 1.5)
assert all([test1, test2])
def writereferenceresult(filename, mesh, icemodel, upc):
assert filename.split('.')[-1] == 'pvd'
variables = 'u,p,c,tau,nu,phydrostatic,jweight,velocitySIA'
if mesh.comm.size > 1:
variables += ',rank'
fd.PETSc.Sys.Print('writing variables (%s) to output file %s ... ' \
% (variables,filename))
u, p, c = upc.split()
u.rename('velocity')
p.rename('pressure')
c.rename('displacement')
tau, nu = stresses(mesh, icemodel, u)
ph = phydrostatic(mesh)
jw = jweight(mesh, icemodel, c)
velocitySIA = siahorizontalvelocity(mesh)
if mesh.comm.size > 1:
# integer-valued element-wise process rank
rank = fd.Function(fd.FunctionSpace(mesh, 'DG', 0))
rank.dat.data[:] = mesh.comm.rank
rank.rename('rank')
fd.File(filename).write(u, p, c, tau, nu, ph, jw, velocitySIA, rank)
else:
fd.File(filename).write(u, p, c, tau, nu, ph, jw, velocitySIA)
return 0
def write_outputs(self, write_headers, plotvars=None):
self.output_directory_path.mkdir(parents=True, exist_ok=True)
if self.solution_file is None:
solution_filepath = self.output_directory_path.joinpath(
"solution").with_suffix(".pvd")
self.solution_file = fe.File(str(solution_filepath))
self = self.postprocess()
sapphire.output.report(sim=self, write_header=write_headers)
sapphire.output.write_solution(sim=self, file=self.solution_file)
sapphire.output.plot(sim=self, plotvars=plotvars)
def writesolutiongeometry(filename, refmesh, mzfine, upc):
# get fields on reference mesh
u, p, c = upc.split()
# compute h on base mesh as updated surface elevation
# h(x,y) = lambda(x,y) + c(x,y,lambda(x,y))
lambase = surfaceelevation(refmesh) # bounded below by Href; space Q1base
cbase, Q1base = _surfacevalue(refmesh, c)
hbase0 = fd.Function(Q1base).interpolate(lambase + cbase)
hbase = fd.Function(Q1base)
hbase.interpolate(fd.conditional(hbase0 > 0.0, hbase0, 0.0))
# duplicate fine mesh and extend h onto it
mesh = extrudedmesh(refmesh._base_mesh,
mzfine,
refine=-1,
temporary_height=1.0)
h = extend(mesh, hbase)
# change mesh coordinate to linear times h
Vcoord = mesh.coordinates.function_space()
if mesh._base_mesh.cell_dimension() == 1:
x, z = fd.SpatialCoordinate(mesh)
Xnew = fd.Function(Vcoord).interpolate(fd.as_vector([x, h * z]))
elif mesh._base_mesh.cell_dimension() == 2:
x, y, z = fd.SpatialCoordinate(mesh)
Xnew = fd.Function(Vcoord).interpolate(fd.as_vector([x, y, h * z]))
else:
raise ValueError('applies only to 2D and 3D extruded meshes')
mesh.coordinates.assign(Xnew)
# interpolate velocity u and pressure p from refmesh onto mesh and write
Vu, Vp, _ = vectorspaces(mesh)
unew = fd.Function(Vu)
pnew = fd.Function(Vp)
unew.rename('velocity')
pnew.rename('pressure')
# note f.at() searches for element to evaluate (thanks L Mitchell)
print(Xnew.dat.data_ro) # FIXME shows inadmissible z: too high
unew.dat.data[:] = u.at(Xnew.dat.data_ro)
pnew.dat.data[:] = p.at(Xnew.dat.data_ro)
fd.File(filename).write(unew, pnew)
return 0
def run_solver(r):
mesh = fd.UnitSquareMesh(2**r, 2**r)
P2 = fd.VectorElement("CG", mesh.ufl_cell(), 1)
P1 = fd.FiniteElement("CG", mesh.ufl_cell(), 1)
TH = P2 * P1
W = fd.FunctionSpace(mesh, TH)
(v, q) = fd.TestFunctions(W)
# Stokes 1
w_sol1 = fd.Function(W)
nu = fd.Constant(0.05)
F = NavierStokesBrinkmannForm(W, w_sol1, nu, beta_gls=2.0)
from firedrake import sin, grad, pi, sym, div, inner
x, y = fd.SpatialCoordinate(mesh)
u_mms = fd.as_vector(
[sin(2.0 * pi * x) * sin(pi * y),
sin(pi * x) * sin(2.0 * pi * y)])
p_mms = -0.5 * (u_mms[0]**2 + u_mms[1]**2)
f_mms_u = (grad(u_mms) * u_mms + grad(p_mms) -
2.0 * nu * div(sym(grad(u_mms))))
f_mms_p = div(u_mms)
F += -inner(f_mms_u, v) * dx - f_mms_p * q * dx
bc1 = fd.DirichletBC(W.sub(0), u_mms, "on_boundary")
bc2 = fd.DirichletBC(W.sub(1), p_mms, "on_boundary")
solver_parameters = {"ksp_max_it": 200}
problem1 = fd.NonlinearVariationalProblem(F, w_sol1, bcs=[bc1, bc2])
solver1 = NavierStokesBrinkmannSolver(
problem1,
options_prefix="navier_stokes",
solver_parameters=solver_parameters,
)
solver1.solve()
u_sol, _ = w_sol1.split()
fd.File("test_u_sol.pvd").write(u_sol)
u_mms_func = fd.interpolate(u_mms, W.sub(0))
error = fd.errornorm(u_sol, u_mms_func)
print(f"Error: {error}")
return error
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
# container for functional value
self.J = 0
# target solution, which also specifies rhs and DirBC
mesh_m = self.Q.mesh_m
x, y = fd.SpatialCoordinate(mesh_m)
sin = fd.sin
cos = fd.cos
pi = fd.pi
self.u_t = lambda t: sin(pi * x) * sin(pi * y) * cos(t)
self.f = lambda t: sin(pi * x) * sin(pi * y) * (2 * pi**2 * cos(t) -
sin(t))
# perturbed initial guess to be fixed by shape optimization
V = fd.FunctionSpace(mesh_m, "CG", 1)
self.u0 = fd.Function(V)
perturbation = 0.25 * sin(x * pi) * sin(y * pi)**2
self.u0.interpolate(sin(pi * x * (1 + perturbation)) * sin(pi * y))
# define self.cb, which is always called after self.solvePDE
self.File = fd.File("u0.pvd")
self.cb = lambda: self.File.write(self.u0)
# heat equation discretized with implicit Euler
self.u = fd.Function(V)
self.u_old = fd.Function(V) # solution at previous time
self.bcs = fd.DirichletBC(V, 0, "on_boundary")
self.dx = fd.dx(metadata={"quadrature_degree": 1})
self.dt = 0.125
v = fd.TestFunction(V)
self.F = lambda t, u, u_old: fd.inner((u-u_old)/self.dt, v)*self.dx \
+ fd.inner(fd.grad(u), fd.grad(v))*self.dx \
- fd.inner(self.f(t+self.dt), v)*self.dx
def test_cone_cg_2D():
mesh = fd.UnitSquareMesh(100, 100)
V = fd.FunctionSpace(mesh, "CG", 1)
radius = 0.2
x, y = fd.SpatialCoordinate(mesh)
x_shift = 0.5
phi_init = ((x - x_shift) * (x - x_shift) + (y - 0.5) * (y - 0.5) -
radius**2)
phi0 = fd.Function(V).interpolate(phi_init)
phi_pvd = fd.File("phi_reinit.pvd")
reinit_solver = ReinitSolverCG(V)
phin = reinit_solver.solve(phi0, iters=10)
phi_pvd.write(phin)
phi_solution = fd.interpolate(
sqrt((x - x_shift) * (x - x_shift) + (y - 0.5) * (y - 0.5)) - radius,
V,
)
error_numeri = fd.errornorm(phin, phi_solution)
print(f"error: {error_numeri}")
assert error_numeri < 1e-4
def __init__(self, model_inputs, in_dir=None):
r"""Initialize model inputs and
Parameters
----------
model_inputs: model input object
"""
self.mesh = model_inputs["mesh"]
self.V_cg = firedrake.FunctionSpace(self.mesh, "CG", 2)
self.model_inputs = model_inputs
# If an input directory is specified, load model inputs from there.
# Otherwise use the specified model inputs dictionary.
if in_dir:
model_inputs = self.load_inputs(in_dir)
# Ice thickness
self.H = self.model_inputs["H"]
# Bed elevation
self.B = self.model_inputs["B"]
# Basal sliding speed
self.u_b = self.model_inputs["u_b"]
# Melt rate
self.m = self.model_inputs["m"]
# Cavity gap height
self.h = self.model_inputs["h_init"]
# Potential
self.phi_prev = self.model_inputs["phi_init"]
# Potential at 0 pressure
self.phi_m = self.model_inputs["phi_m"]
# Ice overburden pressure
self.p_i = self.model_inputs["p_i"]
# Potential at overburden pressure
self.phi_0 = self.model_inputs["phi_0"]
# Dirichlet boundary conditions
self.d_bcs = self.model_inputs["d_bcs"]
# Channel areas
self.S = self.model_inputs["S_init"]
# Drainage width
self.width = self.model_inputs["width"]
# Output directory
self.out_dir = self.model_inputs["out_dir"]
# If there is a dictionary of physical constants specified, use it.
# Otherwise use the defaults.
if "constants" in self.model_inputs:
self.pcs = self.model_inputs["constants"]
else:
self.pcs = pcs
self.n_bcs = []
if "n_bcs" in self.model_inputs:
self.n_bcs = model_inputs["n_bcs"]
### Create some fields
self.V_cg = firedrake.FunctionSpace(self.mesh, "CG", 1)
# Potential
self.phi = firedrake.Function(self.V_cg)
# Effective pressure
self.N = firedrake.Function(self.V_cg)
# Stores the value of S**alpha.
self.S_alpha = firedrake.Function(self.V_cg)
self.update_S_alpha()
# Water pressure
self.p_w = firedrake.Function(self.V_cg)
# Pressure as a fraction of overburden
self.pfo = firedrake.Function(self.V_cg)
# Current time
self.t = 0.0
### Output files
self.S_out = firedrake.File(self.out_dir + "S.pvd")
self.h_out = firedrake.File(self.out_dir + "h.pvd")
self.phi_out = firedrake.File(self.out_dir + "phi.pvd")
self.pfo_out = firedrake.File(self.out_dir + "pfo.pvd")
### Create the solver objects
# Potential solver
self.phi_solver = PhiSolver(self)
# Gap height solver
self.hs_solver = HSSolver(self)
def compliance():
parser = argparse.ArgumentParser(description="Compliance problem with MMA")
parser.add_argument(
"--nref",
action="store",
dest="nref",
type=int,
help="Number of mesh refinements",
default=2,
)
parser.add_argument(
"--uniform",
action="store",
dest="uniform",
type=int,
help="Use uniform mesh",
default=0,
)
parser.add_argument(
"--inner_product",
action="store",
dest="inner_product",
type=str,
help="Inner product, euclidean or L2",
default="L2",
)
parser.add_argument(
"--output_dir",
action="store",
dest="output_dir",
type=str,
help="Directory for all the output",
default="./",
)
args = parser.parse_args()
nref = args.nref
inner_product = args.inner_product
output_dir = args.output_dir
assert inner_product == "L2" or inner_product == "euclidean"
mesh = fd.Mesh("./beam_uniform.msh")
#mh = fd.MeshHierarchy(mesh, 2)
#mesh = mh[-1]
if nref > 0:
mh = fd.MeshHierarchy(mesh, nref)
mesh = mh[-1]
elif nref < 0:
raise RuntimeError("Non valid mesh argument")
V = fd.VectorFunctionSpace(mesh, "CG", 1)
u, v = fd.TrialFunction(V), fd.TestFunction(V)
# Elasticity parameters
E, nu = 1e0, 0.3
mu, lmbda = fd.Constant(E / (2 * (1 + nu))), fd.Constant(
E * nu / ((1 + nu) * (1 - 2 * nu))
)
# Helmholtz solver
RHO = fd.FunctionSpace(mesh, "CG", 1)
rho = fd.interpolate(fd.Constant(0.1), RHO)
af, b = fd.TrialFunction(RHO), fd.TestFunction(RHO)
#filter_radius = fd.Constant(0.2)
#x, y = fd.SpatialCoordinate(mesh)
#x_ = fd.interpolate(x, RHO)
#y_ = fd.interpolate(y, RHO)
#aH = filter_radius * inner(grad(af), grad(b)) * dx + af * b * dx
#LH = rho * b * dx
rhof = fd.Function(RHO)
solver_params = {
"ksp_type": "preonly",
"pc_type": "lu",
"pc_factor_mat_solver_type": "mumps",
"mat_mumps_icntl_14": 200,
"mat_mumps_icntl_24": 1,
}
#fd.solve(aH == LH, rhof, solver_parameters=solver_params)
rhof.assign(rho)
rhofControl = fda.Control(rhof)
eps = fd.Constant(1e-5)
p = fd.Constant(3.0)
def simp(rho):
return eps + (fd.Constant(1.0) - eps) * rho ** p
def epsilon(v):
return sym(nabla_grad(v))
def sigma(v):
return 2.0 * mu * epsilon(v) + lmbda * tr(epsilon(v)) * Identity(2)
DIRICHLET = 3
NEUMANN = 4
a = inner(simp(rhof) * sigma(u), epsilon(v)) * dx
load = fd.Constant((0.0, -1.0))
L = inner(load, v) * ds(NEUMANN)
u_sol = fd.Function(V)
bcs = fd.DirichletBC(V, fd.Constant((0.0, 0.0)), DIRICHLET)
fd.solve(a == L, u_sol, bcs=bcs, solver_parameters=solver_params)
c = fda.Control(rho)
J = fd.assemble(fd.Constant(1e-4) * inner(u_sol, load) * ds(NEUMANN))
Vol = fd.assemble(rhof * dx)
VolControl = fda.Control(Vol)
with fda.stop_annotating():
Vlimit = fd.assemble(fd.Constant(1.0) * dx(domain=mesh)) * 0.5
rho_viz_f = fd.Function(RHO, name="rho")
plot_file = f"{output_dir}/design_{inner_product}.pvd"
controls_f = fd.File(plot_file)
def deriv_cb(j, dj, rho):
with fda.stop_annotating():
rho_viz_f.assign(rhofControl.tape_value())
controls_f.write(rho_viz_f)
Jhat = fda.ReducedFunctional(J, c, derivative_cb_post=deriv_cb)
Volhat = fda.ReducedFunctional(Vol, c)
class VolumeConstraint(fda.InequalityConstraint):
def __init__(self, Vhat, Vlimit, VolControl):
self.Vhat = Vhat
self.Vlimit = float(Vlimit)
self.VolControl = VolControl
def function(self, m):
# Compute the integral of the control over the domain
integral = self.VolControl.tape_value()
with fda.stop_annotating():
value = -integral / self.Vlimit + 1.0
return [value]
def jacobian(self, m):
with fda.stop_annotating():
gradients = self.Vhat.derivative()
with gradients.dat.vec as v:
v.scale(-1.0 / self.Vlimit)
return [gradients]
def output_workspace(self):
return [0.0]
def length(self):
"""Return the number of components in the constraint vector (here, one)."""
return 1
lb = 1e-5
ub = 1.0
problem = fda.MinimizationProblem(
Jhat,
bounds=(lb, ub),
constraints=[VolumeConstraint(Volhat, Vlimit, VolControl)],
)
parameters_mma = {
"move": 0.2,
"maximum_iterations": 200,
"m": 1,
"IP": 0,
"tol": 1e-6,
"accepted_tol": 1e-4,
"norm": inner_product,
#"norm": "euclidean",
"gcmma": False,
}
solver = MMASolver(problem, parameters=parameters_mma)
rho_opt = solver.solve()
with open(f"{output_dir}/finished_{inner_product}.txt", "w") as f:
f.write("Done")
def heat_exchanger_optimization(mu=0.03, n_iters=1000):
output_dir = "2D/"
path = os.path.abspath(__file__)
dir_path = os.path.dirname(path)
mesh = fd.Mesh(f"{dir_path}/2D_mesh.msh")
# Perturb the mesh coordinates. Necessary to calculate shape derivatives
S = fd.VectorFunctionSpace(mesh, "CG", 1)
s = fd.Function(S, name="deform")
mesh.coordinates.assign(mesh.coordinates + s)
# Initial level set function
x, y = fd.SpatialCoordinate(mesh)
PHI = fd.FunctionSpace(mesh, "CG", 1)
phi_expr = sin(y * pi / 0.2) * cos(x * pi / 0.2) - fd.Constant(0.8)
# Avoid recording the operation interpolate into the tape.
# Otherwise, the shape derivatives will not be correct
with fda.stop_annotating():
phi = fd.interpolate(phi_expr, PHI)
phi.rename("LevelSet")
fd.File(output_dir + "phi_initial.pvd").write(phi)
# Physics
mu = fd.Constant(mu) # viscosity
alphamin = 1e-12
alphamax = 2.5 / (2e-4)
parameters = {
"mat_type": "aij",
"ksp_type": "preonly",
"ksp_converged_reason": None,
"pc_type": "lu",
"pc_factor_mat_solver_type": "mumps",
}
stokes_parameters = parameters
temperature_parameters = parameters
u_inflow = 2e-3
tin1 = fd.Constant(10.0)
tin2 = fd.Constant(100.0)
P2 = fd.VectorElement("CG", mesh.ufl_cell(), 2)
P1 = fd.FiniteElement("CG", mesh.ufl_cell(), 1)
TH = P2 * P1
W = fd.FunctionSpace(mesh, TH)
U = fd.TrialFunction(W)
u, p = fd.split(U)
V = fd.TestFunction(W)
v, q = fd.split(V)
epsilon = fd.Constant(10000.0)
def hs(phi, epsilon):
return fd.Constant(alphamax) * fd.Constant(1.0) / (
fd.Constant(1.0) + exp(-epsilon * phi)) + fd.Constant(alphamin)
def stokes(phi, BLOCK_INLET_MOUTH, BLOCK_OUTLET_MOUTH):
a_fluid = mu * inner(grad(u), grad(v)) - div(v) * p - q * div(u)
darcy_term = inner(u, v)
return (a_fluid * dx + hs(phi, epsilon) * darcy_term * dx(0) +
alphamax * darcy_term *
(dx(BLOCK_INLET_MOUTH) + dx(BLOCK_OUTLET_MOUTH)))
# Dirichlet boundary conditions
inflow1 = fd.as_vector([
u_inflow * sin(
((y - (line_sep -
(dist_center + inlet_width))) * pi) / inlet_width),
0.0,
])
inflow2 = fd.as_vector([
u_inflow * sin(((y - (line_sep + dist_center)) * pi) / inlet_width),
0.0,
])
noslip = fd.Constant((0.0, 0.0))
# Stokes 1
bcs1_1 = fd.DirichletBC(W.sub(0), noslip, WALLS)
bcs1_2 = fd.DirichletBC(W.sub(0), inflow1, INLET1)
bcs1_3 = fd.DirichletBC(W.sub(1), fd.Constant(0.0), OUTLET1)
bcs1_4 = fd.DirichletBC(W.sub(0), noslip, INLET2)
bcs1_5 = fd.DirichletBC(W.sub(0), noslip, OUTLET2)
bcs1 = [bcs1_1, bcs1_2, bcs1_3, bcs1_4, bcs1_5]
# Stokes 2
bcs2_1 = fd.DirichletBC(W.sub(0), noslip, WALLS)
bcs2_2 = fd.DirichletBC(W.sub(0), inflow2, INLET2)
bcs2_3 = fd.DirichletBC(W.sub(1), fd.Constant(0.0), OUTLET2)
bcs2_4 = fd.DirichletBC(W.sub(0), noslip, INLET1)
bcs2_5 = fd.DirichletBC(W.sub(0), noslip, OUTLET1)
bcs2 = [bcs2_1, bcs2_2, bcs2_3, bcs2_4, bcs2_5]
# Forward problems
U1, U2 = fd.Function(W), fd.Function(W)
L = inner(fd.Constant((0.0, 0.0, 0.0)), V) * dx
problem = fd.LinearVariationalProblem(stokes(-phi, INMOUTH2, OUTMOUTH2),
L,
U1,
bcs=bcs1)
solver_stokes1 = fd.LinearVariationalSolver(
problem,
solver_parameters=stokes_parameters,
options_prefix="stokes_1")
solver_stokes1.solve()
problem = fd.LinearVariationalProblem(stokes(phi, INMOUTH1, OUTMOUTH1),
L,
U2,
bcs=bcs2)
solver_stokes2 = fd.LinearVariationalSolver(
problem,
solver_parameters=stokes_parameters,
options_prefix="stokes_2")
solver_stokes2.solve()
# Convection difussion equation
ks = fd.Constant(1e0)
cp_value = 5.0e5
cp = fd.Constant(cp_value)
T = fd.FunctionSpace(mesh, "DG", 1)
t = fd.Function(T, name="Temperature")
w = fd.TestFunction(T)
# Mesh-related functions
n = fd.FacetNormal(mesh)
h = fd.CellDiameter(mesh)
u1, p1 = fd.split(U1)
u2, p2 = fd.split(U2)
def upwind(u):
return (dot(u, n) + abs(dot(u, n))) / 2.0
u1n = upwind(u1)
u2n = upwind(u2)
# Penalty term
alpha = fd.Constant(500.0)
# Bilinear form
a_int = dot(grad(w), ks * grad(t) - cp * (u1 + u2) * t) * dx
a_fac = (fd.Constant(-1.0) * ks * dot(avg(grad(w)), jump(t, n)) * dS +
fd.Constant(-1.0) * ks * dot(jump(w, n), avg(grad(t))) * dS +
ks("+") *
(alpha("+") / avg(h)) * dot(jump(w, n), jump(t, n)) * dS)
a_vel = (dot(
jump(w),
cp * (u1n("+") + u2n("+")) * t("+") - cp *
(u1n("-") + u2n("-")) * t("-"),
) * dS + dot(w,
cp * (u1n + u2n) * t) * ds)
a_bnd = (dot(w,
cp * dot(u1 + u2, n) * t) * (ds(INLET1) + ds(INLET2)) +
w * t * (ds(INLET1) + ds(INLET2)) - w * tin1 * ds(INLET1) -
w * tin2 * ds(INLET2) + alpha / h * ks * w * t *
(ds(INLET1) + ds(INLET2)) - ks * dot(grad(w), t * n) *
(ds(INLET1) + ds(INLET2)) - ks * dot(grad(t), w * n) *
(ds(INLET1) + ds(INLET2)))
aT = a_int + a_fac + a_vel + a_bnd
LT_bnd = (alpha / h * ks * tin1 * w * ds(INLET1) +
alpha / h * ks * tin2 * w * ds(INLET2) -
tin1 * ks * dot(grad(w), n) * ds(INLET1) -
tin2 * ks * dot(grad(w), n) * ds(INLET2))
problem = fd.LinearVariationalProblem(derivative(aT, t), LT_bnd, t)
solver_temp = fd.LinearVariationalSolver(
problem,
solver_parameters=temperature_parameters,
options_prefix="temperature",
)
solver_temp.solve()
# fd.solve(eT == 0, t, solver_parameters=temperature_parameters)
# Cost function: Flux at the cold outlet
scale_factor = 4e-4
Jform = fd.assemble(
fd.Constant(-scale_factor * cp_value) * inner(t * u1, n) * ds(OUTLET1))
# Constraints: Pressure drop on each fluid
power_drop = 1e-2
Power1 = fd.assemble(p1 / power_drop * ds(INLET1))
Power2 = fd.assemble(p2 / power_drop * ds(INLET2))
phi_pvd = fd.File("phi_evolution.pvd")
def deriv_cb(phi):
with stop_annotating():
phi_pvd.write(phi[0])
c = fda.Control(s)
# Reduced Functionals
Jhat = LevelSetFunctional(Jform, c, phi, derivative_cb_pre=deriv_cb)
P1hat = LevelSetFunctional(Power1, c, phi)
P1control = fda.Control(Power1)
P2hat = LevelSetFunctional(Power2, c, phi)
P2control = fda.Control(Power2)
Jhat_v = Jhat(phi)
print("Initial cost function value {:.5f}".format(Jhat_v), flush=True)
print("Power drop 1 {:.5f}".format(Power1), flush=True)
print("Power drop 2 {:.5f}".format(Power2), flush=True)
beta_param = 0.08
# Regularize the shape derivatives only in the domain marked with 0
reg_solver = RegularizationSolver(S,
mesh,
beta=beta_param,
gamma=1e5,
dx=dx,
design_domain=0)
tol = 1e-5
dt = 0.05
params = {
"alphaC": 1.0,
"debug": 5,
"alphaJ": 1.0,
"dt": dt,
"K": 1e-3,
"maxit": n_iters,
"maxtrials": 5,
"itnormalisation": 10,
"tol_merit":
5e-3, # new merit can be within 0.5% of the previous merit
# "normalize_tol" : -1,
"tol": tol,
}
solver_parameters = {
"reinit_solver": {
"h_factor": 2.0,
}
}
# Optimization problem
problem = InfDimProblem(
Jhat,
reg_solver,
ineqconstraints=[
Constraint(P1hat, 1.0, P1control),
Constraint(P2hat, 1.0, P2control),
],
solver_parameters=solver_parameters,
)
results = nlspace_solve(problem, params)
return results
"Line Search": {
"Descent Method": {
"Type": "Quasi-Newton Step"
}
}
},
"Status Test": {
"Gradient Tolerance": 1e-8,
"Step Tolerance": 1e-8,
"Iteration Limit": args.maxiter,
},
}
outdir = "./output/annulus/base-%s-cr-%s-weighted-%s-rstar-%.2f/" % (
args.base_inner, args.alpha, args.weighted, args.rstar)
out = fd.File(outdir + "domain.pvd")
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q)
solver = ROL.OptimizationSolver(problem, params)
boundary_derivatives = []
gradient_norms = []
objective_values = []
def cb(*args):
out.write(mesh_m.coordinates)
gradient_norms.append(solver.getAlgorithmState().gnorm)
objective_values.append(solver.getAlgorithmState().value)
boundary_derivatives.append(fd.assemble(fd.inner(expr, expr) * fd.ds)**0.5)
#
# Now we're ready to solve the variational problem. We define `w` to be a
# function to hold the solution on the mixed space.
w = fd.Function(W)
# solve
fd.solve(a == L, w, bcs=[bc0, bc1])
# %%
# Post-process and plot interesting fields
print('* post-process')
# collect fields
vel, press = w.split()
press.rename('pressure')
# Projecting velocity field to a continuous space (visualization purporse)
P1 = fd.VectorFunctionSpace(mesh, "CG", 1)
vel_proj = fd.project(vel, P1)
vel_proj.rename('velocity_proj')
# project permeability Kxx
kxx = fd.Function(DG)
kxx.rename('Kxx')
kxx.dat.data[...] = 1 / Kinv.dat.data[:, 0, 0]
# print results
fd.File("plots/darcy_rt.pvd").write(vel_proj, press, kxx)
print('* normal termination')
def test_levelset(dim, inner_t, controlspace_t, use_extension, pytestconfig):
verbose = pytestconfig.getoption("verbose")
""" Test template for fsz.LevelsetFunctional."""
clscale = 0.1 if dim == 2 else 0.2
# make the mesh a bit coarser if we are using a multigrid control space as
# we are refining anyway
if controlspace_t == fs.FeMultiGridControlSpace:
clscale *= 4
if dim == 2:
mesh = fs.DiskMesh(clscale)
elif dim == 3:
mesh = fs.SphereMesh(clscale)
else:
raise NotImplementedError
if controlspace_t == fs.BsplineControlSpace:
if dim == 2:
bbox = [(-2, 2), (-2, 2)]
orders = [2, 2]
levels = [4, 4]
else:
bbox = [(-3, 3), (-3, 3), (-3, 3)]
orders = [2, 2, 2]
levels = [3, 3, 3]
Q = fs.BsplineControlSpace(mesh, bbox, orders, levels)
elif controlspace_t == fs.FeMultiGridControlSpace:
Q = fs.FeMultiGridControlSpace(mesh, refinements=1, order=2)
else:
Q = controlspace_t(mesh)
inner = inner_t(Q)
# if running with -v or --verbose, then export the shapes
if verbose:
out = fd.File("domain.pvd")
def cb(*args):
out.write(Q.mesh_m.coordinates)
cb()
else:
cb = None
# levelset test case
if dim == 2:
(x, y) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(1.3 * y, 2) - 1.
elif dim == 3:
(x, y, z) = fd.SpatialCoordinate(Q.mesh_m)
f = (pow(x, 2)) + pow(0.8 * y, 2) + pow(1.3 * z, 2) - 1.
else:
raise NotImplementedError
J = fsz.LevelsetFunctional(f, Q, cb=cb, scale=0.1)
if use_extension == "w_ext":
ext = fs.ElasticityExtension(Q.V_r)
if use_extension == "w_ext_fixed_dim":
ext = fs.ElasticityExtension(Q.V_r, fixed_dims=[0])
else:
ext = None
q = fs.ControlVector(Q, inner, boundary_extension=ext)
# these tolerances are not very stringent, but solutions are correct with
# tighter tolerances, the combination
# FeMultiGridControlSpace-ElasticityInnerProduct fails because the mesh
# self-intersects (one should probably be more careful with the opt params)
grad_tol = 1e-1
itlim = 15
itlimsub = 15
# Volume constraint
vol = fsz.LevelsetFunctional(fd.Constant(1.0), Q, scale=1)
initial_vol = vol.value(q, None)
econ = fs.EqualityConstraint([vol], target_value=[initial_vol])
emul = ROL.StdVector(1)
# ROL parameters
params_dict = {
'Step': {
'Type': 'Augmented Lagrangian',
'Augmented Lagrangian': {
'Subproblem Step Type': 'Line Search',
'Penalty Parameter Growth Factor': 1.05,
'Print Intermediate Optimization History': True,
'Subproblem Iteration Limit': itlimsub
},
'Line Search': {
'Descent Method': {
'Type': 'Quasi-Newton Step'
}
},
},
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 50
}
},
'Status Test': {
'Gradient Tolerance': grad_tol,
'Step Tolerance': 1e-10,
'Iteration Limit': itlim
}
}
params = ROL.ParameterList(params_dict, "Parameters")
problem = ROL.OptimizationProblem(J, q, econ=econ, emul=emul)
solver = ROL.OptimizationSolver(problem, params)
solver.solve()
# verify that the norm of the gradient at optimum is small enough
# and that the volume has not changed too much
state = solver.getAlgorithmState()
assert (state.gnorm < grad_tol)
assert abs(vol.value(q, None) - initial_vol) < 1e-2
bexpr = 2000.0 * (1 - fd.sqrt(minarg) / rl)
b.interpolate(bexpr)
alpha = args.alpha
theta = 0.5
PD = asQ.paradiag(form_function=form_function,
form_mass=form_mass,
W=W,
w0=w0,
dt=dt,
theta=theta,
alpha=alpha,
M=M,
solver_parameters=solver_parameters_diag,
circ="quasi")
PD.solve()
# write output:
file0 = fd.File("output/output1.pvd")
pun = fd.Function(W, name="pun")
puns = pun.split()
for i in range(M):
walls = PD.w_all.split()[2 * i:2 * i + 2]
for k in range(2):
puns[k].assign(walls[k])
u_out = puns[0]
h_out = puns[1]
file0.write(u_out, h_out)
# Res.
R = F_p + F_s
prob = fd.NonlinearVariationalProblem(R, U, bcs=[bc0, bc1, bc3])
solver2ph = fd.NonlinearVariationalSolver(prob)
# %%
# 4) Solve problem
# initialize variables
xv, xp, xs = U.split()
vel = fd.project(u0, P1)
xp.rename('pressure')
xs.rename('saturation')
vel.rename('velocity')
outfile = fd.File(oFile)
it = 0
t = 0.0
while t < sim_time:
t += dt
print("*iteration= {:3d}, dtime= {:8.6f}, time={:8.6f}".format(it, dt, t))
solver2ph.solve()
# update solution
U0.assign(U)
# 5) print results
if it % freq_res == 0 or t == sim_time:
vel.assign(fd.project(U.sub(0), P1))
xp.assign(U.sub(1))
fd.Constant(0.))
# shock terms
# F1 += vshock*fd.dot(fd.grad(w), fd.grad(c_mid))*fd.dx
F1 += vshock * np.abs(R) * fd.inner(fd.grad(w), fd.grad(c_mid)) * fd.dx
F = F1
prob = fd.NonlinearVariationalProblem(F, c, bcs=t_bc)
transport = fd.NonlinearVariationalSolver(prob)
# %%
# 4) Solve problem
c0.assign(0.)
t = it = 0
outfile = fd.File("plots/adr_supg_shock.pvd")
c0.rename("c")
dt = CFL * fd.interpolate(h / vnorm, DG0).dat.data.min()
Dt.assign(dt)
dt0 = dt
Pe = vnorm * h / (2.0 * Diff)
print('Peclet = {}; dt = {}'.format(
fd.interpolate(Pe, DG0).dat.data.mean(), dt))
D = fd.interpolate(vshock * np.abs(R), DG0)
D.rename("visc_shock")
while t < sim_time:
# move next time step
t += np.min([sim_time - t, dt])
shock = fd.interpolate(vshock * np.abs(R), DG0)
shock.rename('vshock')
F = F1
prob = fd.NonlinearVariationalProblem(F, c, bcs=t_bc)
transport = fd.NonlinearVariationalSolver(prob)
# %%
# 4) Solve problem
# -----------------
t = 0.0
it = 0
dt0 = dt
cfl_conditional = fd.conditional(fd.lt(np.abs(vnorm), tol), 1 / tol, h / vnorm)
outfile = fd.File("plots/sb_t_supg.pvd")
sol = fd.Function(W)
c0.assign(0.)
# initialize timestep
while t < sim_time:
# move next time step
print("* iteration= {:4d}, dtime= {:8.6f}, time={:8.6f}".format(it, dt, t))
# SB
idt.assign(1 / dt)
fd.solve(a == L, sol, bcs=bcs)
vel.assign(sol.sub(0))
Pe = vnorm * h / (2.0 * fd.det(Diff))
numCFL = dt / fd.interpolate(cfl_conditional, DG0).dat.data.min()
if equation == "heat":
nu = fd.Constant(0.1) # for heat
M = fd.derivative(fd.inner(u, v) * fd.dx, u)
R = -(fd.inner(fd.grad(u) * u, v) + nu * fd.inner(fd.grad(u), fd.grad(v))) * fd.dx
if equation == "heat":
R = -nu * fd.inner(fd.grad(u), fd.grad(v)) * fd.dx
F = fd.action(M, u_dot) - R
bc = fd.DirichletBC(V, (0.0, 0.0), "on_boundary")
t = 0.0
end = 0.1
tspan = (t, end)
state_out = fd.File("result/state.pvd")
def ts_monitor(ts, steps, time, X):
state_out.write(u, time=time)
problem = firedrake_ts.DAEProblem(F, u, u_dot, tspan, bcs=bc)
solver = firedrake_ts.DAESolver(problem, monitor_callback=ts_monitor)
ts = solver.ts
ts.setTimeStep(0.01)
ts.setExactFinalTime(PETSc.TS.ExactFinalTime.MATCHSTEP)
ts.setSaveTrajectory()
ts.setType(PETSc.TS.Type.THETA)
V = fire.FunctionSpace(mesh, finite_element_space, 1)
bc = fire.DirichletBC(V, fire.Constant(1.0), 1)
u = fire.Function(V)
# Initialize the transport solver
transport = rok.TransportSolver(method=method)
transport.setVelocity(v)
transport.setDiffusion(D)
transport.setSource(q)
transport.setBoundaryConditions([bc])
t = 0.0
step = 0
outfile = fire.File("results_demo-transport/u.pvd")
outfile.write(u)
while step < nsteps:
transport.step(u, dt)
t += dt
step += 1
if step % 1 == 0:
outfile.write(u)
print("t = {:<15.3f} step = {:<15}".format(t, step))
# "snes_monitor": None, "ksp_monitor": None,
}
def solve(self):
super().solve()
self.failed_to_solve = False
u_old = self.solution.copy(deepcopy=True)
try:
fd.solve(self.F == 0,
self.solution,
bcs=self.bcs,
solver_parameters=self.params)
except fd.ConvergenceError:
self.failed_to_solve = True
self.solution.assign(u_old)
if __name__ == "__main__":
mesh = fd.Mesh("pipe.msh")
if mesh.topological_dimension() == 2: # in 2D
viscosity = fd.Constant(1. / 400.)
elif mesh.topological_dimension() == 3: # in 3D
viscosity = fd.Constant(1 / 10.) # simpler problem in 3D
else:
raise NotImplementedError
e = NavierStokesSolver(mesh, viscosity)
e.solve()
print(e.failed_to_solve)
out = fd.File("temp_PDEConstrained_u.pvd")
out.write(e.solution.split()[0])
"pc_sc_eliminate_fields": "0, 1",
"condensed_field": {
"ksp_type": "preonly",
"pc_type": "lu",
"pc_factor_mat_solver_type": "mumps"
}
}
solver = fd.NonlinearVariationalSolver(problem,
solver_parameters=hybrid_solver_params)
# -----------------
wave_speed = fd.conditional(fd.lt(np.abs(vnorm), tol), h / tol, h / vnorm)
# CFL
dt_ = fd.interpolate(wave_speed, DG1).dat.data.min() * cfl
outfile = fd.File(f"plots/adr-hdg-n-{refine}-p-{order}.pvd",
project_output=True)
dt = dt_ # dtime
dtc.assign(dt_)
# %%
# solve problem
# initialize timestep
t = 0.0
it = 0
p = 0
while t < sim_time:
# check dt
dt = np.min([sim_time - t, dt])
import ROL
n = 30
# mesh = fd.UnitSquareMesh(n, n)
mesh = fd.Mesh("UnitSquareCrossed.msh")
mesh = fd.MeshHierarchy(mesh, 1)[-1]
Q = fs.FeMultiGridControlSpace(mesh, refinements=3, order=2)
inner = fs.LaplaceInnerProduct(Q)
mesh_m = Q.mesh_m
V_m = fd.FunctionSpace(mesh_m, "CG", 1)
f_m = fd.Function(V_m)
(x, y) = fd.SpatialCoordinate(mesh_m)
f = (pow(x - 0.5, 2)) + pow(y - 0.5, 2) - 2.
out = fd.File("domain.pvd")
J = fsz.LevelsetFunctional(f, Q, cb=lambda: out.write(mesh_m.coordinates))
q = fs.ControlVector(Q, inner)
params_dict = {
'General': {
'Secant': {
'Type': 'Limited-Memory BFGS',
'Maximum Storage': 5
}
},
'Step': {
'Type': 'Line Search',
'Line Search': {
'Descent Method': {
Q = fs.FeControlSpace(mesh)
inner = fs.LaplaceInnerProduct(Q, fixed_bids=[10, 11, 12])
q = fs.ControlVector(Q, inner)
# setup PDE constraint
if mesh.topological_dimension() == 2: # in 2D
viscosity = fd.Constant(1./400.)
elif mesh.topological_dimension() == 3: # in 3D
viscosity = fd.Constant(1/10.) # simpler problem in 3D
else:
raise NotImplementedError
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