def calc_value_differences(file_path1, file_path2, output_path, func_space,
t_func_space, parameters):
f1 = XDMFFile(file_path1)
f2 = XDMFFile(file_path2)
f_out = XDMFFile(output_path)
value_func1 = Function(func_space)
value_func2 = Function(func_space)
result = Function(t_func_space)
f1.read_checkpoint(value_func1, 'value_func', 0)
f2.read_checkpoint(value_func2, 'value_func', 0)
result.vector()[:] \
= value_func1.vector()[:] - value_func2.vector()[:]
f_out.write_checkpoint(result, 'diff', parameters.T,
XDMFFile.Encoding.HDF5, True)
i = 1
dt = parameters.T / parameters.M
for k in range(parameters.M - 1, -1, -1):
if k % parameters.save_interval != 0:
continue
f1.read_checkpoint(value_func1, 'value_func', i)
f2.read_checkpoint(value_func2, 'value_func', i)
result.vector()[:] \
= value_func1.vector()[:] - value_func2.vector()[:]
f_out.write_checkpoint(result, 'diff', k * dt, XDMFFile.Encoding.HDF5,
True)
i += 1
class SolutionFile(SolutionFile_Base):
# DOLFIN 2018.1.0.dev added (throughout the developement cycle) an optional append
# attribute to XDMFFile.write_checkpoint, which should be set to its non-default value,
# thus breaking backwards compatibility
append_attribute = XDMFFile.write_checkpoint.__doc__.find(
"append: bool") > -1
def __init__(self, directory, filename):
SolutionFile_Base.__init__(self, directory, filename)
self._visualization_file = XDMFFile(self._full_filename + ".xdmf")
self._visualization_file.parameters["flush_output"] = True
self._restart_file = XDMFFile(self._full_filename +
"_checkpoint.xdmf")
self._restart_file.parameters["flush_output"] = True
@staticmethod
def remove_files(directory, filename):
SolutionFile_Base.remove_files(directory, filename)
#
full_filename = os.path.join(str(directory), filename)
if is_io_process() and os.path.exists(full_filename + ".xdmf"):
os.remove(full_filename + ".xdmf")
os.remove(full_filename + ".h5")
os.remove(full_filename + "_checkpoint.xdmf")
os.remove(full_filename + "_checkpoint.h5")
def write(self, function, name, index):
assert index in (self._last_index, self._last_index + 1)
if index == self._last_index + 1: # writing out solutions after time stepping
self._update_function_container(function)
time = float(index)
self._visualization_file.write(self._function_container, time)
bak_log_level = get_log_level()
set_log_level(int(WARNING) + 1) # disable xdmf logs)
if self.append_attribute:
self._restart_file.write_checkpoint(
self._function_container, name, time, append=True)
else:
self._restart_file.write_checkpoint(
self._function_container, name, time)
set_log_level(bak_log_level)
# Once solutions have been written to file, update last written index
self._write_last_index(index)
elif index == self._last_index:
# corner case for problems with two (or more) unknowns which are written separately to file;
# one unknown was written to file, while the other was not: since the problem might be coupled,
# a recomputation of both is required, but there is no need to update storage
pass
else:
raise ValueError("Invalid index")
def read(self, function, name, index):
if index <= self._last_index:
time = float(index)
self._restart_file.read_checkpoint(function, name, index)
self._update_function_container(function)
self._visualization_file.write(self._function_container, time)
else:
raise OSError
class SolutionFileXDMF(SolutionFile_Base):
# DOLFIN 2018.1.0.dev added (throughout the developement cycle) an optional append
# attribute to XDMFFile.write_checkpoint, which should be set to its non-default value,
# thus breaking backwards compatibility
append_attribute = XDMFFile.write_checkpoint.__doc__.find("append: bool") > - 1
def __init__(self, directory, filename):
SolutionFile_Base.__init__(self, directory, filename)
self._visualization_file = XDMFFile(self._full_filename + ".xdmf")
self._visualization_file.parameters["flush_output"] = True
self._restart_file = XDMFFile(self._full_filename + "_checkpoint.xdmf")
self._restart_file.parameters["flush_output"] = True
@staticmethod
def remove_files(directory, filename):
SolutionFile_Base.remove_files(directory, filename)
#
full_filename = os.path.join(str(directory), filename)
def remove_files_task():
if os.path.exists(full_filename + ".xdmf"):
os.remove(full_filename + ".xdmf")
os.remove(full_filename + ".h5")
os.remove(full_filename + "_checkpoint.xdmf")
os.remove(full_filename + "_checkpoint.h5")
parallel_io(remove_files_task)
def write(self, function, name, index):
time = float(index)
# Write visualization file (no append available, will overwrite)
self._update_function_container(function)
self._visualization_file.write(self._function_container, time)
# Write restart file. It might be possible that the solution was written to file in a previous run
# and the execution was interrupted before last written index was updated. In this corner case
# there would be two functions corresponding to the same time, with two consecutive indices.
# For now the inelegant way is to try to read: if that works, assume that we are in the corner case;
# otherwise, we are in the standard case and we should write to file.
try:
self._restart_file.read_checkpoint(self._function_container, name, index)
except RuntimeError:
from dolfin.cpp.log import get_log_level, LogLevel, set_log_level
self._update_function_container(function)
bak_log_level = get_log_level()
set_log_level(int(LogLevel.WARNING) + 1) # disable xdmf logs
if self.append_attribute:
self._restart_file.write_checkpoint(self._function_container, name, time, append=True)
else:
self._restart_file.write_checkpoint(self._function_container, name, time)
set_log_level(bak_log_level)
# Once solutions have been written to file, update last written index
self._write_last_index(index)
def read(self, function, name, index):
if index <= self._last_index:
time = float(index)
self._restart_file.read_checkpoint(function, name, index)
self._update_function_container(function)
self._visualization_file.write(self._function_container, time) # because there is no append option available
else:
raise OSError
def plot_deltas_2D(vertex_vector, mesh_path, save_dir):
mesh = Mesh()
with XDMFFile(mesh_path) as f:
f.read(mesh)
V = FunctionSpace(mesh, 'CG', 1)
value = Function(V)
value.vector()[:] = vertex_vector[dof_to_vertex_map(V)]
delta_S = project(value.dx(0), V)
delta_file = XDMFFile(save_dir)
delta_file.write_checkpoint(delta_S, 'delta_S', 0, XDMFFile.Encoding.HDF5,
True)
delta_v = project(value.dx(1), V)
delta_file.write_checkpoint(delta_v, 'delta_v', 0, XDMFFile.Encoding.HDF5,
True)
def CladdingR_solver(FC_mesh, FC_facets, FC_fs, FC_info, D_post, R_path):
FC_fi, FC_fo = FC_fs
h, Tfc_inner, Tb, FC_Tave = FC_info
# Reading mesh data stored in .xdmf files.
mesh = Mesh()
with XDMFFile(FC_mesh) as infile:
infile.read(mesh)
mvc = MeshValueCollection("size_t", mesh, 1)
with XDMFFile(FC_facets) as infile:
infile.read(mvc, "name_to_read")
mf = cpp.mesh.MeshFunctionSizet(mesh, mvc)
#File("Circle_facet.pvd").write(mf)
# Mesh data
print('CladdingRod_mesh data\n', 'Number of cells: ', mesh.num_cells(),
'\n Number of nodes: ', mesh.num_vertices())
# Define variational problem
V = FunctionSpace(mesh, 'P', 1)
u = Function(V)
v = TestFunction(V)
# Define boundary conditions base on pygmsh mesh mark
bc = DirichletBC(V, Constant(Tfc_inner), mf, FC_fi)
ds = Measure("ds", domain=mesh, subdomain_data=mf, subdomain_id=FC_fo)
# Variational formulation
# Klbda_ZrO2 = 18/1000 # W/(m K) --> Nuclear reactor original source
# Klbda_ZrO2 = Constant(K_ZrO2(FC_Tave))
F = K_ZrO2(u) * dot(grad(u), grad(v)) * dx + h * (u - Tb) * v * ds
# Compute solution
du = TrialFunction(V)
Gain = derivative(F, u, du)
solve(F==0, u, bc, J=Gain, \
solver_parameters={"newton_solver": {"linear_solver": "lu",
"relative_tolerance": 1e-9}}, \
form_compiler_parameters={"cpp_optimize": True,
"representation": "uflacs",
"quadrature_degree" : 2}
) # mumps
# Save solution
if D_post:
fU_out = XDMFFile(os.path.join(R_path, 'FuelCladding', 'u.xdmf'))
fU_out.write_checkpoint(u, "T", 0, XDMFFile.Encoding.HDF5, False)
fU_out.close()
def FuelR_solver(FR_mesh, FR_facets, FR_f, FRod_info, D_post, R_path):
Qv, Tfr_outer, FR_Tave = FRod_info
# Reading mesh data stored in .xdmf files.
mesh = Mesh()
with XDMFFile(FR_mesh) as infile:
infile.read(mesh)
mvc = MeshValueCollection("size_t", mesh, 1)
with XDMFFile(FR_facets) as infile:
infile.read(mvc, "name_to_read")
mf = cpp.mesh.MeshFunctionSizet(mesh, mvc)
#File("Circle_facet.pvd").write(mf)
# Mesh data
print('FuelRod_mesh data\n', 'Number of cells: ', mesh.num_cells(),
'\n Number of nodes: ', mesh.num_vertices())
# Define variational problem
V = FunctionSpace(mesh, 'P', 1)
u = Function(V)
v = TestFunction(V)
f = Constant(Qv)
# Define boundary conditions base on pygmsh mesh mark
bc = DirichletBC(V, Constant(Tfr_outer), mf, FR_f)
# Variational formulation
# Klbda_UO2 = Constant(K_UO2(FR_Tave))
F = K_UO2(u) * dot(grad(u), grad(v)) * dx - f * v * dx
# Compute solution
du = TrialFunction(V)
Gain = derivative(F, u, du)
solve(F==0, u, bc, J=Gain, \
solver_parameters={"newton_solver": {"linear_solver": "lu",
"relative_tolerance": 1e-9}}, \
form_compiler_parameters={"cpp_optimize": True,
"representation": "uflacs",
"quadrature_degree" : 2}
) # mumps
# Save solution
if D_post:
fU_out = XDMFFile(os.path.join(R_path, 'FuelRod', 'u.xdmf'))
fU_out.write_checkpoint(u, "T", 0, XDMFFile.Encoding.HDF5, False)
fU_out.close()
2)
# Set-up Stokes Solve
forms_stokes = FormsStokes(mesh, mixedL, mixedG, alpha,
ds=ds).forms_multiphase(rho, ustar, dt, rho * nu, f)
ssc = StokesStaticCondensation(mesh, forms_stokes['A_S'], forms_stokes['G_S'],
forms_stokes['B_S'], forms_stokes['Q_S'],
forms_stokes['S_S'])
# Loop and output
step = 0
t = 0.
# Store tstep 0
assign(rho, rho0)
xdmf_rho.write_checkpoint(rho, "rho", t)
xdmf_u.write(Uh.sub(0), t)
xdmf_p.write(Uh.sub(1), t)
p.dump2file(mesh, fname_list, property_list, 'wb')
comm.barrier()
# Save some data in txt files
nc = mesh.num_entities_global(2)
npt = p.number_of_particles()
with open(meta_data, "w") as write_file:
write_file.write("%-12s %-12s %-15s %-20s %-15s %-15s \n" %
("Time step", "Number of steps", "Number of cells",
"Number of particles", "Projection", "Solver"))
write_file.write("%-12.5g %-15d %-15d %-20d %-15s %-15s \n" %
(float(dt), num_steps, nc, npt, projection_type, solver))
# Init projection and get initial condition
lstsq_psi = l2projection(p, W, 1)
lstsq_psi.project(psi_h, lb, ub)
assign(psi_h0, psi_h)
step = 0
t = 0.0
area_0 = assemble(psi_h * dx)
(psi_h_min, psi_h_max) = (0.0, 0.0)
timer = Timer()
timer.start()
# Write initial field and dump initial particle field
outfile.write_checkpoint(psi_h, function_name="psi", time_step=0)
p.dump2file(mesh, fname_list, property_list, "wb")
while step < num_steps:
step += 1
t += float(dt)
if comm.Get_rank() == 0:
print("Step " + str(step))
# Advect and project
ap.do_step(float(dt))
lstsq_psi.project(psi_h, lb, ub)
psi_h_min = min(psi_h_min, psi_h.vector().min())
psi_h_max = max(psi_h_max, psi_h.vector().max())
property_idx,
)
# Initialize the l2 projection
lstsq_psi = l2projection(p, W, property_idx)
# Set initial condition at mesh and particles
psi0_h.interpolate(psi0_expression)
p.interpolate(psi0_h, property_idx)
step = 0
area_0 = assemble(psi0_h * dx)
timer = Timer("[P] Advection loop")
timer.start()
output_field.write_checkpoint(psi0_h, function_name="psi", time_step=0)
while step < num_steps:
step += 1
if comm.rank == 0:
print("Step number" + str(step))
# Advect particle, assemble and solve pde projection
t1 = Timer("[P] Advect particles step")
ap.do_step(float(dt))
del t1
if projection_type == "PDE":
t1 = Timer("[P] Assemble PDE system")
pde_projection.assemble(True, True)
del t1
t1 = Timer("[P] Solve projection")
class Solver:
def __init__(self,
fbvp,
howard_infsup=True,
return_result=False,
output_mode=True,
get_error=False,
save_dir=None,
linear_mode=False,
verbose=True,
record_control=True):
self.fbvp = fbvp
self.solver = fbvp.parameters.solver
self.howard_infsup = howard_infsup
self.output_mode = output_mode
self.get_error = get_error
self.return_result = return_result
self.linear_mode = linear_mode
self.record_control = record_control
if self.linear_mode:
self.linear_control = [0, 0]
self.verbose = verbose
# Initialize solution vector with final time data
self.v = interpolate(fbvp.parameters.ft, fbvp.V)
self.control = interpolate(Constant(0), fbvp.V)
if not save_dir:
save_dir = f'out/{fbvp.parameters.experiment}/'\
f'{fbvp.parameters.domain}/{fbvp.mesh_name}/v.xdmf'
if self.output_mode:
self.file = XDMFFile(save_dir)
self.file.parameters['rewrite_function_mesh'] = False
self.file.write_checkpoint(self.v, 'value_func', fbvp.parameters.T)
print('Ready to begin calculation')
def Howard_outer(self, beta):
# v coresponds to v^{k+1}
alpha = [0] * self.fbvp.dim
ell = 0 # iteration counter
while ell < self.fbvp.parameters.howmaxit:
ell += 1
how, alpha = self.Howard_inner(alpha, beta)
# Create list of vectors (I*v^k+E*v^{k+1} -F) under different controls
w = np.array(how[:])
spv = np.array(self.v.vector()[:])
Ev = [[Exp.dot(spv) for Exp in Exp_b_list]
for Exp_b_list in self.fbvp.explicit_matrices]
multlist = np.empty(
[self.fbvp.csize_beta, self.fbvp.csize_alpha, self.fbvp.dim])
for ind_b in range(self.fbvp.csize_beta):
for ind_a in range(self.fbvp.csize_alpha):
multlist[ind_b][ind_a] = \
(self.fbvp.scipy_implicit_matrices[ind_b][ind_a].dot(w) +
Ev[ind_b][ind_a] -
self.fbvp.forcing_terms[ind_b][ind_a])
# Loop over vectors of values of (I*v^k+E*v^{k+1} -F) at each node and
# record control which optimizes each of them
if self.howard_infsup:
next_ctr = np.argmin(np.max(multlist, axis=1), axis=0)
else:
next_ctr = np.argmax(np.min(multlist, axis=1), axis=0)
return (how, next_ctr)
def Howard_inner(self, alpha, beta):
# v coresponds to v^{k+1}, save it to numpy array
spv = np.array(self.v.vector()[:])
Ev = {
b: [Ea.dot(spv) for Ea in self.fbvp.explicit_matrices[b]]
for b in set(beta)
}
# construct RHS under input control alfa
rhs = self.v.vector().copy()
rhs[:] = [
self.fbvp.forcing_terms[beta[i]][a][i] - Ev[beta[i]][a][i]
for i, a in enumerate(alpha)
]
# initialise vector with correct dimension to store solution
how = self.v.vector().copy()
# initalise matrix with a suitable sparsity pattern
lhs = self.fbvp.implicit_matrices[0][0].copy()
# construct implicit matrix under control (alfa, beta)
for i, a in enumerate(alpha):
lhs.set([self.fbvp.implicit_matrices[beta[i]][a].getrow(i)[1]],
[i], self.fbvp.implicit_matrices[beta[i]][a].getrow(i)[0])
lhs.apply('insert')
# solve linear problem to get next iterate of u
for bc in self.fbvp.dirichlet_bcs:
bc.apply(lhs, rhs)
self.solver.solve(lhs, how, rhs)
# Create list of vectors (I*v^k+E*v^{k+1} -F) under different controls
spw = np.array(how[:])
multlist = np.empty([self.fbvp.csize_alpha, self.fbvp.dim])
Iw = {
b: [Ia.dot(spw) for Ia in self.fbvp.scipy_implicit_matrices[b]]
for b in set(beta)
}
for ind_a, _ in enumerate(self.fbvp.ctrset_alpha):
for j in range(self.fbvp.dim):
multlist[ind_a][j] = Iw[beta[j]][ind_a][j] \
+ Ev[beta[j]][ind_a][j] - \
self.fbvp.forcing_terms[beta[j]][ind_a][j]
# Loop over vectors of values of (I*v^k+E*v^{k+1} -F) at each node and
# record control which optimizes each of them
if self.howard_infsup:
next_ctr = [np.argmax(vector) for vector in zip(*multlist)]
else:
next_ctr = [np.argmin(vector) for vector in zip(*multlist)]
return (how, next_ctr)
def time_iter(self):
alpha = [0] * self.fbvp.dim # initialize control
for k in range(self.fbvp.timesteps - 1, -1,
-1): # go backwards in time
time_start = time.perf_counter()
t = k * self.fbvp.timestep_size # Current time
# update dirichlet boundary conditions if necessary
if any(boundary_region in
self.fbvp.parameters.time_dependent['boundary']
for boundary_region in self.fbvp.parameters.omegas):
self.update_dirichlet_boundary(t)
if self.fbvp.parameters.time_dependent['rhs']:
self.fbvp.assemble_RHS(t)
if self.fbvp.parameters.time_dependent['pde']:
self.fbvp.assemble_HJBe(t + self.fbvp.timestep_size)
self.fbvp.assemble_HJBi(t)
if self.linear_mode:
alpha = self.linear_control[0]
beta = self.linear_control[1]
A = self.fbvp.implicit_matrices[beta][alpha]
b = self.v.vector().copy()
b[:] = (self.fbvp.forcing_terms[beta][alpha] -
self.fbvp.explicit_matrices[beta][alpha].dot(
np.array(self.v.vector()[:])))
for bc in self.fbvp.dirichlet_bcs:
bc.apply(A, b)
howit = self.v.vector().copy()
self.solver.solve(A, howit, b)
else:
beta = [0] * self.fbvp.dim
ell = 0 # iteration counter
while ell < self.fbvp.parameters.howmaxit:
ell += 1
howit, beta = self.Howard_outer(beta)
self.v.vector()[:] = howit
if self.output_mode and k % self.fbvp.parameters.save_interval == 0:
self.file.write_checkpoint(self.v, 'value_func', t,
XDMFFile.Encoding.HDF5, True)
if self.record_control:
self.control.vector()[:] = alpha
self.file.write_checkpoint(self.control, 'control', t,
XDMFFile.Encoding.HDF5, True)
time_elapsed = (time.perf_counter() - time_start)
if self.verbose:
print(f'Time step {self.fbvp.timesteps - k} out of'
f' {self.fbvp.timesteps} took {time_elapsed}')
if self.return_result:
return self.v
if self.get_error:
save_dir = f'out/{self.fbvp.parameters.experiment}/' \
f'{self.fbvp.parameters.domain}/errors.json'
error_calc(self.v,
self.fbvp.parameters.v_e,
self.fbvp.mesh,
self.fbvp.mesh_name,
save_dir=save_dir)
def update_dirichlet_boundary(self, t):
new_dirichlet_bcs = []
for region in self.fbvp.parameters.omegas:
if region in self.fbvp.parameters.time_dependent['boundary']:
boundary_data = self.fbvp.parameters.RHS_bound[region]
boundary_data.t = t
new_dirichlet_bcs.append(
DirichletBC(self.fbvp.V, boundary_data,
self.fbvp.boundary_markers, region))
else:
new_dirichlet_bcs.append(self.fbvp.dirichlet_bcs[region])
self.fbvp.dirichlet_bcs = new_dirichlet_bcs
def heston_transform(parameters,
get_error=False,
file_path=None,
plot_deltas=False):
experiment = parameters.experiment
domain_name = parameters.domain
mesh_name = parameters.mesh
mesh = Mesh()
mesh_path = parameters.get_mesh_path()
with XDMFFile(mesh_path) as f:
f.read(mesh)
# Create functions in function spaces defined by both original and
# transformed meshes and copy value function data from one to another
t_mesh_path = f'meshes/{domain_name}/t_{domain_name}_{mesh_name}.xdmf'
if not os.path.exists(t_mesh_path):
mesh2 = get_original_mesh(t_mesh_path, mesh, parameters)
else:
mesh2 = Mesh()
with XDMFFile(t_mesh_path) as f:
f.read(mesh2)
V = FunctionSpace(mesh, 'CG', 1)
t_V = FunctionSpace(mesh2, 'CG', 1)
value = Function(V)
control = Function(V)
t_value = Function(t_V)
t_control = Function(t_V)
if not file_path:
f = XDMFFile(f'out/{experiment}/{domain_name}/{mesh_name}/v.xdmf')
t_f = XDMFFile(f'out/{experiment}/{domain_name}/{mesh_name}/t_v.xdmf')
else:
f = XDMFFile(file_path)
path, file_name = os.path.split(file_path)
t_f = XDMFFile(os.path.join(path, f't_{file_name}'))
# Save Final Time Condition
f.read_checkpoint(value, 'value_func', 0)
t_value.vector()[:] = value.vector()[:]
t_f.write_checkpoint(t_value, 'value_func', parameters.T)
# Iterate through remaining timesteps (only some of them are
# saved to the file)
i = 1
parameters.calculate_save_interval()
dt = parameters.T / parameters.M
for k in range(parameters.M - 1, -1, -1):
if k % parameters.save_interval != 0:
continue
f.read_checkpoint(value, 'value_func', i)
f.read_checkpoint(control, 'control', i - 1)
t_value.vector()[:] = value.vector()[:]
t_control.vector()[:] = control.vector()[:]
t_f.write_checkpoint(t_value, 'value_func', k * dt,
XDMFFile.Encoding.HDF5, True)
t_f.write_checkpoint(t_control, 'control', k * dt,
XDMFFile.Encoding.HDF5, True)
if plot_deltas:
delta_S = project(t_value.dx(0), t_V)
t_f.write_checkpoint(delta_S, 'delta_S', k * dt,
XDMFFile.Encoding.HDF5, True)
delta_v = project(t_value.dx(1), t_V)
t_f.write_checkpoint(delta_v, 'delta_v', k * dt,
XDMFFile.Encoding.HDF5, True)
i += 1
if k == 0 and get_error:
error_calc(t_value, parameters.t_v_e, mesh2, f't_{mesh_name}',
f'out/{experiment}/{domain_name}/errors.json')
class Solver:
def __init__(self,
fbvp,
howard_inf=True,
return_result=False,
output_mode=True,
get_error=False,
save_dir=None,
linear_mode=False,
verbose=True,
record_control=True):
self.fbvp = fbvp
self.solver = fbvp.parameters.solver
self.howard_inf = howard_inf
self.output_mode = output_mode
self.get_error = get_error
self.return_result = return_result
self.linear_mode = linear_mode
self.record_control = record_control
if self.linear_mode:
self.linear_control = 0
self.verbose = verbose
# Initialize solution vector with final time data
self.v = interpolate(fbvp.parameters.ft, fbvp.V)
self.control = interpolate(Constant(0), fbvp.V)
if not save_dir:
save_dir = f'out/{fbvp.parameters.experiment}/'\
f'{fbvp.parameters.domain}/{fbvp.mesh_name}/v.xdmf'
if self.output_mode:
self.file = XDMFFile(save_dir)
self.file.parameters['rewrite_function_mesh'] = False
self.file.write_checkpoint(self.v, 'value_func', fbvp.parameters.T)
print('Ready to begin calculation')
def time_iter(self):
alpha = [0] * self.fbvp.dim # initialize control
for k in range(self.fbvp.timesteps - 1, -1, -1):
time_start = time.perf_counter()
t = k * self.fbvp.timestep_size # Current time
# update dirichlet boundary conditions if necessary
# TODO: Similar update for Robin boundaries
if any(elem in self.fbvp.parameters.time_dependent['boundary']
for elem in self.fbvp.parameters.regions['Dirichlet']):
self.update_dirichlet_boundary(t)
if self.fbvp.parameters.time_dependent['rhs']:
self.fbvp.assemble_RHS(t)
if self.fbvp.parameters.time_dependent['pde']:
self.fbvp.assemble_HJBe(t + self.fbvp.timestep_size)
self.fbvp.assemble_HJBi(t)
if self.linear_mode:
A = self.fbvp.Ilist[self.linear_control]
b = self.v.vector().copy()
b[:] = (self.fbvp.Flist[self.linear_control] -
self.fbvp.Elist[self.linear_control].dot(
np.array(self.v.vector()[:])))
for bc in self.fbvp.dirichlet_bcs:
bc.apply(A, b)
howit = self.v.vector().copy()
self.solver.solve(A, howit, b)
else:
ell = 0 # iteration counter
while ell < self.fbvp.parameters.howmaxit:
ell += 1
howit, alpha = self.Howard(self.v.vector(), alpha)
self.v.vector()[:] = howit
if self.output_mode and k % self.fbvp.parameters.save_interval == 0:
self.file.write_checkpoint(self.v, 'value_func', t,
XDMFFile.Encoding.HDF5, True)
if self.record_control:
self.control.vector()[:] = alpha
self.file.write_checkpoint(self.control, 'control', t,
XDMFFile.Encoding.HDF5, True)
time_elapsed = (time.perf_counter() - time_start)
if self.verbose:
print(f'Time step {self.fbvp.timesteps - k} out of'
f' {self.fbvp.timesteps} took {time_elapsed}')
if self.return_result:
return self.v
if self.get_error:
error_file_path = (f'out/{self.fbvp.parameters.experiment}/'
f'{self.fbvp.parameters.domain}/errors.json')
error_calc(self.v, self.fbvp.parameters.v_e, self.fbvp.mesh,
self.fbvp.mesh_name, error_file_path)
def Howard(self, v, alpha):
# v coresponds to v^{k+1}, save it to numpy array
spv = np.array(v[:])
Ev = [E.dot(spv) for E in self.fbvp.explicit_matrices]
# construct RHS under input control alfa
rhs = v.copy()
rhs[:] = [
self.fbvp.forcing_terms[control][i] - Ev[control][i]
for i, control in enumerate(alpha)
]
# initialise vector with correct dimension to store solution
how = v.copy()
# initalise matrix with a suitable sparameterssity pattern
lhs = self.fbvp.implicit_matrices[0].copy()
# construct implicit matrix from control alpha
for i, control in enumerate(alpha):
lhs.set([self.fbvp.implicit_matrices[control].getrow(i)[1]], [i],
self.fbvp.implicit_matrices[control].getrow(i)[0])
lhs.apply('insert')
# solve linear problem to get next iterate of u
for bc in self.fbvp.dirichlet_bcs:
bc.apply(lhs, rhs)
self.solver.solve(lhs, how, rhs)
# Create list of vectors (I*v^k+E*v^{k+1} -F) under different controls
spw = np.array(how[:])
multlist = (Imp.dot(spw) + Exp - F for Imp, Exp, F in zip(
self.fbvp.scipy_implicit_matrices, Ev, self.fbvp.forcing_terms))
# Loop over vectors of values of (I*v^k+E*v^{k+1} -F) at each node and
# record control which optimizes each of them
if self.howard_inf:
next_ctr = [np.argmin(vector) for vector in zip(*multlist)]
else:
next_ctr = [np.argmax(vector) for vector in zip(*multlist)]
return (how, next_ctr)
def update_dirichlet_boundary(self, t):
new_dirichlet_bcs = []
for i, region in enumerate(self.fbvp.parameters.regions['Dirichlet']):
if region in self.fbvp.parameters.time_dependent['boundary']:
new_dirichlet_bcs.append(
self.fbvp.parameters.update_dispenser[region](self.fbvp,
t))
else:
new_dirichlet_bcs.append(self.fbvp.dirichlet_bcs[i])
self.fbvp.dirichlet_bcs = new_dirichlet_bcs
"newton_solver": {
"maximum_iterations": 10
}
})
print('solver done')
# Save solution to files for visualization and data postprocessing
_u_A, _u_B, _u_C, _u_T = u_n.split()
Uvector = 3 * as_backend_type(u_n.vector()).get_local()
_3u_n.vector().set_local(Uvector)
_3u_A, _3u_B, _3u_C, _3u_T = _3u_n.split()
_u_D = _3u_C
if Data_postprocessing:
fA_out.write_checkpoint(_u_A, "A", t, XDMFFile.Encoding.HDF5, True)
fB_out.write_checkpoint(_u_B, "B", t, XDMFFile.Encoding.HDF5, True)
fC_out.write_checkpoint(_u_C, "C", t, XDMFFile.Encoding.HDF5, True)
fD_out.write_checkpoint(_u_D, "D", t, XDMFFile.Encoding.HDF5, True)
fT_out.write_checkpoint(_u_T, "T", t, XDMFFile.Encoding.HDF5, True)
Twall_n = Twall
ufl_integral = assemble(_u_T * ds_wall)
Numer = (roW * Vw *
Cpw) / dt * Twall_n + fw * Cpw * Tcool_in + hw * A * ufl_integral
Twall_new = Numer / Denom
print('Wall temperature {} K'.format(np.around(float(Twall_new), 4)))
Twall.assign(Twall_new)
u_n.assign(u)
