def _init_operators(self, current_stage="online"):
# The difference between this method and the parent one is that non-hierarchical affine
# expansion storage is requested during the online stage and during the postprocessing
# of the offline stage.
if current_stage == "online":
# Initialize all terms using a non-hierarchical affine expansion storage, and then loading from file
for term in self.terms:
self.operator[term] = OnlineNonHierarchicalAffineExpansionStorage(0) # it will be resized by assemble_operator
self.assemble_operator(term, "online")
self.Q[term] = len(self.operator[term])
# Initialize additional reduced operator related to vanishing viscosity
self.operator["vanishing_viscosity"] = OnlineNonHierarchicalAffineExpansionStorage(1)
self.assemble_operator("vanishing_viscosity", "online")
elif current_stage == "offline":
# Call Parent
EllipticCoerciveReducedProblem_DerivedClass._init_operators(self, current_stage)
elif current_stage == "offline_vanishing_viscosity_postprocessing":
# Initialize additional truth operators
self.truth_problem.operator["k"] = AffineExpansionStorage(self.truth_problem.assemble_operator("k"))
self.truth_problem.operator["m"] = AffineExpansionStorage(self.truth_problem.assemble_operator("m"))
# Initialize all terms using a non-hierarchical affine expansion storage
for term in self.terms:
self.Q[term] = self.truth_problem.Q[term]
self.operator[term] = OnlineNonHierarchicalAffineExpansionStorage(self.Q[term])
# Initialize additional reduced operator related to vanishing viscosity
self.operator["vanishing_viscosity"] = OnlineNonHierarchicalAffineExpansionStorage(1)
else:
# Call Parent, which may eventually raise an error
EllipticCoerciveReducedProblem_DerivedClass._init_operators(self, current_stage)
def _init_inner_products(self, current_stage="online"):
# The difference between this method and the parent one is that non-hierarchical affine
# expansion storage is requested during the online stage and during the postprocessing
# of the offline stage.
if current_stage == "online":
self.inner_product = OnlineNonHierarchicalAffineExpansionStorage(
1)
self.projection_inner_product = OnlineNonHierarchicalAffineExpansionStorage(
1)
self.assemble_operator("inner_product", "online")
self.assemble_operator("projection_inner_product", "online")
self._disable_inner_product_combination = True
elif current_stage == "offline":
EllipticCoerciveReducedProblem_DerivedClass._init_inner_products(
self, current_stage)
elif current_stage == "offline_vanishing_viscosity_postprocessing":
self.inner_product = OnlineNonHierarchicalAffineExpansionStorage(
1)
self.projection_inner_product = OnlineNonHierarchicalAffineExpansionStorage(
1)
self._disable_inner_product_combination = True
else:
# Call Parent, which may eventually raise an error
EllipticCoerciveReducedProblem_DerivedClass._init_inner_products(
self, current_stage)
def _init_operators(self, current_stage="online"):
# Initialize additional reduced operators related to rectification. Note that these operators
# are not hierarchical because:
# * the basis is possibly non-hierarchical
# * the coefficients of the reduced solution for different reduced sizes are definitely not hierarchical
if current_stage == "online":
self.operator[
"projection_truth_snapshots"] = OnlineNonHierarchicalAffineExpansionStorage(
1)
assert len(self.online_solve_kwargs_with_rectification) is len(
self.online_solve_kwargs_without_rectification)
self.operator[
"projection_reduced_snapshots"] = OnlineNonHierarchicalAffineExpansionStorage(
len(self.online_solve_kwargs_with_rectification))
self.assemble_operator("projection_truth_snapshots", "online")
self.assemble_operator("projection_reduced_snapshots",
"online")
# Call Parent
EllipticCoerciveReducedProblem_DerivedClass._init_operators(
self, current_stage)
elif current_stage == "offline":
# Call Parent
EllipticCoerciveReducedProblem_DerivedClass._init_operators(
self, current_stage)
elif current_stage == "offline_rectification_postprocessing":
self.operator[
"projection_truth_snapshots"] = OnlineNonHierarchicalAffineExpansionStorage(
1)
assert len(self.online_solve_kwargs_with_rectification) is len(
self.online_solve_kwargs_without_rectification)
self.operator[
"projection_reduced_snapshots"] = OnlineNonHierarchicalAffineExpansionStorage(
len(self.online_solve_kwargs_with_rectification))
# We do not call Parent method as there is no need to re-initialize offline operators
else:
# Call Parent, which may eventually raise an error
EllipticCoerciveReducedProblem_DerivedClass._init_operators(
self, current_stage)
class OnlineVanishingViscosityDecoratedReducedProblem_Class(EllipticCoerciveReducedProblem_DerivedClass):
def __init__(self, truth_problem, **kwargs):
# Call to parent
EllipticCoerciveReducedProblem_DerivedClass.__init__(self, truth_problem, **kwargs)
# Store vanishing viscosity data
self._viscosity = truth_problem._viscosity
self._N_threshold_min = truth_problem._N_threshold_min
self._N_threshold_max = truth_problem._N_threshold_max
# Temporary storage for vanishing viscosity eigenvalues
self.vanishing_viscosity_eigenvalues = list()
# Default values for keyword arguments in solve
self._online_solve_default_kwargs = OrderedDict()
self._online_solve_default_kwargs["online_stabilization"] = False
self._online_solve_default_kwargs["online_vanishing_viscosity"] = True
self.OnlineSolveKwargs = OnlineSolveKwargsGenerator(**self._online_solve_default_kwargs)
# Flag to disable inner product combination after vanishing viscosity operator has been setup
self._disable_inner_product_combination = False
# Flag to disable error estimation after vanishing viscosity operator has been setup
self._disable_error_estimation = False
def _init_operators(self, current_stage="online"):
# The difference between this method and the parent one is that non-hierarchical affine
# expansion storage is requested during the online stage and during the postprocessing
# of the offline stage.
if current_stage == "online":
# Initialize all terms using a non-hierarchical affine expansion storage, and then loading from file
for term in self.terms:
self.operator[term] = OnlineNonHierarchicalAffineExpansionStorage(0) # it will be resized by assemble_operator
self.assemble_operator(term, "online")
self.Q[term] = len(self.operator[term])
# Initialize additional reduced operator related to vanishing viscosity
self.operator["vanishing_viscosity"] = OnlineNonHierarchicalAffineExpansionStorage(1)
self.assemble_operator("vanishing_viscosity", "online")
elif current_stage == "offline":
# Call Parent
EllipticCoerciveReducedProblem_DerivedClass._init_operators(self, current_stage)
elif current_stage == "offline_vanishing_viscosity_postprocessing":
# Initialize additional truth operators
self.truth_problem.operator["k"] = AffineExpansionStorage(self.truth_problem.assemble_operator("k"))
self.truth_problem.operator["m"] = AffineExpansionStorage(self.truth_problem.assemble_operator("m"))
# Initialize all terms using a non-hierarchical affine expansion storage
for term in self.terms:
self.Q[term] = self.truth_problem.Q[term]
self.operator[term] = OnlineNonHierarchicalAffineExpansionStorage(self.Q[term])
# Initialize additional reduced operator related to vanishing viscosity
self.operator["vanishing_viscosity"] = OnlineNonHierarchicalAffineExpansionStorage(1)
else:
# Call Parent, which may eventually raise an error
EllipticCoerciveReducedProblem_DerivedClass._init_operators(self, current_stage)
def _init_inner_products(self, current_stage="online"):
# The difference between this method and the parent one is that non-hierarchical affine
# expansion storage is requested during the online stage and during the postprocessing
# of the offline stage.
if current_stage == "online":
self.inner_product = OnlineNonHierarchicalAffineExpansionStorage(1)
self.projection_inner_product = OnlineNonHierarchicalAffineExpansionStorage(1)
self.assemble_operator("inner_product", "online")
self.assemble_operator("projection_inner_product", "online")
self._disable_inner_product_combination = True
elif current_stage == "offline":
EllipticCoerciveReducedProblem_DerivedClass._init_inner_products(self, current_stage)
elif current_stage == "offline_vanishing_viscosity_postprocessing":
self.inner_product = OnlineNonHierarchicalAffineExpansionStorage(1)
self.projection_inner_product = OnlineNonHierarchicalAffineExpansionStorage(1)
self._disable_inner_product_combination = True
else:
# Call Parent, which may eventually raise an error
EllipticCoerciveReducedProblem_DerivedClass._init_inner_products(self, current_stage)
def _combine_all_inner_products(self):
if self._disable_inner_product_combination:
return NotImplemented
else:
return EllipticCoerciveReducedProblem_DerivedClass._combine_all_inner_products(self)
def _combine_all_projection_inner_products(self):
if self._disable_inner_product_combination:
return NotImplemented
else:
return EllipticCoerciveReducedProblem_DerivedClass._combine_all_projection_inner_products(self)
def _init_basis_functions(self, current_stage="online"):
if current_stage == "online":
if self.basis_functions is None: # avoid re-initializing basis functions matrix multiple times
self.basis_functions = NonHierarchicalBasisFunctionsMatrix(self.truth_problem.V)
self.basis_functions.init(self.truth_problem.components)
basis_functions_loaded = self.basis_functions.load(self.folder["basis"], "basis")
if basis_functions_loaded:
self.N = len(self.basis_functions)
self.N_bc = 0 # TODO handle inhomogeneous bcs
elif current_stage == "offline":
EllipticCoerciveReducedProblem_DerivedClass._init_basis_functions(self, current_stage)
elif current_stage == "offline_vanishing_viscosity_postprocessing":
self.basis_functions = NonHierarchicalBasisFunctionsMatrix(self.truth_problem.V)
self.basis_functions.init(self.truth_problem.components)
else:
# Call Parent, which may eventually raise an error
EllipticCoerciveReducedProblem_DerivedClass._init_basis_functions(self, current_stage)
def _init_error_estimation_operators(self, current_stage="online"):
if current_stage in ("online", "offline_vanishing_viscosity_postprocessing"):
# Disable error estimation, which would not take into account the additional vanishing viscosity operator
self._disable_error_estimation = True
elif current_stage == "offline":
# Call Parent
EllipticCoerciveReducedProblem_DerivedClass._init_error_estimation_operators(self, current_stage)
else:
# Call Parent, which may eventually raise an error
EllipticCoerciveReducedProblem_DerivedClass._init_error_estimation_operators(self, current_stage)
def build_reduced_operators(self, current_stage="offline"):
if current_stage == "offline_vanishing_viscosity_postprocessing":
EllipticCoerciveReducedProblem_DerivedClass.build_reduced_operators(self, "offline_vanishing_viscosity_postprocessing")
# Compute vanishing viscosity reduced operator
print("build vanishing viscosity reduced operator")
self.operator["vanishing_viscosity"] = self.assemble_operator("vanishing_viscosity", "offline_vanishing_viscosity_postprocessing")
else:
# Call Parent, which may eventually raise an error
EllipticCoerciveReducedProblem_DerivedClass.build_reduced_operators(self, current_stage)
def assemble_operator(self, term, current_stage="online"):
if term == "vanishing_viscosity":
assert current_stage in ("online", "offline_vanishing_viscosity_postprocessing")
if current_stage == "online": # load from file
self.operator["vanishing_viscosity"].load(self.folder["reduced_operators"], "operator_vanishing_viscosity")
return self.operator["vanishing_viscosity"]
elif current_stage == "offline_vanishing_viscosity_postprocessing":
assert len(self.vanishing_viscosity_eigenvalues) is self.N
assert all([len(vanishing_viscosity_eigenvalues_n) is n + 1 for (n, vanishing_viscosity_eigenvalues_n) in enumerate(self.vanishing_viscosity_eigenvalues)])
print("build reduced vanishing viscosity operator")
for n in range(1, self.N + 1):
vanishing_viscosity_expansion = OnlineAffineExpansionStorage(1)
vanishing_viscosity_eigenvalues = self.vanishing_viscosity_eigenvalues[n - 1]
vanishing_viscosity_operator = OnlineMatrix(n, n)
n_min = int(n*self._N_threshold_min)
n_max = int(n*self._N_threshold_max)
lambda_n_min = vanishing_viscosity_eigenvalues[n_min]
lambda_n_max = vanishing_viscosity_eigenvalues[n_max]
for i in range(n):
lambda_i = vanishing_viscosity_eigenvalues[i]
if i < n_min:
viscosity_i = 0.
elif i < n_max:
viscosity_i = (
self._viscosity *
(lambda_i - lambda_n_min)**2/(lambda_n_max - lambda_n_min)**3 *
(2*lambda_n_max**2 - (lambda_n_min + lambda_n_max)*lambda_i)
)
else:
viscosity_i = self._viscosity*lambda_i
vanishing_viscosity_operator[i, i] = viscosity_i*lambda_i
vanishing_viscosity_expansion[0] = vanishing_viscosity_operator
self.operator["vanishing_viscosity"][:n, :n] = vanishing_viscosity_expansion
# Save to file
self.operator["vanishing_viscosity"].save(self.folder["reduced_operators"], "operator_vanishing_viscosity")
return self.operator["vanishing_viscosity"]
else:
raise ValueError("Invalid stage in assemble_operator().")
else:
if current_stage == "offline_vanishing_viscosity_postprocessing":
if term in self.terms:
for n in range(1, self.N + 1):
assert self.Q[term] == self.truth_problem.Q[term]
term_expansion = OnlineAffineExpansionStorage(self.Q[term])
assert self.terms_order[term] in (1, 2)
if self.terms_order[term] == 2:
for q in range(self.Q[term]):
term_expansion[q] = transpose(self.basis_functions[:n])*self.truth_problem.operator[term][q]*self.basis_functions[:n]
self.operator[term][:n, :n] = term_expansion
elif self.terms_order[term] == 1:
for q in range(self.Q[term]):
term_expansion[q] = transpose(self.basis_functions[:n])*self.truth_problem.operator[term][q]
self.operator[term][:n] = term_expansion
else:
raise ValueError("Invalid value for order of term " + term)
self.operator[term].save(self.folder["reduced_operators"], "operator_" + term)
return self.operator[term]
elif term.startswith("inner_product"):
assert len(self.inner_product) == 1 # the affine expansion storage contains only the inner product matrix
assert len(self.truth_problem.inner_product) == 1 # the affine expansion storage contains only the inner product matrix
for n in range(1, self.N + 1):
inner_product_expansion = OnlineAffineExpansionStorage(1)
inner_product_expansion[0] = transpose(self.basis_functions[:n])*self.truth_problem.inner_product[0]*self.basis_functions[:n]
self.inner_product[:n, :n] = inner_product_expansion
self.inner_product.save(self.folder["reduced_operators"], term)
return self.inner_product
elif term.startswith("projection_inner_product"):
assert len(self.projection_inner_product) == 1 # the affine expansion storage contains only the inner product matrix
assert len(self.truth_problem.projection_inner_product) == 1 # the affine expansion storage contains only the inner product matrix
for n in range(1, self.N + 1):
projection_inner_product_expansion = OnlineAffineExpansionStorage(1)
projection_inner_product_expansion[0] = transpose(self.basis_functions[:n])*self.truth_problem.projection_inner_product[0]*self.basis_functions[:n]
self.projection_inner_product[:n, :n] = projection_inner_product_expansion
self.projection_inner_product.save(self.folder["reduced_operators"], term)
return self.projection_inner_product
elif term.startswith("dirichlet_bc"):
raise ValueError("There should be no need to assemble Dirichlet BCs when querying the offline vanishing viscosity postprocessing stage.")
else:
raise ValueError("Invalid term for assemble_operator().")
else:
return EllipticCoerciveReducedProblem_DerivedClass.assemble_operator(self, term, current_stage)
def _online_size_from_kwargs(self, N, **kwargs):
N, kwargs = EllipticCoerciveReducedProblem_DerivedClass._online_size_from_kwargs(self, N, **kwargs)
kwargs = self.OnlineSolveKwargs(**kwargs)
return N, kwargs
def _solve(self, N, **kwargs):
# Temporarily change value of stabilized attribute in truth problem
bak_stabilized = self.truth_problem.stabilized
self.truth_problem.stabilized = kwargs["online_stabilization"]
# Solve reduced problem
if kwargs["online_vanishing_viscosity"]:
assembled_operator = dict()
assembled_operator["a"] = (
sum(product(self.compute_theta("a"), self.operator["a"][:N, :N])) +
self.operator["vanishing_viscosity"][:N, :N][0]
)
assembled_operator["f"] = sum(product(self.compute_theta("f"), self.operator["f"][:N]))
self._solution = OnlineFunction(N)
solver = LinearSolver(assembled_operator["a"], self._solution, assembled_operator["f"])
solver.set_parameters(self._linear_solver_parameters)
solver.solve()
else:
EllipticCoerciveReducedProblem_DerivedClass._solve(self, N, **kwargs)
# Restore original value of stabilized attribute in truth problem
self.truth_problem.stabilized = bak_stabilized
def estimate_error(self):
if self._disable_error_estimation:
return NotImplemented
else:
return EllipticCoerciveReducedProblem_DerivedClass.estimate_error(self)