def postprocess_snapshot(self, snapshot_over_time, snapshot_index):
postprocessed_snapshot = TimeSeries(snapshot_over_time)
for (k, t) in enumerate(snapshot_over_time.stored_times()):
self.reduced_problem.set_time(t)
postprocessed_snapshot_k = DifferentialProblemReductionMethod_DerivedClass.postprocess_snapshot(
self, snapshot_over_time[k], snapshot_index)
postprocessed_snapshot.append(postprocessed_snapshot_k)
return postprocessed_snapshot
def _compute_relative_error_output(self, absolute_error_output_over_time, **kwargs):
relative_error_output_over_time = TimeSeries(self._output_over_time)
assert len(self.truth_problem._output_over_time) == len(absolute_error_output_over_time)
for (k, t) in enumerate(self.truth_problem._output_over_time.stored_times()):
self.set_time(t)
self.truth_problem._output = self.truth_problem._output_over_time[k]
relative_error_output = ParametrizedReducedDifferentialProblem_DerivedClass._compute_relative_error_output(self, absolute_error_output_over_time[k], **kwargs)
relative_error_output_over_time.append(relative_error_output)
return relative_error_output_over_time
def project(self,
snapshot_over_time,
N=None,
on_dirichlet_bc=True,
**kwargs):
projected_snapshot_N_over_time = TimeSeries(snapshot_over_time)
for snapshot in snapshot_over_time:
projected_snapshot_N = ParametrizedReducedDifferentialProblem_DerivedClass.project(
self, snapshot, N, on_dirichlet_bc, **kwargs)
projected_snapshot_N_over_time.append(projected_snapshot_N)
return projected_snapshot_N_over_time
def _compute_relative_error(self, absolute_error_over_time, **kwargs):
relative_error_over_time = TimeSeries(self._solution_over_time)
assert len(self._solution_over_time) == len(absolute_error_over_time)
for (k, t) in enumerate(self.truth_problem._solution_over_time.stored_times()):
self.set_time(t)
assign(self.truth_problem._solution, self.truth_problem._solution_over_time[k])
absolute_error = self._convert_error_at_time(k, absolute_error_over_time)
relative_error = ParametrizedReducedDifferentialProblem_DerivedClass._compute_relative_error(self, absolute_error, **kwargs)
relative_error_over_time.append(relative_error)
relative_error_over_time = self._convert_error_over_time(relative_error_over_time)
return relative_error_over_time
def postprocess_snapshot(self, snapshot_over_time, snapshot_index):
# Call parent: this will solve for supremizers at each time step
snapshot_and_supremizer_over_time = AbstractCFDUnsteadyReductionMethod_Base.postprocess_snapshot(self, snapshot_over_time, snapshot_index)
# Convert from a time series of tuple (snapshot, supremizer) to a tuple of two lists (snapshot over time, supremizer over time)
supremizer_over_time = TimeSeries(snapshot_over_time)
for (k, snapshot_and_supremizer) in enumerate(snapshot_and_supremizer_over_time):
assert isinstance(snapshot_and_supremizer, tuple)
assert len(snapshot_and_supremizer) is 2
assert snapshot_and_supremizer[0] is snapshot_over_time[k]
supremizer_over_time.append(snapshot_and_supremizer[1])
# Return a tuple
return (snapshot_over_time, supremizer_over_time)
def estimate_error(self):
eps2_over_time = self.get_residual_norm_squared()
alpha = self.get_stability_factor()
# Compute error bound
error_bound_over_time = TimeSeries(eps2_over_time)
for (k, t) in enumerate(eps2_over_time.stored_times()):
if not isclose(t, self.t0, self.dt/2.):
eps2 = eps2_over_time[k]
assert eps2 >= 0. or isclose(eps2, 0.)
assert alpha >= 0.
error_bound_over_time.append(sqrt(abs(eps2)/alpha))
else:
initial_error_estimate_squared = self.get_initial_error_estimate_squared()
assert initial_error_estimate_squared >= 0. or isclose(initial_error_estimate_squared, 0.)
error_bound_over_time.append(sqrt(abs(initial_error_estimate_squared)))
#
return error_bound_over_time
def get_residual_norm_squared(self):
residual_norm_squared_over_time = TimeSeries(
self._solution_over_time)
assert len(self._solution_over_time) == len(
self._solution_dot_over_time)
for (k, t) in enumerate(self._solution_over_time.stored_times()):
if not isclose(t, self.t0, self.dt / 2.):
# Set current time
self.set_time(t)
# Set current solution and solution_dot
assign(self._solution, self._solution_over_time[k])
assign(self._solution_dot, self._solution_dot_over_time[k])
# Compute the numerator of the error bound at the current time, first
# by computing residual of elliptic part
elliptic_residual_norm_squared = AbstractParabolicRBReducedProblem_Base.get_residual_norm_squared(
self)
# ... and then adding terms related to time derivative
N = self._solution.N
theta_m = self.compute_theta("m")
theta_a = self.compute_theta("a")
theta_f = self.compute_theta("f")
residual_norm_squared_over_time.append(
elliptic_residual_norm_squared + 2.0 *
(transpose(self._solution_dot) * sum(
product(
theta_m, self.error_estimation_operator[
"m", "f"][:N], theta_f))) + 2.0 *
(transpose(self._solution_dot) * sum(
product(
theta_m, self.error_estimation_operator[
"m", "a"][:N, :N], theta_a)) *
self._solution) +
(transpose(self._solution_dot) * sum(
product(
theta_m, self.error_estimation_operator[
"m", "m"][:N, :N], theta_m)) *
self._solution_dot))
else:
# Error estimator on initial condition does not use the residual
residual_norm_squared_over_time.append(0.)
return residual_norm_squared_over_time