def build_rom(self, projected_operators, error_estimator):
fom = self.fom
return InstationaryModel(T=fom.T,
time_stepper=fom.time_stepper,
num_values=fom.num_values,
error_estimator=error_estimator,
**projected_operators)
def discretize(n, nt, blocks):
h = 1. / blocks
ops = [WrappedDiffusionOperator.create(n, h * i, h * (i + 1)) for i in range(blocks)]
pfs = [ProjectionParameterFunctional('diffusion_coefficients', blocks, i) for i in range(blocks)]
operator = LincombOperator(ops, pfs)
initial_data = operator.source.zeros()
# use data property of WrappedVector to setup rhs
# note that we cannot use the data property of ListVectorArray,
# since ListVectorArray will always return a copy
rhs_vec = operator.range.zeros()
rhs_data = rhs_vec._list[0].to_numpy()
rhs_data[:] = np.ones(len(rhs_data))
rhs_data[0] = 0
rhs_data[len(rhs_data) - 1] = 0
rhs = VectorOperator(rhs_vec)
# hack together a visualizer ...
grid = OnedGrid(domain=(0, 1), num_intervals=n)
visualizer = OnedVisualizer(grid)
time_stepper = ExplicitEulerTimeStepper(nt)
fom = InstationaryModel(T=1e-0, operator=operator, rhs=rhs, initial_data=initial_data,
time_stepper=time_stepper, num_values=20,
visualizer=visualizer, name='C++-Model')
return fom
def build_rom(self, projected_operators, estimator):
fom = self.fom
return InstationaryModel(T=fom.T,
time_stepper=fom.time_stepper,
num_values=fom.num_values,
parameter_space=self.fom.parameter_space,
estimator=estimator,
**projected_operators)
def discretize_instationary_cg(analytical_problem,
diameter=None,
domain_discretizer=None,
grid_type=None,
grid=None,
boundary_info=None,
num_values=None,
time_stepper=None,
nt=None,
preassemble=True):
"""Discretizes an |InstationaryProblem| with a |StationaryProblem| as stationary part
using finite elements.
Parameters
----------
analytical_problem
The |InstationaryProblem| to discretize.
diameter
If not `None`, `diameter` is passed as an argument to the `domain_discretizer`.
domain_discretizer
Discretizer to be used for discretizing the analytical domain. This has
to be a function `domain_discretizer(domain_description, diameter, ...)`.
If `None`, |discretize_domain_default| is used.
grid_type
If not `None`, this parameter is forwarded to `domain_discretizer` to specify
the type of the generated |Grid|.
grid
Instead of using a domain discretizer, the |Grid| can also be passed directly
using this parameter.
boundary_info
A |BoundaryInfo| specifying the boundary types of the grid boundary entities.
Must be provided if `grid` is specified.
num_values
The number of returned vectors of the solution trajectory. If `None`, each
intermediate vector that is calculated is returned.
time_stepper
The :class:`time-stepper <pymor.algorithms.timestepping.TimeStepperInterface>`
to be used by :class:`~pymor.models.basic.InstationaryModel.solve`.
nt
If `time_stepper` is not specified, the number of time steps for implicit
Euler time stepping.
preassemble
If `True`, preassemble all operators in the resulting |Model|.
Returns
-------
m
The |Model| that has been generated.
data
Dictionary with the following entries:
:grid: The generated |Grid|.
:boundary_info: The generated |BoundaryInfo|.
:unassembled_m: In case `preassemble` is `True`, the generated |Model|
before preassembling operators.
"""
assert isinstance(analytical_problem, InstationaryProblem)
assert isinstance(analytical_problem.stationary_part, StationaryProblem)
assert grid is None or boundary_info is not None
assert boundary_info is None or grid is not None
assert grid is None or domain_discretizer is None
assert (time_stepper is None) != (nt is None)
p = analytical_problem
m, data = discretize_stationary_cg(p.stationary_part,
diameter=diameter,
domain_discretizer=domain_discretizer,
grid_type=grid_type,
grid=grid,
boundary_info=boundary_info)
if p.initial_data.parametric:
I = InterpolationOperator(data['grid'], p.initial_data)
else:
I = p.initial_data.evaluate(data['grid'].centers(data['grid'].dim))
I = m.solution_space.make_array(I)
if time_stepper is None:
if p.stationary_part.diffusion is None:
time_stepper = ExplicitEulerTimeStepper(nt=nt)
else:
time_stepper = ImplicitEulerTimeStepper(nt=nt)
mass = m.l2_0_product
m = InstationaryModel(operator=m.operator,
rhs=m.rhs,
mass=mass,
initial_data=I,
T=p.T,
products=m.products,
output_functional=m.output_functional,
time_stepper=time_stepper,
parameter_space=p.parameter_space,
visualizer=m.visualizer,
num_values=num_values,
name=f'{p.name}_CG')
if preassemble:
data['unassembled_m'] = m
m = preassemble_(m)
return m, data
def discretize_instationary_fv(analytical_problem, diameter=None, domain_discretizer=None, grid_type=None,
num_flux='lax_friedrichs', lxf_lambda=1., eo_gausspoints=5, eo_intervals=1,
grid=None, boundary_info=None, num_values=None, time_stepper=None, nt=None,
preassemble=True):
"""Discretizes an |InstationaryProblem| with a |StationaryProblem| as stationary part
using the finite volume method.
Parameters
----------
analytical_problem
The |InstationaryProblem| to discretize.
diameter
If not `None`, `diameter` is passed to the `domain_discretizer`.
domain_discretizer
Discretizer to be used for discretizing the analytical domain. This has
to be a function `domain_discretizer(domain_description, diameter, ...)`.
If further arguments should be passed to the discretizer, use
:func:`functools.partial`. If `None`, |discretize_domain_default| is used.
grid_type
If not `None`, this parameter is forwarded to `domain_discretizer` to specify
the type of the generated |Grid|.
num_flux
The numerical flux to use in the finite volume formulation. Allowed
values are `'lax_friedrichs'`, `'engquist_osher'`, `'simplified_engquist_osher'`
(see :mod:`pymor.discretizers.builtin.fv`).
lxf_lambda
The stabilization parameter for the Lax-Friedrichs numerical flux
(ignored, if different flux is chosen).
eo_gausspoints
Number of Gauss points for the Engquist-Osher numerical flux
(ignored, if different flux is chosen).
eo_intervals
Number of sub-intervals to use for integration when using Engquist-Osher
numerical flux (ignored, if different flux is chosen).
grid
Instead of using a domain discretizer, the |Grid| can also be passed directly
using this parameter.
boundary_info
A |BoundaryInfo| specifying the boundary types of the grid boundary entities.
Must be provided if `grid` is specified.
num_values
The number of returned vectors of the solution trajectory. If `None`, each
intermediate vector that is calculated is returned.
time_stepper
The :class:`time-stepper <pymor.algorithms.timestepping.TimeStepper>`
to be used by :class:`~pymor.models.basic.InstationaryModel.solve`.
nt
If `time_stepper` is not specified, the number of time steps for implicit
Euler time stepping.
preassemble
If `True`, preassemble all operators in the resulting |Model|.
Returns
-------
m
The |Model| that has been generated.
data
Dictionary with the following entries:
:grid: The generated |Grid|.
:boundary_info: The generated |BoundaryInfo|.
:unassembled_m: In case `preassemble` is `True`, the generated |Model|
before preassembling operators.
"""
assert isinstance(analytical_problem, InstationaryProblem)
assert isinstance(analytical_problem.stationary_part, StationaryProblem)
assert grid is None or boundary_info is not None
assert boundary_info is None or grid is not None
assert grid is None or domain_discretizer is None
assert (time_stepper is None) != (nt is None)
p = analytical_problem
m, data = discretize_stationary_fv(p.stationary_part, diameter=diameter, domain_discretizer=domain_discretizer,
grid_type=grid_type, num_flux=num_flux, lxf_lambda=lxf_lambda,
eo_gausspoints=eo_gausspoints, eo_intervals=eo_intervals, grid=grid,
boundary_info=boundary_info)
grid = data['grid']
if p.initial_data.parametric:
def initial_projection(U, mu):
I = p.initial_data.evaluate(grid.quadrature_points(0, order=2), mu).squeeze()
I = np.sum(I * grid.reference_element.quadrature(order=2)[1], axis=1) * (1. / grid.reference_element.volume)
I = m.solution_space.make_array(I)
return I.lincomb(U).to_numpy()
I = NumpyGenericOperator(initial_projection, dim_range=grid.size(0), linear=True, range_id=m.solution_space.id,
parameter_type=p.initial_data.parameter_type)
else:
I = p.initial_data.evaluate(grid.quadrature_points(0, order=2)).squeeze()
I = np.sum(I * grid.reference_element.quadrature(order=2)[1], axis=1) * (1. / grid.reference_element.volume)
I = m.solution_space.make_array(I)
if time_stepper is None:
if p.stationary_part.diffusion is None:
time_stepper = ExplicitEulerTimeStepper(nt=nt)
else:
time_stepper = ImplicitEulerTimeStepper(nt=nt)
rhs = None if isinstance(m.rhs, ZeroOperator) else m.rhs
m = InstationaryModel(operator=m.operator, rhs=rhs, mass=None, initial_data=I, T=p.T,
products=m.products, time_stepper=time_stepper,
parameter_space=p.parameter_space, visualizer=m.visualizer,
num_values=num_values, name=f'{p.name}_FV')
if preassemble:
data['unassembled_m'] = m
m = preassemble_(m)
return m, data
def discretize_instationary_from_disk(parameter_file,
T=None,
steps=None,
u0=None,
time_stepper=None):
"""Load a linear affinely decomposed |InstationaryModel| from file.
Similarly to :func:`discretize_stationary_from_disk`, the model is
specified via an `ini.`-file of the following form ::
[system-matrices]
L_1.mat: l_1(μ_1,...,μ_n)
L_2.mat: l_2(μ_1,...,μ_n)
...
[rhs-vectors]
F_1.mat: f_1(μ_1,...,μ_n)
F_2.mat: f_2(μ_1,...,μ_n)
...
[mass-matrix]
D.mat
[initial-solution]
u0: u0.mat
[parameter]
μ_1: a_1,b_1
...
μ_n: a_n,b_n
[products]
Prod1: P_1.mat
Prod2: P_2.mat
...
[time]
T: final time
steps: number of time steps
Parameters
----------
parameter_file
Path to the '.ini' parameter file.
T
End-time of desired solution. If `None`, the value specified in the
parameter file is used.
steps
Number of time steps to. If `None`, the value specified in the
parameter file is used.
u0
Initial solution. If `None` the initial solution is obtained
from parameter file.
time_stepper
The desired :class:`time stepper <pymor.algorithms.timestepping.TimeStepper>`
to use. If `None`, implicit Euler time stepping is used.
Returns
-------
m
The |InstationaryModel| that has been generated.
"""
assert ".ini" == parameter_file[-4:], "Given file is not an .ini file"
assert os.path.isfile(parameter_file)
base_path = os.path.dirname(parameter_file)
# Get input from parameter file
config = configparser.ConfigParser()
config.optionxform = str
config.read(parameter_file)
# Assert that all needed entries given
assert 'system-matrices' in config.sections()
assert 'mass-matrix' in config.sections()
assert 'rhs-vectors' in config.sections()
assert 'parameter' in config.sections()
system_mat = config.items('system-matrices')
mass_mat = config.items('mass-matrix')
rhs_vec = config.items('rhs-vectors')
parameter = config.items('parameter')
# Dict of parameters types and ranges
parameter_type = {}
parameter_range = {}
# get parameters
for i in range(len(parameter)):
parameter_name = parameter[i][0]
parameter_list = tuple(
float(j) for j in parameter[i][1].replace(" ", "").split(','))
parameter_range[parameter_name] = parameter_list
# Assume scalar parameter dependence
parameter_type[parameter_name] = 0
# Create parameter space
parameter_space = CubicParameterSpace(parameter_type=parameter_type,
ranges=parameter_range)
# Assemble operators
system_operators, system_functionals = [], []
# get parameter functionals and system matrices
for i in range(len(system_mat)):
path = os.path.join(base_path, system_mat[i][0])
expr = system_mat[i][1]
parameter_functional = ExpressionParameterFunctional(
expr, parameter_type=parameter_type)
system_operators.append(
NumpyMatrixOperator.from_file(path,
source_id='STATE',
range_id='STATE'))
system_functionals.append(parameter_functional)
system_lincombOperator = LincombOperator(system_operators,
coefficients=system_functionals)
# get rhs vectors
rhs_operators, rhs_functionals = [], []
for i in range(len(rhs_vec)):
path = os.path.join(base_path, rhs_vec[i][0])
expr = rhs_vec[i][1]
parameter_functional = ExpressionParameterFunctional(
expr, parameter_type=parameter_type)
op = NumpyMatrixOperator.from_file(path, range_id='STATE')
assert isinstance(op.matrix, np.ndarray)
op = op.with_(matrix=op.matrix.reshape((-1, 1)))
rhs_operators.append(op)
rhs_functionals.append(parameter_functional)
rhs_lincombOperator = LincombOperator(rhs_operators,
coefficients=rhs_functionals)
# get mass matrix
path = os.path.join(base_path, mass_mat[0][1])
mass_operator = NumpyMatrixOperator.from_file(path,
source_id='STATE',
range_id='STATE')
# Obtain initial solution if not given
if u0 is None:
u_0 = config.items('initial-solution')
path = os.path.join(base_path, u_0[0][1])
op = NumpyMatrixOperator.from_file(path, range_id='STATE')
assert isinstance(op.matrix, np.ndarray)
u0 = op.with_(matrix=op.matrix.reshape((-1, 1)))
# get products if given
if 'products' in config.sections():
product = config.items('products')
products = {}
for i in range(len(product)):
product_name = product[i][0]
product_path = os.path.join(base_path, product[i][1])
products[product_name] = NumpyMatrixOperator.from_file(
product_path, source_id='STATE', range_id='STATE')
else:
products = None
# Further specifications
if 'time' in config.sections():
if T is None:
assert 'T' in config.options('time')
T = float(config.get('time', 'T'))
if steps is None:
assert 'steps' in config.options('time')
steps = int(config.get('time', 'steps'))
# Use implicit euler time stepper if no time-stepper given
if time_stepper is None:
time_stepper = ImplicitEulerTimeStepper(steps)
else:
time_stepper = time_stepper(steps)
# Create and return instationary model
return InstationaryModel(operator=system_lincombOperator,
rhs=rhs_lincombOperator,
parameter_space=parameter_space,
initial_data=u0,
T=T,
time_stepper=time_stepper,
mass=mass_operator,
products=products)