def parabolic_demo():
p = ThermalBlockProblem(parameter_range=(0.01, 1))
d_stat, d_data = discretize_elliptic_cg(p, diameter=1. / 100)
U0 = NumpyVectorArray(np.zeros(d_stat.operator.source.dim))
time_stepper = ImplicitEulerTimeStepper(50)
d = InstationaryDiscretization(operator=d_stat.operator,
rhs=d_stat.rhs,
mass=d_stat.l2_product,
initial_data=U0,
T=1,
products=d_stat.products,
time_stepper=time_stepper,
parameter_space=d_stat.parameter_space,
visualizer=d_stat.visualizer)
mu = next(d.parameter_space.sample_randomly(1))
R = d.solve(mu)
d.visualize(R)
def discretize(grid_and_problem_data, T, nt, polorder):
d, data = discretize_stationary(grid_and_problem_data, polorder)
assert isinstance(d.parameter_space, CubicParameterSpace)
parameter_range = grid_and_problem_data['parameter_range']
d = InstationaryDiscretization(T,
d.operator.source.zeros(1),
d.operator,
d.rhs,
mass=d.operators['l2'],
time_stepper=ImplicitEulerTimeStepper(nt=nt,
solver_options='operator'),
products=d.products,
operators={kk: vv for kk, vv in d.operators.items()
if kk not in ('operator', 'rhs') and vv not in (d.operators, d.rhs)},
visualizer=DuneGDTVisualizer(data['space']))
d = d.with_(parameter_space=CubicParameterSpace(d.parameter_type, parameter_range[0], parameter_range[1]))
return d, data
def parabolic_demo():
p = ThermalBlockProblem(parameter_range=(0.01, 1))
d_stat, d_data = discretize_elliptic_cg(p, diameter=1.0 / 100)
U0 = NumpyVectorArray(np.zeros(d_stat.operator.source.dim))
time_stepper = ImplicitEulerTimeStepper(50)
d = InstationaryDiscretization(
operator=d_stat.operator,
rhs=d_stat.rhs,
mass=d_stat.l2_product,
initial_data=U0,
T=1,
products=d_stat.products,
time_stepper=time_stepper,
parameter_space=d_stat.parameter_space,
visualizer=d_stat.visualizer,
)
mu = next(d.parameter_space.sample_randomly(1))
R = d.solve(mu)
d.visualize(R)
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].data
rhs_data[:] = np.ones(len(rhs_data))
rhs_data[0] = 0
rhs_data[len(rhs_data) - 1] = 0
rhs = VectorFunctional(rhs_vec)
# hack together a visualizer ...
grid = OnedGrid(domain=(0, 1), num_intervals=n)
visualizer = Matplotlib1DVisualizer(grid)
time_stepper = ExplicitEulerTimeStepper(nt)
parameter_space = CubicParameterSpace(operator.parameter_type, 0.1, 1)
d = InstationaryDiscretization(T=1e-0,
operator=operator,
rhs=rhs,
initial_data=initial_data,
time_stepper=time_stepper,
num_values=20,
parameter_space=parameter_space,
visualizer=visualizer,
name='C++-Discretization',
cache_region=None)
return d
def discretize_nonlinear_instationary_advection_fv(analytical_problem,
diameter=None,
nt=100,
num_flux='lax_friedrichs',
lxf_lambda=1.,
eo_gausspoints=5,
eo_intervals=1,
num_values=None,
domain_discretizer=None,
grid=None,
boundary_info=None):
"""Discretizes an |InstationaryAdvectionProblem| using the finite volume method.
Simple explicit Euler time-stepping is used for time-discretization.
Parameters
----------
analytical_problem
The |InstationaryAdvectionProblem| to discretize.
diameter
If not `None`, `diameter` is passed to the `domain_discretizer`.
nt
The number of time-steps.
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.operators.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.)
num_values
The number of returned vectors of the solution trajectory. If `None`, each
intermediate vector that is calculated is returned.
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
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.
Returns
-------
discretization
The |Discretization| that has been generated.
data
Dictionary with the following entries:
:grid: The generated |Grid|.
:boundary_info: The generated |BoundaryInfo|.
"""
assert isinstance(analytical_problem, InstationaryAdvectionProblem)
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 num_flux in ('lax_friedrichs', 'engquist_osher',
'simplified_engquist_osher')
if grid is None:
domain_discretizer = domain_discretizer or discretize_domain_default
if diameter is None:
grid, boundary_info = domain_discretizer(analytical_problem.domain)
else:
grid, boundary_info = domain_discretizer(analytical_problem.domain,
diameter=diameter)
p = analytical_problem
if num_flux == 'lax_friedrichs':
L = nonlinear_advection_lax_friedrichs_operator(
grid,
boundary_info,
p.flux_function,
dirichlet_data=p.dirichlet_data,
lxf_lambda=lxf_lambda)
elif num_flux == 'engquist_osher':
L = nonlinear_advection_engquist_osher_operator(
grid,
boundary_info,
p.flux_function,
p.flux_function_derivative,
gausspoints=eo_gausspoints,
intervals=eo_intervals,
dirichlet_data=p.dirichlet_data)
else:
L = nonlinear_advection_simplified_engquist_osher_operator(
grid,
boundary_info,
p.flux_function,
p.flux_function_derivative,
dirichlet_data=p.dirichlet_data)
F = None if p.rhs is None else L2ProductFunctional(grid, p.rhs)
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 = NumpyVectorArray(I, copy=False)
return I.lincomb(U).data
inject_sid(
initial_projection, __name__ +
'.discretize_nonlinear_instationary_advection_fv.initial_data',
p.initial_data, grid)
I = NumpyGenericOperator(initial_projection,
dim_range=grid.size(0),
linear=True,
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 = NumpyVectorArray(I, copy=False)
inject_sid(
I, __name__ +
'.discretize_nonlinear_instationary_advection_fv.initial_data',
p.initial_data, grid)
products = {'l2': L2Product(grid, boundary_info)}
if grid.dim == 2:
visualizer = PatchVisualizer(grid=grid,
bounding_box=grid.domain,
codim=0)
elif grid.dim == 1:
visualizer = Matplotlib1DVisualizer(grid, codim=0)
else:
visualizer = None
parameter_space = p.parameter_space if hasattr(p,
'parameter_space') else None
time_stepper = ExplicitEulerTimeStepper(nt=nt)
discretization = InstationaryDiscretization(
operator=L,
rhs=F,
initial_data=I,
T=p.T,
products=products,
time_stepper=time_stepper,
parameter_space=parameter_space,
visualizer=visualizer,
num_values=num_values,
name='{}_FV'.format(p.name))
return discretization, {'grid': grid, 'boundary_info': boundary_info}
def discretize_parabolic_fv(analytical_problem, diameter=None, domain_discretizer=None,
grid=None, boundary_info=None, num_values=None, time_stepper=None, nt=None):
"""Discretizes an |ParabolicProblem| using the finite volume method.
Parameters
----------
analytical_problem
The |ParabolicProblem| 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
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 time-stepper to be used by :class:`~pymor.discretizations.basic.InstationaryDiscretization.solve`. Has to
satisfy the :class:`~pymor.algorithms.timestepping.TimeStepperInterface`.
nt
The number of time-steps. If provided implicit euler time-stepping is used.
Returns
-------
discretization
The |Discretization| that has been generated.
data
Dictionary with the following entries:
:grid: The generated |Grid|.
:boundary_info: The generated |BoundaryInfo|.
"""
assert isinstance(analytical_problem, ParabolicProblem)
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 or nt is None
p = analytical_problem
d, data = discretize_elliptic_fv(p.elliptic_part(), diameter=diameter, domain_discretizer=domain_discretizer,
grid=grid, boundary_info=boundary_info)
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 = NumpyVectorArray(I, copy=False)
return I.lincomb(U).data
I = NumpyGenericOperator(initial_projection, dim_range=grid.size(0), linear=True,
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 = NumpyVectorArray(I, copy=False)
if time_stepper is None:
time_stepper = ImplicitEulerTimeStepper(nt=nt)
discretization = InstationaryDiscretization(operator=d.operator, rhs=d.rhs, mass=None, initial_data=I, T=p.T,
products=d.products, time_stepper=time_stepper,
parameter_space=d.parameter_space, visualizer=d.visualizer,
num_values=num_values, name='{}_FV'.format(p.name))
return discretization, data
def discretize_parabolic_cg(analytical_problem, diameter=None, domain_discretizer=None,
grid=None, boundary_info=None, num_values=None, time_stepper=None, nt=None):
"""Discretizes an |ParabolicProblem| using finite elements.
Parameters
----------
analytical_problem
The |ParabolicProblem| 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
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 time-stepper to be used by :class:`~pymor.discretizations.basic.InstationaryDiscretization.solve`. Has to
satisfy the :class:`~pymor.algorithms.timestepping.TimeStepperInterface`.
nt
The number of time-steps. If provided implicit euler time-stepping is used.
Returns
-------
discretization
The |Discretization| that has been generated.
data
Dictionary with the following entries:
:grid: The generated |Grid|.
:boundary_info: The generated |BoundaryInfo|.
"""
assert isinstance(analytical_problem, ParabolicProblem)
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 or nt is None
p = analytical_problem
d, data = discretize_elliptic_cg(p.elliptic_part(), diameter=diameter, domain_discretizer=domain_discretizer,
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 = NumpyVectorArray(I, copy=False)
if time_stepper is None:
time_stepper = ImplicitEulerTimeStepper(nt=nt)
mass = d.l2_0_product
discretization = InstationaryDiscretization(operator=d.operator, rhs=d.rhs, mass=mass, initial_data=I, T=p.T,
products=d.products, time_stepper=time_stepper,
parameter_space=d.parameter_space, visualizer=d.visualizer,
num_values=num_values, name='{}_CG'.format(p.name))
return discretization, data
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 an |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.discretizations.basic.InstationaryDiscretization.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 |Discretization|.
Returns
-------
d
The |Discretization| that has been generated.
data
Dictionary with the following entries:
:grid: The generated |Grid|.
:boundary_info: The generated |BoundaryInfo|.
"""
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
d, 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 = d.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 = d.l2_0_product
d = InstationaryDiscretization(operator=d.operator,
rhs=d.rhs,
mass=mass,
initial_data=I,
T=p.T,
products=d.products,
time_stepper=time_stepper,
parameter_space=p.parameter_space,
visualizer=d.visualizer,
num_values=num_values,
name='{}_CG'.format(p.name))
if preassemble:
data['unassembled_d'] = d
d = preassemble_(d)
return d, data
def discretize_instationary_from_disk(parameter_file, T=None, steps=None, u0=None, time_stepper=None):
"""Generates instationary discretization based on data given loaded from files.
The path and further specifications to these objects are given in an '.ini'
parameter file (see example below). Suitable for discrete problems given by::
M(u(t), w) + L(u(t), w, t) = F(t, w)
u(0) = u_0
for t in [0,T], where L is a linear time-dependent
|Operator|, F is a time-dependent linear |Functional|, u_0 the
initial data and w the parameter. The mass |Operator| M is assumed to be linear,
time-independent and |Parameter|-independent.
Parameters
----------
parameter_file
String containing the path to the '.ini' parameter file.
T
End-time of desired solution, if None obtained from parameter file
steps
Number of time steps to do, if None obtained from parameter file
u0
Initial solution, if None obtained from parameter file
time_stepper
The desired time_stepper to use, if None an Implicit euler scheme is used.
Returns
-------
discretization
The |Discretization| that has been generated.
Example
-------
Following parameter file is suitable for a discrete parabolic problem with
L(u(w), w) = (f_1(w)*K1 + f_2(w)*K2+...)*u, F(w) = g_1(w)*L1+g_2(w)*L2+..., M = D and
u_0(w)=u0 with parameter w_i in [a_i,b_i], where f_i(w) and g_i(w) are strings of valid python
expressions.
Optional products can be provided to introduce a dict of inner products on the discrete space.
Time specifications like T and steps can also be provided, but are optional when already given
by call of this method. The content of the file is then given as::
[system-matrices]
# path_to_object: parameter_functional_associated_with_object
K1.mat: f_1(w_1,...,w_n)
K2.mat: f_2(w_1,...,w_n)
...
[rhs-vectors]
L1.mat: g_1(w_1,...,w_n)
L2.mat: g_2(w_1,...,w_n)
...
[mass-matrix]
D.mat
[initial-solution]
u0: u0.mat
[parameter]
# Name: lower_bound,upper_bound
w_1: a_1,b_1
...
w_n: a_n,b_n
[products]
# Name: path_to_object
Prod1: S.mat
Prod2: T.mat
...
[time]
# fixed_Name: value
T: 10.0
steps: 100
"""
assert ".ini" == parameter_file[-4:], "Given file is not an .ini 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))
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)
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)
# 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)
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)
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 discretization
return InstationaryDiscretization(operator=system_lincombOperator, rhs=rhs_lincombOperator,
parameter_space=parameter_space, initial_data=u0, T=T,
time_stepper=time_stepper, mass=mass_operator, products=products)
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 an |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.operators.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.TimeStepperInterface>`
to be used by :class:`~pymor.discretizations.basic.InstationaryDiscretization.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 |Discretization|.
Returns
-------
discretization
The |Discretization| that has been generated.
data
Dictionary with the following entries:
:grid: The generated |Grid|.
:boundary_info: The generated |BoundaryInfo|.
"""
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
d, 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 = d.solution_space.make_array(I)
return I.lincomb(U).data
I = NumpyGenericOperator(initial_projection,
dim_range=grid.size(0),
linear=True,
range_id=d.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 = d.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(d.rhs, ZeroOperator) else d.rhs
discretization = InstationaryDiscretization(
operator=d.operator,
rhs=rhs,
mass=None,
initial_data=I,
T=p.T,
products=d.products,
time_stepper=time_stepper,
parameter_space=p.parameter_space,
visualizer=d.visualizer,
num_values=num_values,
name='{}_FV'.format(p.name))
if preassemble:
data['unassembled_discretization'] = discretization
discretization = preassemble_(discretization)
return discretization, data
def discretize_instationary_from_disk(parameter_file,
T=None,
steps=None,
u0=None,
time_stepper=None):
"""Load a linear affinely decomposed |InstationaryDiscretization| from file.
Similarly to :func:`discretize_stationary_from_disk`, the discretization 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.TimeStepperInterface>`
to use. If `None`, implicit Euler time stepping is used.
Returns
-------
discretization
The |InstationaryDiscretization| 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, source_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 discretization
return InstationaryDiscretization(operator=system_lincombOperator,
rhs=rhs_lincombOperator,
parameter_space=parameter_space,
initial_data=u0,
T=T,
time_stepper=time_stepper,
mass=mass_operator,
products=products)
def reductor(discretization,
RB,
vector_product=None,
disable_caching=True,
extends=None):
if RB is None:
RB = [
stat_blocked_disc.local_operator(ss).source.empty()
for ss in np.arange(stat_blocked_disc.num_subdomains)
]
rd, rc, reduction_data = reduce_generic_rb(stat_blocked_disc, RB,
vector_product, disable_caching,
extends)
def unblock_op(op):
assert op._blocks[0][0] is not None
if isinstance(op._blocks[0][0], LincombOperator):
coefficients = op._blocks[0][0].coefficients
operators = [
None for kk in np.arange(len(op._blocks[0][0].operators))
]
for kk in np.arange(len(op._blocks[0][0].operators)):
ops = [[
op._blocks[ii][jj].operators[kk]
if op._blocks[ii][jj] is not None else None
for jj in np.arange(op.num_source_blocks)
] for ii in np.arange(op.num_range_blocks)]
operators[kk] = unblock_op(BlockOperator(ops))
return LincombOperator(operators=operators,
coefficients=coefficients)
else:
assert all(
all([
isinstance(block, NumpyMatrixOperator
) if block is not None else True
for block in row
]) for row in op._blocks)
if op.source.dim == 0 and op.range.dim == 0:
return NumpyMatrixOperator(np.zeros((0, 0)))
elif op.source.dim == 1:
mat = np.concatenate([
op._blocks[ii][0]._matrix
for ii in np.arange(op.num_range_blocks)
],
axis=1)
elif op.range.dim == 1:
mat = np.concatenate([
op._blocks[0][jj]._matrix
for jj in np.arange(op.num_source_blocks)
],
axis=1)
else:
mat = bmat([[
coo_matrix(op._blocks[ii][jj]._matrix)
if op._blocks[ii][jj] is not None else coo_matrix(
(op._range_dims[ii], op._source_dims[jj]))
for jj in np.arange(op.num_source_blocks)
] for ii in np.arange(op.num_range_blocks)]).toarray()
return NumpyMatrixOperator(mat)
reduced_op = unblock_op(rd.operator)
reduced_rhs = unblock_op(rd.rhs)
return (InstationaryDiscretization(
T=config['end_time'],
initial_data=reduced_op.source.zeros(1),
operator=reduced_op,
rhs=unblock_op(rd.rhs),
mass=unblock_op(rd.products['l2']),
time_stepper=ImplicitEulerTimeStepper(config['nt']),
products={
kk: unblock_op(rd.products[kk])
for kk in rd.products.keys()
},
operators={
kk: unblock_op(rd.operators[kk])
for kk in rd.operators.keys() if kk != 'operator'
},
functionals={
kk: unblock_op(rd.functionals[kk])
for kk in rd.functionals.keys() if kk != 'rhs'
},
vector_operators={
kk: unblock_op(rd.vector_operators[kk])
for kk in rd.vector_operators.keys()
},
parameter_space=rd.parameter_space,
cache_region='disk',
name='reduced non-blocked discretization'),
Reconstructor(stat_blocked_disc, RB), reduction_data)
stat_nonblocked_disc.solution_space.dim))
logger.info(' parameter type is {}'.format(
stat_nonblocked_disc.parameter_type))
# logger.info('visualizing grid and data functions ...')
# example.visualize(problem_cfg.get_str('type'))
nonblocked_disc = InstationaryDiscretization(
T=config['end_time'],
initial_data=make_listvectorarray(
wrapper[stat_nonblocked_disc._impl.create_vector()]),
operator=stat_nonblocked_disc.operator,
rhs=stat_nonblocked_disc.rhs,
mass=stat_nonblocked_disc.products['l2'],
time_stepper=ImplicitEulerTimeStepper(
config['nt'], invert_options=solver_options.get_str('type')),
products=stat_nonblocked_disc.products,
operators=stat_nonblocked_disc.operators,
functionals=stat_nonblocked_disc.functionals,
vector_operators=stat_nonblocked_disc.vector_operators,
visualizer=InstationaryDuneVisualizer(
stat_nonblocked_disc,
problem_cfg.get_str('type') + '.solution'),
parameter_space=CubicParameterSpace(stat_nonblocked_disc.parameter_type,
0.1, 10),
cache_region='disk',
name='detailed non-blocked discretization')
# mu = 0.6
# U = nonblocked_disc.solve(mu)
# logger.info('visualizing trajectory ...')
# nonblocked_disc.visualize(U)
def reductor(config,
detailed_data,
discretization,
RB,
vector_product=None,
disable_caching=True,
extends=None):
elliptic_disc = detailed_data['elliptic_disc']
elliptic_LRBMS_disc = detailed_data['elliptic_LRBMS_disc']
T = config['end_time']
nt = config['nt']
if RB is None:
RB = [
elliptic_LRBMS_disc.local_operator(ss).source.empty()
for ss in np.arange(elliptic_LRBMS_disc.num_subdomains)
]
rd, rc, reduction_data = reduce_generic_rb(elliptic_LRBMS_disc, RB,
vector_product, disable_caching,
extends)
rc = Reconstructor(elliptic_LRBMS_disc, RB)
def unblock_op(op, sparse=False):
assert op._blocks[0][0] is not None
if isinstance(op._blocks[0][0], LincombOperator):
coefficients = op._blocks[0][0].coefficients
operators = [
None for kk in np.arange(len(op._blocks[0][0].operators))
]
for kk in np.arange(len(op._blocks[0][0].operators)):
ops = [[
op._blocks[ii][jj].operators[kk]
if op._blocks[ii][jj] is not None else None
for jj in np.arange(op.num_source_blocks)
] for ii in np.arange(op.num_range_blocks)]
operators[kk] = unblock_op(BlockOperator(ops))
return LincombOperator(operators=operators,
coefficients=coefficients)
else:
assert all(
all([
isinstance(block, NumpyMatrixOperator
) if block is not None else True
for block in row
]) for row in op._blocks)
if op.source.dim == 0 and op.range.dim == 0:
return NumpyMatrixOperator(np.zeros((0, 0)))
elif op.source.dim == 1:
mat = np.concatenate([
op._blocks[ii][0]._matrix
for ii in np.arange(op.num_range_blocks)
],
axis=1)
elif op.range.dim == 1:
mat = np.concatenate([
op._blocks[0][jj]._matrix
for jj in np.arange(op.num_source_blocks)
],
axis=1)
else:
mat = bmat([[
coo_matrix(op._blocks[ii][jj]._matrix)
if op._blocks[ii][jj] is not None else coo_matrix(
(op._range_dims[ii], op._source_dims[jj]))
for jj in np.arange(op.num_source_blocks)
] for ii in np.arange(op.num_range_blocks)])
mat = mat.toarray()
return NumpyMatrixOperator(mat)
reduced_op = unblock_op(rd.operator, True)
reduced_rhs = unblock_op(rd.rhs)
estimator = ReducedAgainstWeak(
rc, detailed_data['example'], detailed_data['wrapper'],
detailed_data['bochner_norms']['elliptic_penalty'],
detailed_data['space_products']['l2'], T, detailed_data['mu_min'],
detailed_data['mu_max'], detailed_data['mu_hat'],
detailed_data['mu_bar'], detailed_data['mu_tilde'])
return (InstationaryDiscretization(
T=T,
initial_data=reduced_op.source.zeros(1),
operator=reduced_op,
rhs=unblock_op(rd.rhs),
mass=unblock_op(rd.products['l2']),
time_stepper=ImplicitEulerTimeStepper(nt),
products={
kk: unblock_op(rd.products[kk])
for kk in rd.products.keys()
},
operators={
kk: unblock_op(rd.operators[kk])
for kk in rd.operators.keys() if kk != 'operator'
},
functionals={
kk: unblock_op(rd.functionals[kk])
for kk in rd.functionals.keys() if kk != 'rhs'
},
vector_operators={
kk: unblock_op(rd.vector_operators[kk])
for kk in rd.vector_operators.keys()
},
parameter_space=rd.parameter_space,
estimator=estimator,
cache_region='disk',
name='reduced discretization ({} DoFs)'.format(reduced_op.source.dim)),
rc, reduction_data)
def discretize(num_elements,
num_partitions,
T,
nt,
initial_data,
parameter_range,
name='detailed discretization'):
Example = examples[2]['aluconformgrid']['fem']['istl']
logger_cfg = Example.logger_options()
logger_cfg.set('info', -1, True)
logger_cfg.set('info_color', 'blue', True)
grid_cfg = Example.grid_options('grid.multiscale.provider.cube')
grid_cfg.set('lower_left', '[0 0]', True)
grid_cfg.set('upper_right', '[5 1]', True)
grid_cfg.set('num_elements', num_elements, True)
grid_cfg.set('num_partitions', num_partitions, True)
boundary_cfg = Example.boundary_options(
'stuff.grid.boundaryinfo.alldirichlet')
problem_cfg = Example.problem_options(
'hdd.linearelliptic.problem.OS2015.spe10model1')
problem_cfg.set('parametric_channel', 'true', True)
problem_cfg.set('channel_boundary_layer', '0', True)
problem_cfg.set('filename', 'perm_case1.dat', True)
problem_cfg.set('lower_left', '[0 0]', True)
problem_cfg.set('upper_right', '[5 1]', True)
problem_cfg.set('num_elements', '[100 20]', True)
problem_cfg.set('forces.0.domain', '[0.95 1.10; 0.30 0.45]', True)
problem_cfg.set('forces.0.value', '2000', True)
problem_cfg.set('forces.1.domain', '[3.00 3.15; 0.75 0.90]', True)
problem_cfg.set('forces.1.value', '-1000', True)
problem_cfg.set('forces.2.domain', '[4.25 4.40; 0.25 0.40]', True)
problem_cfg.set('forces.2.value', '-1000', True)
problem_cfg.set('channel.0.value', '-1.07763239495', True)
problem_cfg.set('channel.1.value', '-1.07699512772', True)
problem_cfg.set('channel.2.value', '-1.07356156439', True)
problem_cfg.set('channel.3.value', '-1.06602281736', True)
problem_cfg.set('channel.4.value', '-1.06503683743', True)
problem_cfg.set('channel.5.value', '-1.07974870426', True)
problem_cfg.set('channel.6.value', '-1.05665895923', True)
problem_cfg.set('channel.7.value', '-1.08310334837', True)
problem_cfg.set('channel.8.value', '-1.05865484973', True)
problem_cfg.set('channel.9.value', '-1.05871039535', True)
problem_cfg.set('channel.10.value', '-1.08136695901', True)
problem_cfg.set('channel.11.value', '-1.08490172721', True)
problem_cfg.set('channel.12.value', '-1.06641120758', True)
problem_cfg.set('channel.13.value', '-1.06812773298', True)
problem_cfg.set('channel.14.value', '-1.07695652049', True)
problem_cfg.set('channel.15.value', '-1.08630079205', True)
problem_cfg.set('channel.16.value', '-1.08273722112', True)
problem_cfg.set('channel.17.value', '-1.07500402155', True)
problem_cfg.set('channel.18.value', '-1.08607142562', True)
problem_cfg.set('channel.19.value', '-1.07268761799', True)
problem_cfg.set('channel.20.value', '-1.08537037362', True)
problem_cfg.set('channel.21.value', '-1.08466927273', True)
problem_cfg.set('channel.22.value', '-1.08444661815', True)
problem_cfg.set('channel.23.value', '-1.08957037967', True)
problem_cfg.set('channel.24.value', '-1.08047394052', True)
problem_cfg.set('channel.25.value', '-1.08221229083', True)
problem_cfg.set('channel.26.value', '-1.08568599863', True)
problem_cfg.set('channel.27.value', '-1.08428347872', True)
problem_cfg.set('channel.28.value', '-1.09104098734', True)
problem_cfg.set('channel.29.value', '-1.09492700673', True)
problem_cfg.set('channel.30.value', '-1.09760440537', True)
problem_cfg.set('channel.31.value', '-1.09644989453', True)
problem_cfg.set('channel.32.value', '-1.09441681025', True)
problem_cfg.set('channel.33.value', '-1.09533290654', True)
problem_cfg.set('channel.34.value', '-1.1001430808', True)
problem_cfg.set('channel.35.value', '-1.10065627621', True)
problem_cfg.set('channel.36.value', '-1.10125877186', True)
problem_cfg.set('channel.37.value', '-1.10057485893', True)
problem_cfg.set('channel.38.value', '-1.10002261906', True)
problem_cfg.set('channel.39.value', '-1.10219154209', True)
problem_cfg.set('channel.40.value', '-1.09994463801', True)
problem_cfg.set('channel.41.value', '-1.10265630533', True)
problem_cfg.set('channel.42.value', '-1.10448566526', True)
problem_cfg.set('channel.43.value', '-1.10735820121', True)
problem_cfg.set('channel.44.value', '-1.1070022367', True)
problem_cfg.set('channel.45.value', '-1.10777650387', True)
problem_cfg.set('channel.46.value', '-1.10892785562', True)
problem_cfg.set('channel.0.domain', '[1.7 1.75; 0.5 0.55]', True)
problem_cfg.set('channel.1.domain', '[1.75 1.8; 0.5 0.55]', True)
problem_cfg.set('channel.2.domain', '[1.8 1.85; 0.5 0.55]', True)
problem_cfg.set('channel.3.domain', '[1.85 1.9; 0.5 0.55]', True)
problem_cfg.set('channel.4.domain', '[1.9 1.95; 0.5 0.55]', True)
problem_cfg.set('channel.5.domain', '[1.95 2.0; 0.5 0.55]', True)
problem_cfg.set('channel.6.domain', '[2.0 2.05; 0.5 0.55]', True)
problem_cfg.set('channel.7.domain', '[2.05 2.1; 0.5 0.55]', True)
problem_cfg.set('channel.8.domain', '[2.1 2.15; 0.5 0.55]', True)
problem_cfg.set('channel.9.domain', '[2.15 2.2; 0.5 0.55]', True)
problem_cfg.set('channel.10.domain', '[2.2 2.25; 0.5 0.55]', True)
problem_cfg.set('channel.11.domain', '[2.25 2.3; 0.5 0.55]', True)
problem_cfg.set('channel.12.domain', '[2.3 2.35; 0.5 0.55]', True)
problem_cfg.set('channel.13.domain', '[2.35 2.4; 0.5 0.55]', True)
problem_cfg.set('channel.14.domain', '[2.4 2.45; 0.5 0.55]', True)
problem_cfg.set('channel.15.domain', '[2.45 2.5; 0.5 0.55]', True)
problem_cfg.set('channel.16.domain', '[2.5 2.55; 0.5 0.55]', True)
problem_cfg.set('channel.17.domain', '[2.55 2.6; 0.5 0.55]', True)
problem_cfg.set('channel.18.domain', '[2.6 2.65; 0.5 0.55]', True)
problem_cfg.set('channel.19.domain', '[2.65 2.7; 0.5 0.55]', True)
problem_cfg.set('channel.20.domain', '[2.7 2.75; 0.5 0.55]', True)
problem_cfg.set('channel.21.domain', '[2.75 2.8; 0.5 0.55]', True)
problem_cfg.set('channel.22.domain', '[2.8 2.85; 0.5 0.55]', True)
problem_cfg.set('channel.23.domain', '[2.85 2.9; 0.5 0.55]', True)
problem_cfg.set('channel.24.domain', '[2.9 2.95; 0.5 0.55]', True)
problem_cfg.set('channel.25.domain', '[2.95 3.0; 0.5 0.55]', True)
problem_cfg.set('channel.26.domain', '[3.0 3.05; 0.5 0.55]', True)
problem_cfg.set('channel.27.domain', '[3.05 3.1; 0.5 0.55]', True)
problem_cfg.set('channel.28.domain', '[3.1 3.15; 0.5 0.55]', True)
problem_cfg.set('channel.29.domain', '[3.15 3.2; 0.5 0.55]', True)
problem_cfg.set('channel.30.domain', '[3.2 3.25; 0.5 0.55]', True)
problem_cfg.set('channel.31.domain', '[3.25 3.3; 0.5 0.55]', True)
problem_cfg.set('channel.32.domain', '[3.3 3.35; 0.5 0.55]', True)
problem_cfg.set('channel.33.domain', '[3.35 3.4; 0.5 0.55]', True)
problem_cfg.set('channel.34.domain', '[3.4 3.45; 0.5 0.55]', True)
problem_cfg.set('channel.35.domain', '[3.45 3.5; 0.5 0.55]', True)
problem_cfg.set('channel.36.domain', '[3.5 3.55; 0.5 0.55]', True)
problem_cfg.set('channel.37.domain', '[3.55 3.6; 0.5 0.55]', True)
problem_cfg.set('channel.38.domain', '[3.6 3.65; 0.5 0.55]', True)
problem_cfg.set('channel.39.domain', '[3.65 3.7; 0.5 0.55]', True)
problem_cfg.set('channel.40.domain', '[3.7 3.75; 0.5 0.55]', True)
problem_cfg.set('channel.41.domain', '[3.75 3.8; 0.5 0.55]', True)
problem_cfg.set('channel.42.domain', '[3.8 3.85; 0.5 0.55]', True)
problem_cfg.set('channel.43.domain', '[3.85 3.9; 0.5 0.55]', True)
problem_cfg.set('channel.44.domain', '[3.9 3.95; 0.5 0.55]', True)
problem_cfg.set('channel.45.domain', '[3.95 4.0; 0.5 0.55]', True)
problem_cfg.set('channel.46.domain', '[4.0 4.05; 0.5 0.55]', True)
problem_cfg.set('channel.47.value', '-1.10372589211', True)
problem_cfg.set('channel.48.value', '-1.1020889988', True)
problem_cfg.set('channel.49.value', '-1.09806955069', True)
problem_cfg.set('channel.50.value', '-1.10000902421', True)
problem_cfg.set('channel.51.value', '-1.08797468724', True)
problem_cfg.set('channel.52.value', '-1.08827472176', True)
problem_cfg.set('channel.53.value', '-1.08692237109', True)
problem_cfg.set('channel.54.value', '-1.07893190093', True)
problem_cfg.set('channel.55.value', '-1.08748373853', True)
problem_cfg.set('channel.56.value', '-1.07445197324', True)
problem_cfg.set('channel.57.value', '-1.08246613163', True)
problem_cfg.set('channel.58.value', '-1.06726790504', True)
problem_cfg.set('channel.59.value', '-1.07891217847', True)
problem_cfg.set('channel.60.value', '-1.07260827126', True)
problem_cfg.set('channel.61.value', '-1.07094062748', True)
problem_cfg.set('channel.62.value', '-1.0692399429', True)
problem_cfg.set('channel.63.value', '-1.00099885701', True)
problem_cfg.set('channel.64.value', '-1.00109544002', True)
problem_cfg.set('channel.65.value', '-0.966491003242', True)
problem_cfg.set('channel.66.value', '-0.802284684014', True)
problem_cfg.set('channel.67.value', '-0.980790923021', True)
problem_cfg.set('channel.68.value', '-0.614478271687', True)
problem_cfg.set('channel.69.value', '-0.288129858959', True)
problem_cfg.set('channel.70.value', '-0.929509396842', True)
problem_cfg.set('channel.71.value', '-0.992376505995', True)
problem_cfg.set('channel.72.value', '-0.968162494855', True)
problem_cfg.set('channel.73.value', '-0.397316938901', True)
problem_cfg.set('channel.74.value', '-0.970934956609', True)
problem_cfg.set('channel.75.value', '-0.784344730096', True)
problem_cfg.set('channel.76.value', '-0.539725422323', True)
problem_cfg.set('channel.77.value', '-0.915632282372', True)
problem_cfg.set('channel.78.value', '-0.275089177273', True)
problem_cfg.set('channel.79.value', '-0.949684959286', True)
problem_cfg.set('channel.80.value', '-0.936132529794', True)
problem_cfg.set('channel.47.domain', '[2.6 2.65; 0.45 0.50]', True)
problem_cfg.set('channel.48.domain', '[2.65 2.7; 0.45 0.50]', True)
problem_cfg.set('channel.49.domain', '[2.7 2.75; 0.45 0.50]', True)
problem_cfg.set('channel.50.domain', '[2.75 2.8; 0.45 0.50]', True)
problem_cfg.set('channel.51.domain', '[2.8 2.85; 0.45 0.50]', True)
problem_cfg.set('channel.52.domain', '[2.85 2.9; 0.45 0.50]', True)
problem_cfg.set('channel.53.domain', '[2.9 2.95; 0.45 0.50]', True)
problem_cfg.set('channel.54.domain', '[2.95 3.0; 0.45 0.50]', True)
problem_cfg.set('channel.55.domain', '[3.0 3.05; 0.45 0.50]', True)
problem_cfg.set('channel.56.domain', '[3.05 3.1; 0.45 0.50]', True)
problem_cfg.set('channel.57.domain', '[3.1 3.15; 0.45 0.50]', True)
problem_cfg.set('channel.58.domain', '[3.15 3.2; 0.45 0.50]', True)
problem_cfg.set('channel.59.domain', '[3.2 3.25; 0.45 0.50]', True)
problem_cfg.set('channel.60.domain', '[3.25 3.3; 0.45 0.50]', True)
problem_cfg.set('channel.61.domain', '[3.3 3.35; 0.45 0.50]', True)
problem_cfg.set('channel.62.domain', '[3.35 3.4; 0.45 0.50]', True)
problem_cfg.set('channel.63.domain', '[3.4 3.45; 0.45 0.50]', True)
problem_cfg.set('channel.64.domain', '[3.45 3.5; 0.45 0.50]', True)
problem_cfg.set('channel.65.domain', '[3.5 3.55; 0.45 0.50]', True)
problem_cfg.set('channel.66.domain', '[3.55 3.6; 0.45 0.50]', True)
problem_cfg.set('channel.67.domain', '[3.6 3.65; 0.45 0.50]', True)
problem_cfg.set('channel.68.domain', '[3.65 3.7; 0.45 0.50]', True)
problem_cfg.set('channel.69.domain', '[3.7 3.75; 0.45 0.50]', True)
problem_cfg.set('channel.70.domain', '[3.75 3.8; 0.45 0.50]', True)
problem_cfg.set('channel.71.domain', '[3.8 3.85; 0.45 0.50]', True)
problem_cfg.set('channel.72.domain', '[3.85 3.9; 0.45 0.50]', True)
problem_cfg.set('channel.73.domain', '[3.9 3.95; 0.45 0.50]', True)
problem_cfg.set('channel.74.domain', '[3.95 4.0; 0.45 0.50]', True)
problem_cfg.set('channel.75.domain', '[4.0 4.05; 0.45 0.50]', True)
problem_cfg.set('channel.76.domain', '[4.05 4.1; 0.45 0.50]', True)
problem_cfg.set('channel.77.domain', '[4.1 4.15; 0.45 0.50]', True)
problem_cfg.set('channel.78.domain', '[4.15 4.2; 0.45 0.50]', True)
problem_cfg.set('channel.79.domain', '[4.2 4.25; 0.45 0.50]', True)
problem_cfg.set('channel.80.domain', '[4.25 4.3; 0.45 0.50]', True)
problem_cfg.set('channel.81.value', '-1.10923642795', True)
problem_cfg.set('channel.82.value', '-1.10685618623', True)
problem_cfg.set('channel.83.value', '-1.1057800376', True)
problem_cfg.set('channel.84.value', '-1.10187723629', True)
problem_cfg.set('channel.85.value', '-1.10351710464', True)
problem_cfg.set('channel.86.value', '-1.10037551137', True)
problem_cfg.set('channel.87.value', '-1.09724407076', True)
problem_cfg.set('channel.88.value', '-1.09604600208', True)
problem_cfg.set('channel.89.value', '-1.09354469656', True)
problem_cfg.set('channel.90.value', '-1.08934455354', True)
problem_cfg.set('channel.91.value', '-1.08155476586', True)
problem_cfg.set('channel.92.value', '-1.07815397899', True)
problem_cfg.set('channel.93.value', '-1.09174062023', True)
problem_cfg.set('channel.94.value', '-1.07433616068', True)
problem_cfg.set('channel.95.value', '-1.08030587701', True)
problem_cfg.set('channel.81.domain', '[1.95 2.0; 0.40 0.45]', True)
problem_cfg.set('channel.82.domain', '[2.0 2.05; 0.40 0.45]', True)
problem_cfg.set('channel.83.domain', '[2.05 2.1; 0.40 0.45]', True)
problem_cfg.set('channel.84.domain', '[2.1 2.15; 0.40 0.45]', True)
problem_cfg.set('channel.85.domain', '[2.15 2.2; 0.40 0.45]', True)
problem_cfg.set('channel.86.domain', '[2.2 2.25; 0.40 0.45]', True)
problem_cfg.set('channel.87.domain', '[2.25 2.3; 0.40 0.45]', True)
problem_cfg.set('channel.88.domain', '[2.3 2.35; 0.40 0.45]', True)
problem_cfg.set('channel.89.domain', '[2.35 2.4; 0.40 0.45]', True)
problem_cfg.set('channel.90.domain', '[2.4 2.45; 0.40 0.45]', True)
problem_cfg.set('channel.91.domain', '[2.45 2.5; 0.40 0.45]', True)
problem_cfg.set('channel.92.domain', '[2.5 2.55; 0.40 0.45]', True)
problem_cfg.set('channel.93.domain', '[2.55 2.6; 0.40 0.45]', True)
problem_cfg.set('channel.94.domain', '[2.6 2.65; 0.40 0.45]', True)
problem_cfg.set('channel.95.domain', '[2.65 2.7; 0.40 0.45]', True)
problem_cfg.set('channel.96.value', '-1.00032869407', True)
problem_cfg.set('channel.97.value', '-1.01175908905', True)
problem_cfg.set('channel.98.value', '-1.04954395793', True)
problem_cfg.set('channel.99.value', '-1.017967697', True)
problem_cfg.set('channel.100.value', '-1.04647184091', True)
problem_cfg.set('channel.101.value', '-1.01911894831', True)
problem_cfg.set('channel.102.value', '-1.00699340158', True)
problem_cfg.set('channel.103.value', '-0.995492960025', True)
problem_cfg.set('channel.104.value', '-1.0373059007', True)
problem_cfg.set('channel.96.domain', '[2.25 2.3; 0.35 0.40]', True)
problem_cfg.set('channel.97.domain', '[2.3 2.35; 0.35 0.40]', True)
problem_cfg.set('channel.98.domain', '[2.35 2.4; 0.35 0.40]', True)
problem_cfg.set('channel.99.domain', '[2.4 2.45; 0.35 0.40]', True)
problem_cfg.set('channel.100.domain', '[2.45 2.5; 0.35 0.40]', True)
problem_cfg.set('channel.101.domain', '[2.5 2.55; 0.35 0.40]', True)
problem_cfg.set('channel.102.domain', '[2.55 2.6; 0.35 0.40]', True)
problem_cfg.set('channel.103.domain', '[2.6 2.65; 0.35 0.40]', True)
problem_cfg.set('channel.104.domain', '[2.65 2.7; 0.35 0.4]', True)
example = Example(logger_cfg, grid_cfg, boundary_cfg, problem_cfg,
['l2', 'h1', 'elliptic_penalty'])
elliptic_LRBMS_disc = wrapper[example.discretization()]
parameter_space = CubicParameterSpace(elliptic_LRBMS_disc.parameter_type,
parameter_range[0],
parameter_range[1])
elliptic_LRBMS_disc = elliptic_LRBMS_disc.with_(
parameter_space=parameter_space)
elliptic_disc = elliptic_LRBMS_disc.as_nonblocked().with_(
parameter_space=parameter_space)
def prolong(coarse_disc, coarse_U):
time_grid_ref = OnedGrid(domain=(0., T), num_intervals=nt)
time_grid = OnedGrid(domain=(0., T), num_intervals=(len(coarse_U) - 1))
U_fine = [None for ii in time_grid_ref.centers(1)]
for n in np.arange(len(time_grid_ref.centers(1))):
t_n = time_grid_ref.centers(1)[n]
coarse_entity = min((time_grid.centers(1) <= t_n).nonzero()[0][-1],
time_grid.size(0) - 1)
a = time_grid.centers(1)[coarse_entity]
b = time_grid.centers(1)[coarse_entity + 1]
SF = np.array((1. / (a - b) * t_n - b / (a - b),
1. / (b - a) * t_n - a / (b - a)))
U_t = coarse_U.copy(ind=coarse_entity)
U_t.scal(SF[0][0])
U_t.axpy(SF[1][0], coarse_U, x_ind=(coarse_entity + 1))
U_fine[n] = wrapper[example.prolong(coarse_disc._impl,
U_t._list[0]._impl)]
return make_listvectorarray(U_fine)
if isinstance(initial_data, str):
initial_data = make_listvectorarray(
wrapper[example.project(initial_data)])
# initial_data = elliptic_disc.operator.apply_inverse(initial_data, mu=(1, 1))
else:
coarse_disc = initial_data[0]
initial_data = initial_data[1]
assert len(initial_data) == 1
initial_data = example.prolong(coarse_disc._impl,
initial_data._list[0]._impl)
initial_data = make_listvectorarray(wrapper[initial_data])
parabolic_disc = InstationaryDiscretization(
T=T,
initial_data=initial_data,
operator=elliptic_disc.operator,
rhs=elliptic_disc.rhs,
mass=elliptic_disc.products['l2'],
time_stepper=ImplicitEulerTimeStepper(nt, solver_options='operator'),
products=elliptic_disc.products,
operators=elliptic_disc.operators,
functionals=elliptic_disc.functionals,
vector_operators=elliptic_disc.vector_operators,
visualizer=InstationaryDuneVisualizer(elliptic_disc,
'dune_discretization.solution'),
parameter_space=parameter_space,
cache_region='disk',
name='{} ({} DoFs)'.format(name, elliptic_disc.solution_space.dim))
return {
'example': example,
'initial_data': initial_data,
'wrapper': wrapper,
'elliptic_LRBMS_disc': elliptic_LRBMS_disc,
'elliptic_disc': elliptic_disc,
'parabolic_disc': parabolic_disc,
'prolongator': prolong
}