# This file is part of the pyMOR project (http://www.pymor.org).
# Copyright 2013-2019 pyMOR developers and contributors. All rights reserved.
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
from functools import partial
from pymor.algorithms.timestepping import ExplicitEulerTimeStepper, ImplicitEulerTimeStepper
from pymor.algorithms.preassemble import preassemble as preassemble_
from pymor.analyticalproblems.elliptic import StationaryProblem
from pymor.analyticalproblems.instationary import InstationaryProblem
from pymor.models.basic import StationaryModel, InstationaryModel
from pymor.domaindiscretizers.default import discretize_domain_default
from pymor.functions.basic import ConstantFunction, LincombFunction
from pymor.grids.boundaryinfos import EmptyBoundaryInfo
from pymor.grids.referenceelements import line, triangle, square
from pymor.gui.visualizers import PatchVisualizer, OnedVisualizer
from pymor.operators.cg import (DiffusionOperatorP1, DiffusionOperatorQ1,
AdvectionOperatorP1, AdvectionOperatorQ1,
L2ProductP1, L2ProductQ1,
L2ProductFunctionalP1, L2ProductFunctionalQ1,
BoundaryL2ProductFunctional,
BoundaryDirichletFunctional, RobinBoundaryOperator, InterpolationOperator)
from pymor.operators.constructions import LincombOperator
[docs]def discretize_stationary_cg(analytical_problem, diameter=None, domain_discretizer=None,
grid_type=None, grid=None, boundary_info=None,
preassemble=True):
"""Discretizes a |StationaryProblem| using finite elements.
Parameters
----------
analytical_problem
The |StationaryProblem| 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.
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, 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 grid_type is None or grid is None
p = analytical_problem
if not (p.nonlinear_advection
== p.nonlinear_advection_derivative
== p.nonlinear_reaction
== p.nonlinear_reaction_derivative
is None):
raise NotImplementedError
if grid is None:
domain_discretizer = domain_discretizer or discretize_domain_default
if grid_type:
domain_discretizer = partial(domain_discretizer, grid_type=grid_type)
if diameter is None:
grid, boundary_info = domain_discretizer(p.domain)
else:
grid, boundary_info = domain_discretizer(p.domain, diameter=diameter)
assert grid.reference_element in (line, triangle, square)
if grid.reference_element is square:
DiffusionOperator = DiffusionOperatorQ1
AdvectionOperator = AdvectionOperatorQ1
ReactionOperator = L2ProductQ1
L2Functional = L2ProductFunctionalQ1
BoundaryL2Functional = BoundaryL2ProductFunctional
else:
DiffusionOperator = DiffusionOperatorP1
AdvectionOperator = AdvectionOperatorP1
ReactionOperator = L2ProductP1
L2Functional = L2ProductFunctionalP1
BoundaryL2Functional = BoundaryL2ProductFunctional
Li = [DiffusionOperator(grid, boundary_info, diffusion_constant=0, name='boundary_part')]
coefficients = [1.]
# diffusion part
if isinstance(p.diffusion, LincombFunction):
Li += [DiffusionOperator(grid, boundary_info, diffusion_function=df, dirichlet_clear_diag=True,
name=f'diffusion_{i}')
for i, df in enumerate(p.diffusion.functions)]
coefficients += list(p.diffusion.coefficients)
elif p.diffusion is not None:
Li += [DiffusionOperator(grid, boundary_info, diffusion_function=p.diffusion,
dirichlet_clear_diag=True, name='diffusion')]
coefficients.append(1.)
# advection part
if isinstance(p.advection, LincombFunction):
Li += [AdvectionOperator(grid, boundary_info, advection_function=af, dirichlet_clear_diag=True,
name=f'advection_{i}')
for i, af in enumerate(p.advection.functions)]
coefficients += list(p.advection.coefficients)
elif p.advection is not None:
Li += [AdvectionOperator(grid, boundary_info, advection_function=p.advection,
dirichlet_clear_diag=True, name='advection')]
coefficients.append(1.)
# reaction part
if isinstance(p.reaction, LincombFunction):
Li += [ReactionOperator(grid, boundary_info, coefficient_function=rf, dirichlet_clear_diag=True,
name=f'reaction_{i}')
for i, rf in enumerate(p.reaction.functions)]
coefficients += list(p.reaction.coefficients)
elif p.reaction is not None:
Li += [ReactionOperator(grid, boundary_info, coefficient_function=p.reaction,
dirichlet_clear_diag=True, name='reaction')]
coefficients.append(1.)
# robin boundaries
if p.robin_data is not None:
assert isinstance(p.robin_data, tuple) and len(p.robin_data) == 2
if isinstance(p.robin_data[0], LincombFunction):
for i, rd in enumerate(p.robin_data[0].functions):
robin_tuple = (rd, p.robin_data[1])
Li += [RobinBoundaryOperator(grid, boundary_info, robin_data=robin_tuple, name=f'robin_{i}')]
coefficients += list(p.robin_data[0].coefficients)
else:
Li += [RobinBoundaryOperator(grid, boundary_info, robin_data=p.robin_data, name=f'robin')]
coefficients.append(1.)
L = LincombOperator(operators=Li, coefficients=coefficients, name='ellipticOperator')
# right-hand side
rhs = p.rhs or ConstantFunction(0., dim_domain=p.domain.dim)
Fi = []
coefficients_F = []
if isinstance(p.rhs, LincombFunction):
Fi += [L2Functional(grid, rh, dirichlet_clear_dofs=True, boundary_info=boundary_info, name=f'rhs_{i}')
for i, rh in enumerate(p.rhs.functions)]
coefficients_F += list(p.rhs.coefficients)
else:
Fi += [L2Functional(grid, rhs, dirichlet_clear_dofs=True, boundary_info=boundary_info, name='rhs')]
coefficients_F.append(1.)
if p.neumann_data is not None and boundary_info.has_neumann:
if isinstance(p.neumann_data, LincombFunction):
Fi += [BoundaryL2Functional(grid, -ne, boundary_info=boundary_info,
boundary_type='neumann', dirichlet_clear_dofs=True, name=f'neumann_{i}')
for i, ne in enumerate(p.neumann_data.functions)]
coefficients_F += list(p.neumann_data.coefficients)
else:
Fi += [BoundaryL2Functional(grid, -p.neumann_data, boundary_info=boundary_info,
boundary_type='neumann', dirichlet_clear_dofs=True)]
coefficients_F.append(1.)
if p.robin_data is not None and boundary_info.has_robin:
if isinstance(p.robin_data[0], LincombFunction):
Fi += [BoundaryL2Functional(grid, rob * p.robin_data[1], boundary_info=boundary_info,
boundary_type='robin', dirichlet_clear_dofs=True, name=f'robin_{i}')
for i, rob in enumerate(p.robin_data[0].functions)]
coefficients_F += list(p.robin_data[0].coefficients)
else:
Fi += [BoundaryL2Functional(grid, p.robin_data[0] * p.robin_data[1], boundary_info=boundary_info,
boundary_type='robin', dirichlet_clear_dofs=True)]
coefficients_F.append(1.)
if p.dirichlet_data is not None and boundary_info.has_dirichlet:
if isinstance(p.dirichlet_data, LincombFunction):
Fi += [BoundaryDirichletFunctional(grid, di, boundary_info, name=f'dirichlet{i}')
for i, di in enumerate(p.dirichlet_data.functions)]
coefficients_F += list(p.dirichlet_data.coefficients)
else:
Fi += [BoundaryDirichletFunctional(grid, p.dirichlet_data, boundary_info)]
coefficients_F.append(1.)
F = LincombOperator(operators=Fi, coefficients=coefficients_F, name='rhsOperator')
if grid.reference_element in (triangle, square):
visualizer = PatchVisualizer(grid=grid, bounding_box=grid.bounding_box(), codim=2)
elif grid.reference_element is line:
visualizer = OnedVisualizer(grid=grid, codim=1)
else:
visualizer = None
Prod = L2ProductQ1 if grid.reference_element is square else L2ProductP1
empty_bi = EmptyBoundaryInfo(grid)
l2_product = Prod(grid, empty_bi, name='l2')
l2_0_product = Prod(grid, boundary_info, dirichlet_clear_columns=True, name='l2_0')
h1_semi_product = DiffusionOperator(grid, empty_bi, name='h1_semi')
h1_0_semi_product = DiffusionOperator(grid, boundary_info, dirichlet_clear_columns=True, name='h1_0_semi')
products = {'h1': l2_product + h1_semi_product,
'h1_semi': h1_semi_product,
'l2': l2_product,
'h1_0': l2_0_product + h1_0_semi_product,
'h1_0_semi': h1_0_semi_product,
'l2_0': l2_0_product}
# assemble additionals output functionals
if p.outputs:
if any(v[0] not in ('l2', 'l2_boundary') for v in p.outputs):
raise NotImplementedError
outputs = [L2Functional(grid, v[1], dirichlet_clear_dofs=False).H if v[0] == 'l2' else
BoundaryL2Functional(grid, v[1], dirichlet_clear_dofs=False).H
for v in p.outputs]
if len(outputs) > 1:
from pymor.operators.block import BlockColumnOperator
output_functional = BlockColumnOperator(outputs)
else:
output_functional = outputs[0]
else:
output_functional = None
parameter_space = p.parameter_space if hasattr(p, 'parameter_space') else None
m = StationaryModel(L, F, output_functional=output_functional, products=products, visualizer=visualizer,
parameter_space=parameter_space, name=f'{p.name}_CG')
data = {'grid': grid, 'boundary_info': boundary_info}
if preassemble:
data['unassembled_m'] = m
m = preassemble_(m)
return m, data
[docs]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