def elliptic_oned_demo(args):
args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER'])
assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number.')
args['N'] = int(args['N'])
rhss = [ExpressionFunction('ones(x.shape[:-1]) * 10', 1, ()),
ExpressionFunction('(x - 0.5)**2 * 1000', 1, ())]
rhs = rhss[args['PROBLEM-NUMBER']]
d0 = ExpressionFunction('1 - x', 1, ())
d1 = ExpressionFunction('x', 1, ())
parameter_space = CubicParameterSpace({'diffusionl': 0}, 0.1, 1)
f0 = ProjectionParameterFunctional('diffusionl', 0)
f1 = ExpressionParameterFunctional('1', {})
problem = StationaryProblem(
domain=LineDomain(),
rhs=rhs,
diffusion=LincombFunction([d0, d1], [f0, f1]),
dirichlet_data=ConstantFunction(value=0, dim_domain=1),
name='1DProblem'
)
print('Discretize ...')
discretizer = discretize_stationary_fv if args['--fv'] else discretize_stationary_cg
d, data = discretizer(problem, diameter=1 / args['N'])
print(data['grid'])
print()
print('Solve ...')
U = d.solution_space.empty()
for mu in parameter_space.sample_uniformly(10):
U.append(d.solve(mu))
d.visualize(U, title='Solution for diffusionl in [0.1, 1]')
def elliptic_oned_demo(args):
args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER'])
assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number.')
args['N'] = int(args['N'])
rhss = [GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim_domain=1),
GenericFunction(lambda X: (X[..., 0] - 0.5) ** 2 * 1000, dim_domain=1)]
rhs = rhss[args['PROBLEM-NUMBER']]
d0 = GenericFunction(lambda X: 1 - X[..., 0], dim_domain=1)
d1 = GenericFunction(lambda X: X[..., 0], dim_domain=1)
parameter_space = CubicParameterSpace({'diffusionl': 0}, 0.1, 1)
f0 = ProjectionParameterFunctional('diffusionl', 0)
f1 = GenericParameterFunctional(lambda mu: 1, {})
print('Solving on OnedGrid(({0},{0}))'.format(args['N']))
print('Setup Problem ...')
problem = EllipticProblem(domain=LineDomain(), rhs=rhs, diffusion_functions=(d0, d1),
diffusion_functionals=(f0, f1), dirichlet_data=ConstantFunction(value=0, dim_domain=1),
name='1DProblem')
print('Discretize ...')
discretizer = discretize_elliptic_fv if args['--fv'] else discretize_elliptic_cg
discretization, _ = discretizer(problem, diameter=1 / args['N'])
print('The parameter type is {}'.format(discretization.parameter_type))
U = discretization.solution_space.empty()
for mu in parameter_space.sample_uniformly(10):
U.append(discretization.solve(mu))
print('Plot ...')
discretization.visualize(U, title='Solution for diffusionl in [0.1, 1]')
def elliptic_oned_demo(args):
args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER'])
assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number.')
args['N'] = int(args['N'])
rhss = [GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim_domain=1),
GenericFunction(lambda X: (X[..., 0] - 0.5) ** 2 * 1000, dim_domain=1)]
rhs = rhss[args['PROBLEM-NUMBER']]
d0 = GenericFunction(lambda X: 1 - X[..., 0], dim_domain=1)
d1 = GenericFunction(lambda X: X[..., 0], dim_domain=1)
parameter_space = CubicParameterSpace({'diffusionl': 0}, 0.1, 1)
f0 = ProjectionParameterFunctional('diffusionl', 0)
f1 = GenericParameterFunctional(lambda mu: 1, {})
print('Solving on OnedGrid(({0},{0}))'.format(args['N']))
print('Setup Problem ...')
problem = EllipticProblem(domain=LineDomain(), rhs=rhs, diffusion_functions=(d0, d1),
diffusion_functionals=(f0, f1), dirichlet_data=ConstantFunction(value=0, dim_domain=1),
name='1DProblem')
print('Discretize ...')
discretizer = discretize_elliptic_fv if args['--fv'] else discretize_elliptic_cg
discretization, _ = discretizer(problem, diameter=1 / args['N'])
print('The parameter type is {}'.format(discretization.parameter_type))
U = discretization.solution_space.empty()
for mu in parameter_space.sample_uniformly(10):
U.append(discretization.solve(mu))
print('Plot ...')
discretization.visualize(U, title='Solution for diffusionl in [0.1, 1]')
def elliptic_oned_demo(args):
args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER'])
assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number.')
args['N'] = int(args['N'])
rhss = [ExpressionFunction('ones(x.shape[:-1]) * 10', 1, ()),
ExpressionFunction('(x - 0.5)**2 * 1000', 1, ())]
rhs = rhss[args['PROBLEM-NUMBER']]
d0 = ExpressionFunction('1 - x', 1, ())
d1 = ExpressionFunction('x', 1, ())
parameter_space = CubicParameterSpace({'diffusionl': 0}, 0.1, 1)
f0 = ProjectionParameterFunctional('diffusionl', 0)
f1 = ExpressionParameterFunctional('1', {})
problem = StationaryProblem(
domain=LineDomain(),
rhs=rhs,
diffusion=LincombFunction([d0, d1], [f0, f1]),
dirichlet_data=ConstantFunction(value=0, dim_domain=1),
name='1DProblem'
)
print('Discretize ...')
discretizer = discretize_stationary_fv if args['--fv'] else discretize_stationary_cg
d, data = discretizer(problem, diameter=1 / args['N'])
print(data['grid'])
print()
print('Solve ...')
U = d.solution_space.empty()
for mu in parameter_space.sample_uniformly(10):
U.append(d.solve(mu))
d.visualize(U, title='Solution for diffusionl in [0.1, 1]')
def elliptic2_demo(args):
args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER'])
assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number.')
args['N'] = int(args['N'])
rhss = [ExpressionFunction('ones(x.shape[:-1]) * 10', 2, ()),
LincombFunction(
[ExpressionFunction('ones(x.shape[:-1]) * 10', 2, ()), ConstantFunction(1.,2)],
[ProjectionParameterFunctional('mu', 0), ExpressionParameterFunctional('0.1', {})])]
dirichlets = [ExpressionFunction('zeros(x.shape[:-1])', 2, ()),
LincombFunction(
[ExpressionFunction('2 * x[..., 0]', 2, ()), ConstantFunction(1.,2)],
[ProjectionParameterFunctional('mu', 0), ExpressionParameterFunctional('0.5', {})])]
neumanns = [None,
LincombFunction(
[ExpressionFunction('1 - x[..., 1]', 2, ()), ConstantFunction(1.,2)],
[ProjectionParameterFunctional('mu', 0), ExpressionParameterFunctional('0.5**2', {})])]
robins = [None,
(LincombFunction(
[ExpressionFunction('x[..., 1]', 2, ()), ConstantFunction(1.,2)],
[ProjectionParameterFunctional('mu', 0), ExpressionParameterFunctional('1', {})]),
ConstantFunction(1.,2))]
domains = [RectDomain(),
RectDomain(right='neumann', top='dirichlet', bottom='robin')]
rhs = rhss[args['PROBLEM-NUMBER']]
dirichlet = dirichlets[args['PROBLEM-NUMBER']]
neumann = neumanns[args['PROBLEM-NUMBER']]
domain = domains[args['PROBLEM-NUMBER']]
robin = robins[args['PROBLEM-NUMBER']]
problem = StationaryProblem(
domain=RectDomain(),
rhs=rhs,
diffusion=LincombFunction(
[ExpressionFunction('1 - x[..., 0]', 2, ()), ExpressionFunction('x[..., 0]', 2, ())],
[ProjectionParameterFunctional('mu', 0), ExpressionParameterFunctional('1', {})]
),
dirichlet_data=dirichlet,
neumann_data=neumann,
robin_data=robin,
parameter_space=CubicParameterSpace({'mu': 0}, 0.1, 1),
name='2DProblem'
)
print('Discretize ...')
discretizer = discretize_stationary_fv if args['--fv'] else discretize_stationary_cg
m, data = discretizer(problem, diameter=1. / args['N'])
print(data['grid'])
print()
print('Solve ...')
U = m.solution_space.empty()
for mu in m.parameter_space.sample_uniformly(10):
U.append(m.solve(mu))
m.visualize(U, title='Solution for mu in [0.1, 1]')
def __init__(self,
num_blocks=(3, 3),
parameter_range=(0.1, 1),
rhs=ConstantFunction(dim_domain=2)):
domain = RectDomain()
parameter_space = CubicParameterSpace(
{'diffusion': (num_blocks[1], num_blocks[0])}, *parameter_range)
def parameter_functional_factory(x, y):
return ProjectionParameterFunctional(
component_name='diffusion',
component_shape=(num_blocks[1], num_blocks[0]),
coordinates=(num_blocks[1] - y - 1, x),
name='diffusion_{}_{}'.format(x, y))
diffusion_functions = tuple(
ThermalBlockDiffusionFunction(x, y, num_blocks[0], num_blocks[1])
for x, y in product(xrange(num_blocks[0]), xrange(num_blocks[1])))
parameter_functionals = tuple(
parameter_functional_factory(x, y)
for x, y in product(xrange(num_blocks[0]), xrange(num_blocks[1])))
super(ThermalBlockProblem, self).__init__(domain,
rhs,
diffusion_functions,
parameter_functionals,
name='ThermalBlock')
self.parameter_space = parameter_space
self.parameter_range = parameter_range
self.num_blocks = num_blocks
def burgers_problem_2d(vx=1.,
vy=1.,
torus=True,
initial_data_type='sin',
parameter_range=(1., 2.)):
"""Two-dimensional Burgers-type problem.
The problem is to solve ::
∂_t u(x, t, μ) + ∇ ⋅ (v * u(x, t, μ)^μ) = 0
u(x, 0, μ) = u_0(x)
for u with t in [0, 0.3], x in [0, 2] x [0, 1].
Parameters
----------
vx
The x component of the velocity vector v.
vy
The y component of the velocity vector v.
torus
If `True`, impose periodic boundary conditions. Otherwise,
Dirichlet left and bottom, outflow top and right.
initial_data_type
Type of initial data (`'sin'` or `'bump'`).
parameter_range
The interval in which μ is allowed to vary.
"""
assert initial_data_type in ('sin', 'bump')
if initial_data_type == 'sin':
initial_data = ExpressionFunction(
"0.5 * (sin(2 * pi * x[..., 0]) * sin(2 * pi * x[..., 1]) + 1.)",
2, ())
dirichlet_data = ConstantFunction(dim_domain=2, value=0.5)
else:
initial_data = ExpressionFunction(
"(x[..., 0] >= 0.5) * (x[..., 0] <= 1) * 1", 2, ())
dirichlet_data = ConstantFunction(dim_domain=2, value=0.)
return InstationaryProblem(
StationaryProblem(
domain=TorusDomain([[0, 0], [2, 1]])
if torus else RectDomain([[0, 0], [2, 1]], right=None, top=None),
dirichlet_data=dirichlet_data,
rhs=None,
nonlinear_advection=ExpressionFunction("abs(x)**exponent * v", 1,
(2, ), {'exponent': ()},
{'v': np.array([vx, vy])}),
nonlinear_advection_derivative=ExpressionFunction(
"exponent * abs(x)**(exponent-1) * sign(x) * v", 1, (2, ),
{'exponent': ()}, {'v': np.array([vx, vy])}),
),
initial_data=initial_data,
T=0.3,
parameter_space=CubicParameterSpace({'exponent': 0}, *parameter_range),
name="burgers_problem_2d({}, {}, {}, '{}')".format(
vx, vy, torus, initial_data_type))
def burgers_problem(v=1.,
circle=True,
initial_data_type='sin',
parameter_range=(1., 2.)):
"""One-dimensional Burgers-type problem.
The problem is to solve ::
∂_t u(x, t, μ) + ∂_x (v * u(x, t, μ)^μ) = 0
u(x, 0, μ) = u_0(x)
for u with t in [0, 0.3] and x in [0, 2].
Parameters
----------
v
The velocity v.
circle
If `True`, impose periodic boundary conditions. Otherwise Dirichlet left,
outflow right.
initial_data_type
Type of initial data (`'sin'` or `'bump'`).
parameter_range
The interval in which μ is allowed to vary.
"""
assert initial_data_type in ('sin', 'bump')
if initial_data_type == 'sin':
initial_data = ExpressionFunction('0.5 * (sin(2 * pi * x) + 1.)', 1,
())
dirichlet_data = ConstantFunction(dim_domain=1, value=0.5)
else:
initial_data = ExpressionFunction('(x >= 0.5) * (x <= 1) * 1.', 1, ())
dirichlet_data = ConstantFunction(dim_domain=1, value=0.)
return InstationaryProblem(
StationaryProblem(
domain=CircleDomain([0, 2]) if circle else LineDomain([0, 2],
right=None),
dirichlet_data=dirichlet_data,
rhs=None,
nonlinear_advection=ExpressionFunction('abs(x)**exponent * v', 1,
(1, ), {'exponent':
()}, {'v': v}),
nonlinear_advection_derivative=ExpressionFunction(
'exponent * abs(x)**(exponent-1) * sign(x) * v', 1, (1, ),
{'exponent': ()}, {'v': v}),
),
T=0.3,
initial_data=initial_data,
parameter_space=CubicParameterSpace({'exponent': 0}, *parameter_range),
name="burgers_problem({}, {}, '{}')".format(v, circle,
initial_data_type))
def __init__(self, domain=RectDomain(), rhs=None, parameter_range=(0., 100.),
dirichlet_data=None, neumann_data=None):
self.parameter_range = parameter_range # needed for with_
parameter_space = CubicParameterSpace({'k': ()}, *parameter_range)
super().__init__(
diffusion_functions=[ConstantFunction(1., dim_domain=domain.dim)],
diffusion_functionals=[1.],
reaction_functions=[ConstantFunction(1., dim_domain=domain.dim)],
reaction_functionals=[ExpressionParameterFunctional('-k**2', {'k': ()})],
domain=domain,
rhs=rhs or ConstantFunction(1., dim_domain=domain.dim),
parameter_space=parameter_space,
dirichlet_data=dirichlet_data,
neumann_data=neumann_data)
def helmholtz_problem(domain=RectDomain(), rhs=None, parameter_range=(0., 100.),
dirichlet_data=None, neumann_data=None):
"""Helmholtz equation problem.
This problem is to solve the Helmholtz equation ::
- ∆ u(x, k) - k^2 u(x, k) = f(x, k)
on a given domain.
Parameters
----------
domain
A |DomainDescription| of the domain the problem is posed on.
rhs
The |Function| f(x, μ).
parameter_range
A tuple `(k_min, k_max)` describing the interval in which k is allowd to vary.
dirichlet_data
|Function| providing the Dirichlet boundary values.
neumann_data
|Function| providing the Neumann boundary values.
"""
return StationaryProblem(
domain=domain,
rhs=rhs or ConstantFunction(1., dim_domain=domain.dim),
dirichlet_data=dirichlet_data,
neumann_data=neumann_data,
diffusion=ConstantFunction(1., dim_domain=domain.dim),
reaction=LincombFunction([ConstantFunction(1., dim_domain=domain.dim)],
[ExpressionParameterFunctional('-k**2', {'k': ()})]),
parameter_space=CubicParameterSpace({'k': ()}, *parameter_range),
name='helmholtz_problem'
)
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(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 __init__(self,
vx=1.,
vy=1.,
torus=True,
initial_data_type='sin',
parameter_range=(1., 2.)):
assert initial_data_type in ('sin', 'bump')
flux_function = Burgers2DFlux(vx, vy)
flux_function_derivative = Burgers2DFluxDerivative(vx, vy)
if initial_data_type == 'sin':
initial_data = Burgers2DSinInitialData()
dirichlet_data = ConstantFunction(dim_domain=2, value=0.5)
else:
initial_data = Burgers2DBumpInitialData()
dirichlet_data = ConstantFunction(dim_domain=2, value=0)
domain = TorusDomain([[0, 0], [2, 1]]) if torus else RectDomain(
[[0, 0], [2, 1]], right=None, top=None)
super(Burgers2DProblem,
self).__init__(domain=domain,
rhs=None,
flux_function=flux_function,
flux_function_derivative=flux_function_derivative,
initial_data=initial_data,
dirichlet_data=dirichlet_data,
T=0.3,
name='Burgers2DProblem')
self.parameter_space = CubicParameterSpace({'exponent': 0},
*parameter_range)
self.parameter_range = parameter_range
self.initial_data_type = initial_data_type
self.torus = torus
self.vx = vx
self.vy = vy
def __init__(self,
v=1.,
circle=True,
initial_data_type='sin',
parameter_range=(1., 2.)):
assert initial_data_type in ('sin', 'bump')
flux_function = BurgersFlux(v)
flux_function_derivative = BurgersFluxDerivative(v)
if initial_data_type == 'sin':
initial_data = BurgersSinInitialData()
dirichlet_data = ConstantFunction(dim_domain=1, value=0.5)
else:
initial_data = BurgersBumpInitialData()
dirichlet_data = ConstantFunction(dim_domain=1, value=0)
if circle:
domain = CircleDomain([0, 2])
else:
domain = LineDomain([0, 2], right=None)
super(BurgersProblem,
self).__init__(domain=domain,
rhs=None,
flux_function=flux_function,
flux_function_derivative=flux_function_derivative,
initial_data=initial_data,
dirichlet_data=dirichlet_data,
T=0.3,
name='BurgersProblem')
self.parameter_space = CubicParameterSpace({'exponent': 0},
*parameter_range)
self.parameter_range = parameter_range
self.initial_data_type = initial_data_type
self.circle = circle
self.v = v
def elliptic2_demo(args):
args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER'])
assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError(
'Invalid problem number.')
args['N'] = int(args['N'])
rhss = [
ExpressionFunction('ones(x.shape[:-1]) * 10', 2, ()),
ExpressionFunction('(x[..., 0] - 0.5)**2 * 1000', 2, ())
]
rhs = rhss[args['PROBLEM-NUMBER']]
problem = StationaryProblem(
domain=RectDomain(),
rhs=rhs,
diffusion=LincombFunction([
ExpressionFunction('1 - x[..., 0]', 2, ()),
ExpressionFunction('x[..., 0]', 2, ())
], [
ProjectionParameterFunctional('diffusionl', 0),
ExpressionParameterFunctional('1', {})
]),
parameter_space=CubicParameterSpace({'diffusionl': 0}, 0.1, 1),
name='2DProblem')
print('Discretize ...')
discretizer = discretize_stationary_fv if args[
'--fv'] else discretize_stationary_cg
m, data = discretizer(problem, diameter=1. / args['N'])
print(data['grid'])
print()
print('Solve ...')
U = m.solution_space.empty()
for mu in m.parameter_space.sample_uniformly(10):
U.append(m.solve(mu))
m.visualize(U, title='Solution for diffusionl in [0.1, 1]')
def discretize_stationary_from_disk(parameter_file):
"""Load a linear affinely decomposed |StationaryModel| from file.
The model is defined via an `.ini`-style file as follows ::
[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)
...
[parameter]
μ_1: a_1,b_1
...
μ_n: a_n,b_n
[products]
Prod1: P_1.mat
Prod2: P_2.mat
...
Here, `L_1.mat`, `L_2.mat`, ..., `F_1.mat`, `F_2.mat`, ... are files
containing matrices `L_1`, `L_2`, ... and vectors `F_1.mat`, `F_2.mat`, ...
which correspond to the affine components of the operator and right-hand
side. The respective coefficient functionals, are given via the
string expressions `l_1(...)`, `l_2(...)`, ..., `f_1(...)` in the
(scalar-valued) |Parameter| components `w_1`, ..., `w_n`. The allowed lower
and upper bounds `a_i, b_i` for the component `μ_i` are specified in the
`[parameters]` section. The resulting operator and right-hand side are
then of the form ::
L(μ) = l_1(μ)*L_1 + l_2(μ)*L_2+ ...
F(μ) = f_1(μ)*F_1 + f_2(μ)*L_2+ ...
In the `[products]` section, an optional list of inner products `Prod1`, `Prod2`, ..
with corresponding matrices `P_1.mat`, `P_2.mat` can be specified.
Example::
[system-matrices]
matrix1.mat: 1.
matrix2.mat: 1. - theta**2
[rhs-vectors]
rhs.mat: 1.
[parameter]
theta: 0, 0.5
[products]
h1: h1.mat
l2: mass.mat
Parameters
----------
parameter_file
Path to the parameter file.
Returns
-------
m
The |StationaryModel| that has been generated.
"""
assert ".ini" == parameter_file[
-4:], f'Given file is not an .ini file: {parameter_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 'rhs-vectors' in config.sections()
assert 'parameter' in config.sections()
system_mat = config.items('system-matrices')
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 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
# Create and return stationary model
return StationaryModel(operator=system_lincombOperator,
rhs=rhs_lincombOperator,
parameter_space=parameter_space,
products=products)
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)
def prepare(cfg):
logger = getLogger('.OS2015_SISC__6_2.prepare')
logger.setLevel('INFO')
reference_needed = (
(cfg['greedy_use_estimator'] or cfg['estimate_some_errors']) and
('discretization_error' in cfg['estimator_compute']
or 'full_error' in cfg['estimator_compute']
or 'model_reduction_error' in cfg['estimator_compute'])
or cfg['local_indicators'] == 'model_reduction_error')
logger.info('Initializing DUNE module ({}):'.format(cfg['dune_example']))
Example = dune_module.__dict__[cfg['dune_example']]
example = Example(partitioning=cfg['dune_partitioning'],
num_refinements=cfg['dune_num_refinements'],
oversampling_layers=cfg['dune_oversampling_layers'],
products=cfg['dune_products'],
with_reference=reference_needed,
info_log_levels=cfg['dune_log_info_level'],
debug_log_levels=cfg['dune_log_debug_level'],
enable_warnings=cfg['dune_log_enable_warnings'],
enable_colors=True,
info_color='blue')
_, wrapper = wrap_module(dune_module)
discretization = wrapper[example.discretization()]
logger.info(' grid has {} subdomain{}'.format(
discretization.num_subdomains,
'' if discretization.num_subdomains == 1 else 's'))
logger.info(' discretization has {} DoFs'.format(
discretization.solution_space.dim))
discretization = discretization.with_(parameter_space=CubicParameterSpace(
discretization.parameter_type, cfg['parameter_range'][0],
cfg['parameter_range'][1]))
logger.info(' parameter type is {}'.format(discretization.parameter_type))
example.visualize(cfg['dune_example'])
def create_product(products, product_type):
if product_type is None:
return None, 'None'
if not isinstance(product_type, tuple):
return products[product_type], product_type
else:
prods = [products[tt] for tt in product_type]
product_name = product_type[0]
for ii in np.arange(1, len(product_type)):
product_name += '_plus_' + product_type[ii]
return LincombOperator(operators=prods,
coefficients=[1 for pp in prods
]), product_name
logger.info('Preparing products and norms ...')
mu_hat_dune = wrapper.DuneParameter('mu', cfg['mu_hat_value'])
mu_bar_dune = wrapper.DuneParameter('mu', cfg['mu_bar_value'])
all_global_products = {}
all_local_products = [{}
for ss in np.arange(discretization.num_subdomains)]
# get all products from the discretization and assemble the parametric ones
for nm, pr in discretization.products.items():
if not pr.parametric:
all_global_products[nm] = pr
else:
all_global_products[nm] = pr.assemble(mu=wrapper[mu_bar_dune])
for ss in np.arange(discretization.num_subdomains):
pr = discretization.local_product(ss, nm)
if pr.parametric:
all_local_products[ss][nm] = pr.assemble(
mu=wrapper[mu_bar_dune])
else:
all_local_products[ss][nm] = pr
# combine products (if necessarry)
global_product, _ = create_product(all_global_products,
cfg['extension_product'])
local_products, _ = map(
list,
zip(*[
create_product(all_local_pr, cfg['extension_product'])
for all_local_pr in all_local_products
]))
# assert all(nm == local_products_name[0] for nm in local_products_name)
# local_products_name = local_products_name[0]
norm, _ = create_product(all_global_products, cfg['greedy_error_norm'])
norm = induced_norm(norm) if norm is not None else None
return {
'example': example,
'discretization': discretization,
'local_products': local_products,
'norm': norm,
'mu_bar_dune': mu_bar_dune,
'mu_hat_dune': mu_hat_dune,
'wrapper': wrapper
}
def discretize(grid_and_problem_data, T, nt):
d, d_data = discretize_ell(grid_and_problem_data)
assert isinstance(d.parameter_space, CubicParameterSpace)
parameter_range = grid_and_problem_data['parameter_range']
block_space = d_data['block_space']
# assemble global L2 product
l2_mat = d.global_operator.operators[0].matrix.copy(
) # to ensure matching pattern
l2_mat.scal(0.)
for ii in range(block_space.num_blocks):
local_l2_product = d.l2_product._blocks[ii, ii]
block_space.mapper.copy_local_to_global(
local_l2_product.matrix, local_l2_product.matrix.pattern(), ii,
l2_mat)
mass = d.l2_product
operators = {
k: v
for k, v in d.operators.items() if k not in d.special_operators
}
global_mass = DuneXTMatrixOperator(l2_mat)
local_div_ops, local_l2_products, local_projections, local_rt_projections = \
d_data['local_div_ops'], d_data['local_l2_products'], d_data['local_projections'], d_data['local_rt_projections']
for ii in range(d_data['grid'].num_subdomains):
local_div = Concatenation(
[local_div_ops[ii], local_rt_projections[ii]])
operators['r_ud_{}'.format(ii)] = \
Concatenation([local_projections[ii].T, local_l2_products[ii], local_div], name='r_ud_{}'.format(ii))
operators['r_l2_{}'.format(ii)] = \
Concatenation([local_projections[ii].T, local_l2_products[ii], local_projections[ii]],
name='r_l2_{}'.format(ii))
e = d.estimator
estimator = ParabolicEstimator(e.min_diffusion_evs, e.subdomain_diameters,
e.local_eta_rf_squared, e.lambda_coeffs,
e.mu_bar, e.mu_hat, e.flux_reconstruction,
e.oswald_interpolation_error)
d = InstationaryDuneDiscretization(
d.global_operator,
d.global_rhs,
global_mass,
T,
d.operator.source.zeros(1),
d.operator,
d.rhs,
mass=mass,
time_stepper=ImplicitEulerTimeStepper(nt=nt,
solver_options='operator'),
products=d.products,
operators=operators,
estimator=estimator,
visualizer=DuneGDTVisualizer(block_space))
d = d.with_(parameter_space=CubicParameterSpace(
d.parameter_type, parameter_range[0], parameter_range[1]))
return d, d_data
def _discretize_fenics(xblocks, yblocks, grid_num_intervals, element_order):
# assemble system matrices - FEniCS code
########################################
import dolfin as df
mesh = df.UnitSquareMesh(grid_num_intervals, grid_num_intervals, 'crossed')
V = df.FunctionSpace(mesh, 'Lagrange', element_order)
u = df.TrialFunction(V)
v = df.TestFunction(V)
diffusion = df.Expression('(lower0 <= x[0]) * (open0 ? (x[0] < upper0) : (x[0] <= upper0)) *'
'(lower1 <= x[1]) * (open1 ? (x[1] < upper1) : (x[1] <= upper1))',
lower0=0., upper0=0., open0=0,
lower1=0., upper1=0., open1=0,
element=df.FunctionSpace(mesh, 'DG', 0).ufl_element())
def assemble_matrix(x, y, nx, ny):
diffusion.user_parameters['lower0'] = x/nx
diffusion.user_parameters['lower1'] = y/ny
diffusion.user_parameters['upper0'] = (x + 1)/nx
diffusion.user_parameters['upper1'] = (y + 1)/ny
diffusion.user_parameters['open0'] = (x + 1 == nx)
diffusion.user_parameters['open1'] = (y + 1 == ny)
return df.assemble(df.inner(diffusion * df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
mats = [assemble_matrix(x, y, xblocks, yblocks)
for x in range(xblocks) for y in range(yblocks)]
mat0 = mats[0].copy()
mat0.zero()
h1_mat = df.assemble(df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
l2_mat = df.assemble(u * v * df.dx)
f = df.Constant(1.) * v * df.dx
F = df.assemble(f)
bc = df.DirichletBC(V, 0., df.DomainBoundary())
for m in mats:
bc.zero(m)
bc.apply(mat0)
bc.apply(h1_mat)
bc.apply(F)
# wrap everything as a pyMOR model
##################################
# FEniCS wrappers
from pymor.bindings.fenics import FenicsVectorSpace, FenicsMatrixOperator, FenicsVisualizer
# generic pyMOR classes
from pymor.models.basic import StationaryModel
from pymor.operators.constructions import LincombOperator, VectorOperator
from pymor.parameters.functionals import ProjectionParameterFunctional
from pymor.parameters.spaces import CubicParameterSpace
# define parameter functionals (same as in pymor.analyticalproblems.thermalblock)
def parameter_functional_factory(x, y):
return ProjectionParameterFunctional(component_name='diffusion',
component_shape=(yblocks, xblocks),
index=(yblocks - y - 1, x),
name=f'diffusion_{x}_{y}')
parameter_functionals = tuple(parameter_functional_factory(x, y)
for x in range(xblocks) for y in range(yblocks))
# wrap operators
ops = [FenicsMatrixOperator(mat0, V, V)] + [FenicsMatrixOperator(m, V, V) for m in mats]
op = LincombOperator(ops, (1.,) + parameter_functionals)
rhs = VectorOperator(FenicsVectorSpace(V).make_array([F]))
h1_product = FenicsMatrixOperator(h1_mat, V, V, name='h1_0_semi')
l2_product = FenicsMatrixOperator(l2_mat, V, V, name='l2')
# build model
visualizer = FenicsVisualizer(FenicsVectorSpace(V))
parameter_space = CubicParameterSpace(op.parameter_type, 0.1, 1.)
fom = StationaryModel(op, rhs, products={'h1_0_semi': h1_product,
'l2': l2_product},
parameter_space=parameter_space,
visualizer=visualizer)
return fom
def discretize(grid_and_problem_data, solver_options, mpi_comm):
################ Setup
logger = getLogger('discretize_elliptic_block_swipdg.discretize')
logger.info('discretizing ... ')
grid, boundary_info = grid_and_problem_data['grid'], grid_and_problem_data[
'boundary_info']
local_all_dirichlet_boundary_info = make_subdomain_boundary_info(
grid, {'type': 'xt.grid.boundaryinfo.alldirichlet'})
local_subdomains, num_local_subdomains, num_global_subdomains = _get_subdomains(
grid)
local_all_neumann_boundary_info = make_subdomain_boundary_info(
grid, {'type': 'xt.grid.boundaryinfo.allneumann'})
block_space = make_block_dg_space(grid)
global_rt_space = make_rt_space(grid)
subdomain_rt_spaces = [
global_rt_space.restrict_to_dd_subdomain_view(grid, ii)
for ii in range(num_global_subdomains)
]
local_patterns = [
block_space.local_space(ii).compute_pattern('face_and_volume')
for ii in range(block_space.num_blocks)
]
coupling_patterns = {
'in_in': {},
'out_out': {},
'in_out': {},
'out_in': {}
}
coupling_matrices = {
'in_in': {},
'out_out': {},
'in_out': {},
'out_in': {}
}
for ii in range(num_global_subdomains):
ii_size = block_space.local_space(ii).size()
for jj in grid.neighboring_subdomains(ii):
jj_size = block_space.local_space(jj).size()
if ii < jj: # Assemble primally (visit each coupling only once).
coupling_patterns['in_in'][(ii, jj)] = block_space.local_space(
ii).compute_pattern('face_and_volume')
coupling_patterns['out_out'][(
ii, jj)] = block_space.local_space(jj).compute_pattern(
'face_and_volume')
coupling_patterns['in_out'][(
ii, jj)] = block_space.compute_coupling_pattern(
ii, jj, 'face')
coupling_patterns['out_in'][(
ii, jj)] = block_space.compute_coupling_pattern(
jj, ii, 'face')
coupling_matrices['in_in'][(ii, jj)] = Matrix(
ii_size, ii_size, coupling_patterns['in_in'][(ii, jj)])
coupling_matrices['out_out'][(ii, jj)] = Matrix(
jj_size, jj_size, coupling_patterns['out_out'][(ii, jj)])
coupling_matrices['in_out'][(ii, jj)] = Matrix(
ii_size, jj_size, coupling_patterns['in_out'][(ii, jj)])
coupling_matrices['out_in'][(ii, jj)] = Matrix(
jj_size, ii_size, coupling_patterns['out_in'][(ii, jj)])
boundary_patterns = {}
for ii in grid.boundary_subdomains():
boundary_patterns[ii] = block_space.local_space(ii).compute_pattern(
'face_and_volume')
################ Assemble LHS and RHS
lambda_, kappa = grid_and_problem_data['lambda'], grid_and_problem_data[
'kappa']
if isinstance(lambda_, dict):
lambda_funcs = lambda_['functions']
lambda_coeffs = lambda_['coefficients']
else:
lambda_funcs = [
lambda_,
]
lambda_coeffs = [
1,
]
logger.debug('block op ... ')
ops, block_ops = zip(*(discretize_lhs(
lf, grid, block_space, local_patterns, boundary_patterns,
coupling_matrices, kappa, local_all_neumann_boundary_info,
boundary_info, coupling_patterns, solver_options)
for lf in lambda_funcs))
global_operator = LincombOperator(ops,
lambda_coeffs,
solver_options=solver_options,
name='GlobalOperator')
logger.debug('block op global done ')
block_op = LincombOperator(block_ops,
lambda_coeffs,
name='lhs',
solver_options=solver_options)
logger.debug('block op done ')
f = grid_and_problem_data['f']
if isinstance(f, dict):
f_funcs = f['functions']
f_coeffs = f['coefficients']
else:
f_funcs = [
f,
]
f_coeffs = [
1,
]
rhss, block_rhss = zip(*(discretize_rhs(
ff, grid, block_space, global_operator, block_ops, block_op)
for ff in f_funcs))
global_rhs = LincombOperator(rhss, f_coeffs)
block_rhs = LincombOperator(block_rhss, f_coeffs)
solution_space = block_op.source
################ Assemble interpolation and reconstruction operators
logger.info('discretizing interpolation ')
# Oswald interpolation error operator
oi_op = BlockDiagonalOperator([
OswaldInterpolationErrorOperator(ii, block_op.source, grid,
block_space)
for ii in range(num_global_subdomains)
],
name='oswald_interpolation_error')
# Flux reconstruction operator
fr_op = LincombOperator([
BlockDiagonalOperator([
FluxReconstructionOperator(ii, block_op.source, grid, block_space,
global_rt_space, subdomain_rt_spaces,
lambda_xi, kappa)
for ii in range(num_global_subdomains)
]) for lambda_xi in lambda_funcs
],
lambda_coeffs,
name='flux_reconstruction')
################ Assemble inner products and error estimator operators
logger.info('discretizing inner products ')
lambda_bar, lambda_hat = grid_and_problem_data[
'lambda_bar'], grid_and_problem_data['lambda_hat']
mu_bar, mu_hat = grid_and_problem_data['mu_bar'], grid_and_problem_data[
'mu_hat']
operators = {}
local_projections = []
local_rt_projections = []
local_oi_projections = []
local_div_ops = []
local_l2_products = []
data = dict(grid=grid,
block_space=block_space,
local_projections=local_projections,
local_rt_projections=local_rt_projections,
local_oi_projections=local_oi_projections,
local_div_ops=local_div_ops,
local_l2_products=local_l2_products)
for ii in range(num_global_subdomains):
neighborhood = grid.neighborhood_of(ii)
################ Assemble local inner products
local_dg_space = block_space.local_space(ii)
# we want a larger pattern to allow for axpy with other matrices
tmp_local_matrix = Matrix(
local_dg_space.size(), local_dg_space.size(),
local_dg_space.compute_pattern('face_and_volume'))
local_energy_product_ops = []
local_energy_product_coeffs = []
for func, coeff in zip(lambda_funcs, lambda_coeffs):
local_energy_product_ops.append(
make_elliptic_matrix_operator(func,
kappa,
tmp_local_matrix.copy(),
local_dg_space,
over_integrate=0))
local_energy_product_coeffs.append(coeff)
local_energy_product_ops.append(
make_penalty_product_matrix_operator(
grid,
ii,
local_all_dirichlet_boundary_info,
local_dg_space,
func,
kappa,
over_integrate=0))
local_energy_product_coeffs.append(coeff)
local_l2_product = make_l2_matrix_operator(tmp_local_matrix.copy(),
local_dg_space)
del tmp_local_matrix
local_assembler = make_system_assembler(local_dg_space)
for local_product_op in local_energy_product_ops:
local_assembler.append(local_product_op)
local_assembler.append(local_l2_product)
local_assembler.assemble()
local_energy_product_name = 'local_energy_dg_product_{}'.format(ii)
local_energy_product = LincombOperator([
DuneXTMatrixOperator(op.matrix(),
source_id='domain_{}'.format(ii),
range_id='domain_{}'.format(ii))
for op in local_energy_product_ops
],
local_energy_product_coeffs,
name=local_energy_product_name)
operators[local_energy_product_name] = \
local_energy_product.assemble(mu_bar).with_(name=local_energy_product_name)
local_l2_product = DuneXTMatrixOperator(
local_l2_product.matrix(),
source_id='domain_{}'.format(ii),
range_id='domain_{}'.format(ii))
local_l2_products.append(local_l2_product)
# assemble local elliptic product
matrix = make_local_elliptic_matrix_operator(grid, ii, local_dg_space,
lambda_bar, kappa)
matrix.assemble()
local_elliptic_product = DuneXTMatrixOperator(
matrix.matrix(),
range_id='domain_{}'.format(ii),
source_id='domain_{}'.format(ii))
################ Assemble local to global projections
# assemble projection (solution space) -> (ii space)
local_projection = BlockProjectionOperator(block_op.source, ii)
local_projections.append(local_projection)
# assemble projection (RT spaces on neighborhoods of subdomains) -> (local RT space on ii)
ops = np.full(num_global_subdomains, None)
for kk in neighborhood:
component = grid.neighborhood_of(kk).index(ii)
assert fr_op.range.subspaces[kk].subspaces[
component].id == 'LOCALRT_{}'.format(ii)
ops[kk] = BlockProjectionOperator(fr_op.range.subspaces[kk],
component)
local_rt_projection = BlockRowOperator(
ops,
source_spaces=fr_op.range.subspaces,
name='local_rt_projection_{}'.format(ii))
local_rt_projections.append(local_rt_projection)
# assemble projection (OI spaces on neighborhoods of subdomains) -> (ii space)
ops = np.full(num_global_subdomains, None)
for kk in neighborhood:
component = grid.neighborhood_of(kk).index(ii)
assert oi_op.range.subspaces[kk].subspaces[
component].id == 'domain_{}'.format(ii)
ops[kk] = BlockProjectionOperator(oi_op.range.subspaces[kk],
component)
local_oi_projection = BlockRowOperator(
ops,
source_spaces=oi_op.range.subspaces,
name='local_oi_projection_{}'.format(ii))
local_oi_projections.append(local_oi_projection)
################ Assemble additional operators for error estimation
# assemble local divergence operator
local_rt_space = global_rt_space.restrict_to_dd_subdomain_view(
grid, ii)
local_div_op = make_divergence_matrix_operator_on_subdomain(
grid, ii, local_dg_space, local_rt_space)
local_div_op.assemble()
local_div_op = DuneXTMatrixOperator(
local_div_op.matrix(),
source_id='LOCALRT_{}'.format(ii),
range_id='domain_{}'.format(ii),
name='local_divergence_{}'.format(ii))
local_div_ops.append(local_div_op)
################ Assemble error estimator operators -- Nonconformity
operators['nc_{}'.format(ii)] = \
Concatenation([local_oi_projection.T, local_elliptic_product, local_oi_projection],
name='nonconformity_{}'.format(ii))
################ Assemble error estimator operators -- Residual
if len(f_funcs) == 1:
assert f_coeffs[0] == 1
local_div = Concatenation([local_div_op, local_rt_projection])
local_rhs = VectorFunctional(
block_rhs.operators[0]._array._blocks[ii])
operators['r_fd_{}'.format(ii)] = \
Concatenation([local_rhs, local_div], name='r1_{}'.format(ii))
operators['r_dd_{}'.format(ii)] = \
Concatenation([local_div.T, local_l2_product, local_div], name='r2_{}'.format(ii))
################ Assemble error estimator operators -- Diffusive flux
operators['df_aa_{}'.format(ii)] = LincombOperator(
[
assemble_estimator_diffusive_flux_aa(
lambda_xi, lambda_xi_prime, grid, ii, block_space,
lambda_hat, kappa, solution_space)
for lambda_xi in lambda_funcs
for lambda_xi_prime in lambda_funcs
], [
ProductParameterFunctional([c1, c2]) for c1 in lambda_coeffs
for c2 in lambda_coeffs
],
name='diffusive_flux_aa_{}'.format(ii))
operators['df_bb_{}'.format(
ii)] = assemble_estimator_diffusive_flux_bb(
grid, ii, subdomain_rt_spaces, lambda_hat, kappa,
local_rt_projection)
operators['df_ab_{}'.format(ii)] = LincombOperator(
[
assemble_estimator_diffusive_flux_ab(
lambda_xi, grid, ii, block_space, subdomain_rt_spaces,
lambda_hat, kappa, local_rt_projection, local_projection)
for lambda_xi in lambda_funcs
],
lambda_coeffs,
name='diffusive_flux_ab_{}'.format(ii))
################ Final assembly
logger.info('final assembly ')
# instantiate error estimator
min_diffusion_evs = np.array([
min_diffusion_eigenvalue(grid, ii, lambda_hat, kappa)
for ii in range(num_global_subdomains)
])
subdomain_diameters = np.array(
[subdomain_diameter(grid, ii) for ii in range(num_global_subdomains)])
if len(f_funcs) == 1:
assert f_coeffs[0] == 1
local_eta_rf_squared = np.array([
apply_l2_product(grid,
ii,
f_funcs[0],
f_funcs[0],
over_integrate=2)
for ii in range(num_global_subdomains)
])
else:
local_eta_rf_squared = None
estimator = EllipticEstimator(grid,
min_diffusion_evs,
subdomain_diameters,
local_eta_rf_squared,
lambda_coeffs,
mu_bar,
mu_hat,
fr_op,
oswald_interpolation_error=oi_op,
mpi_comm=mpi_comm)
l2_product = BlockDiagonalOperator(local_l2_products)
# instantiate discretization
neighborhoods = [
grid.neighborhood_of(ii) for ii in range(num_global_subdomains)
]
local_boundary_info = make_subdomain_boundary_info(
grid_and_problem_data['grid'],
{'type': 'xt.grid.boundaryinfo.alldirichlet'})
d = DuneDiscretization(global_operator=global_operator,
global_rhs=global_rhs,
neighborhoods=neighborhoods,
enrichment_data=(grid, local_boundary_info, lambda_,
kappa, f, block_space),
operator=block_op,
rhs=block_rhs,
visualizer=DuneGDTVisualizer(block_space),
operators=operators,
products={'l2': l2_product},
estimator=estimator,
data=data)
parameter_range = grid_and_problem_data['parameter_range']
logger.info('final assembly B')
d = d.with_(parameter_space=CubicParameterSpace(
d.parameter_type, parameter_range[0], parameter_range[1]))
logger.info('final assembly C')
return d, data
if __name__ == '__main__':
argvs = sys.argv
parser = OptionParser()
parser.add_option("--dir", dest="dir", default="./")
opt, argc = parser.parse_args(argvs)
print(opt, argc)
rhs = ExpressionFunction('(x[..., 0] - 0.5)**2 * 1000', 2, ())
problem = StationaryProblem(
domain=RectDomain(),
rhs=rhs,
diffusion=LincombFunction(
[ExpressionFunction('1 - x[..., 0]', 2, ()),
ExpressionFunction('x[..., 0]', 2, ())],
[ProjectionParameterFunctional(
'diffusionl', 0), ExpressionParameterFunctional('1', {})]
),
parameter_space=CubicParameterSpace({'diffusionl': 0}, 0.01, 0.1),
name='2DProblem'
)
args = {'N': 100, 'samples': 10}
m, data = discretize_stationary_cg(problem, diameter=1. / args['N'])
U = m.solution_space.empty()
for mu in m.parameter_space.sample_uniformly(args['samples']):
U.append(m.solve(mu))
Us = U * 1.5
plot = m.visualize((U, Us), title='Solution for diffusionl=0.5')
def space():
return CubicParameterSpace({'diffusionl': 1}, 0.1, 1)
def discretize(DIM, N, ORDER):
# ### problem definition
import dolfin as df
if DIM == 2:
mesh = df.UnitSquareMesh(N, N)
elif DIM == 3:
mesh = df.UnitCubeMesh(N, N, N)
else:
raise NotImplementedError
V = df.FunctionSpace(mesh, "CG", ORDER)
g = df.Constant(1.0)
c = df.Constant(1.)
class DirichletBoundary(df.SubDomain):
def inside(self, x, on_boundary):
return abs(x[0] - 1.0) < df.DOLFIN_EPS and on_boundary
db = DirichletBoundary()
bc = df.DirichletBC(V, g, db)
u = df.Function(V)
v = df.TestFunction(V)
f = df.Expression("x[0]*sin(x[1])", degree=2)
F = df.inner(
(1 + c * u**2) * df.grad(u), df.grad(v)) * df.dx - f * v * df.dx
df.solve(F == 0,
u,
bc,
solver_parameters={"newton_solver": {
"relative_tolerance": 1e-6
}})
# ### pyMOR wrapping
from pymor.bindings.fenics import FenicsVectorSpace, FenicsOperator, FenicsVisualizer
from pymor.models.basic import StationaryModel
from pymor.operators.constructions import VectorOperator
from pymor.parameters.spaces import CubicParameterSpace
space = FenicsVectorSpace(V)
op = FenicsOperator(
F,
space,
space,
u, (bc, ),
parameter_setter=lambda mu: c.assign(float(mu['c'])),
parameter_type={'c': ()},
solver_options={'inverse': {
'type': 'newton',
'rtol': 1e-6
}})
rhs = VectorOperator(op.range.zeros())
fom = StationaryModel(op,
rhs,
visualizer=FenicsVisualizer(space),
parameter_space=CubicParameterSpace({'c': ()}, 0.,
1000.))
return fom
def discretize(grid_and_problem_data, polorder=1, solver_options=None):
logger = getLogger('discretize_elliptic_swipdg.discretize')
logger.info('discretizing ... ')
over_integrate = 2
grid, boundary_info = grid_and_problem_data['grid'], grid_and_problem_data[
'boundary_info']
_lambda, kappa, f = (grid_and_problem_data['lambda'],
grid_and_problem_data['kappa'],
grid_and_problem_data['f'])
lambda_bar, lambda_bar = grid_and_problem_data[
'lambda_bar'], grid_and_problem_data['lambda_bar']
mu_bar, mu_hat, parameter_range = (
grid_and_problem_data['mu_bar'], grid_and_problem_data['mu_hat'],
grid_and_problem_data['parameter_range'])
space = make_dg_space(grid)
# prepare operators and functionals
if isinstance(_lambda, dict):
system_ops = [
make_elliptic_swipdg_matrix_operator(lambda_func, kappa,
boundary_info, space,
over_integrate)
for lambda_func in _lambda['functions']
]
elliptic_ops = [
make_elliptic_matrix_operator(lambda_func, kappa, space,
over_integrate)
for lambda_func in _lambda['functions']
]
else:
system_ops = [
make_elliptic_swipdg_matrix_operator(_lambda, kappa, boundary_info,
space, over_integrate),
]
elliptic_ops = [
make_elliptic_matrix_operator(_lambda, kappa, space,
over_integrate),
]
if isinstance(f, dict):
rhs_functionals = [
make_l2_volume_vector_functional(f_func, space, over_integrate)
for f_func in f['functions']
]
else:
rhs_functionals = [
make_l2_volume_vector_functional(f, space, over_integrate),
]
l2_matrix_with_system_pattern = system_ops[0].matrix().copy()
l2_operator = make_l2_matrix_operator(l2_matrix_with_system_pattern, space)
# assemble everything in one grid walk
system_assembler = make_system_assembler(space)
for op in system_ops:
system_assembler.append(op)
for op in elliptic_ops:
system_assembler.append(op)
for func in rhs_functionals:
system_assembler.append(func)
system_assembler.append(l2_operator)
system_assembler.walk()
# wrap everything
if isinstance(_lambda, dict):
op = LincombOperator([
DuneXTMatrixOperator(o.matrix(),
dof_communicator=space.dof_communicator)
for o in system_ops
], _lambda['coefficients'])
elliptic_op = LincombOperator(
[DuneXTMatrixOperator(o.matrix()) for o in elliptic_ops],
_lambda['coefficients'])
else:
op = DuneXTMatrixOperator(system_ops[0].matrix())
elliptic_op = DuneXTMatrixOperator(elliptic_ops[0].matrix())
if isinstance(f, dict):
rhs = LincombOperator([
VectorFunctional(op.range.make_array([func.vector()]))
for func in rhs_functionals
], f['coefficients'])
else:
rhs = VectorFunctional(
op.range.make_array([rhs_functionals[0].vector()]))
operators = {
'l2':
DuneXTMatrixOperator(l2_matrix_with_system_pattern),
'elliptic':
elliptic_op,
'elliptic_mu_bar':
DuneXTMatrixOperator(elliptic_op.assemble(mu=mu_bar).matrix)
}
d = StationaryDiscretization(op,
rhs,
operators=operators,
visualizer=DuneGDTVisualizer(space))
d = d.with_(parameter_space=CubicParameterSpace(
d.parameter_type, parameter_range[0], parameter_range[1]))
return d, {'space': space}
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 thermalblock_demo(args):
args['--grid'] = int(args['--grid'])
args['RBSIZE'] = int(args['RBSIZE'])
args['--test'] = int(args['--test'])
args['--ipython-engines'] = int(args['--ipython-engines'])
args['--extension-alg'] = args['--extension-alg'].lower()
assert args['--extension-alg'] in {'trivial', 'gram_schmidt'}
args['--product'] = args['--product'].lower()
assert args['--product'] in {'trivial', 'h1'}
args['--reductor'] = args['--reductor'].lower()
assert args['--reductor'] in {'traditional', 'residual_basis'}
args['--cache-region'] = args['--cache-region'].lower()
args['--validation-mus'] = int(args['--validation-mus'])
args['--rho'] = float(args['--rho'])
args['--gamma'] = float(args['--gamma'])
args['--theta'] = float(args['--theta'])
problem = thermal_block_problem(num_blocks=(2, 2))
functionals = [
ExpressionParameterFunctional('diffusion[0]', {'diffusion': (2, )}),
ExpressionParameterFunctional('diffusion[1]**2', {'diffusion': (2, )}),
ExpressionParameterFunctional('diffusion[0]', {'diffusion': (2, )}),
ExpressionParameterFunctional('diffusion[1]', {'diffusion': (2, )})
]
problem = problem.with_(
diffusion=problem.diffusion.with_(coefficients=functionals),
parameter_space=CubicParameterSpace({'diffusion': (2, )}, 0.1, 1.))
print('Discretize ...')
fom, _ = discretize_stationary_cg(problem, diameter=1. / args['--grid'])
if args['--list-vector-array']:
from pymor.playground.discretizers.numpylistvectorarray import convert_to_numpy_list_vector_array
fom = convert_to_numpy_list_vector_array(fom)
if args['--cache-region'] != 'none':
fom.enable_caching(args['--cache-region'])
if args['--plot-solutions']:
print('Showing some solutions')
Us = ()
legend = ()
for mu in fom.parameter_space.sample_randomly(2):
print(f"Solving for diffusion = \n{mu['diffusion']} ... ")
sys.stdout.flush()
Us = Us + (fom.solve(mu), )
legend = legend + (str(mu['diffusion']), )
fom.visualize(Us,
legend=legend,
title='Detailed Solutions for different parameters',
block=True)
print('RB generation ...')
product = fom.h1_0_semi_product if args['--product'] == 'h1' else None
coercivity_estimator = ExpressionParameterFunctional(
'min([diffusion[0], diffusion[1]**2])', fom.parameter_type)
reductors = {
'residual_basis':
CoerciveRBReductor(fom,
product=product,
coercivity_estimator=coercivity_estimator),
'traditional':
SimpleCoerciveRBReductor(fom,
product=product,
coercivity_estimator=coercivity_estimator)
}
reductor = reductors[args['--reductor']]
pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'],
ipython_profile=args['--ipython-profile'])
greedy_data = rb_adaptive_greedy(
fom,
reductor,
validation_mus=args['--validation-mus'],
rho=args['--rho'],
gamma=args['--gamma'],
theta=args['--theta'],
use_estimator=not args['--without-estimator'],
error_norm=fom.h1_0_semi_norm,
max_extensions=args['RBSIZE'],
visualize=not args['--no-visualize-refinement'])
rom = greedy_data['rom']
if args['--pickle']:
print(
f"\nWriting reduced model to file {args['--pickle']}_reduced ...")
with open(args['--pickle'] + '_reduced', 'wb') as f:
dump(rom, f)
print(
f"Writing detailed model and reductor to file {args['--pickle']}_detailed ..."
)
with open(args['--pickle'] + '_detailed', 'wb') as f:
dump((fom, reductor), f)
print('\nSearching for maximum error on random snapshots ...')
results = reduction_error_analysis(
rom,
fom=fom,
reductor=reductor,
estimator=True,
error_norms=(fom.h1_0_semi_norm, ),
condition=True,
test_mus=args['--test'],
basis_sizes=25 if args['--plot-error-sequence'] else 1,
plot=True,
pool=pool)
real_rb_size = rom.solution_space.dim
print('''
*** RESULTS ***
Problem:
number of blocks: 2x2
h: sqrt(2)/{args[--grid]}
Greedy basis generation:
estimator disabled: {args[--without-estimator]}
extension method: {args[--extension-alg]}
product: {args[--product]}
prescribed basis size: {args[RBSIZE]}
actual basis size: {real_rb_size}
elapsed time: {greedy_data[time]}
'''.format(**locals()))
print(results['summary'])
sys.stdout.flush()
if args['--plot-error-sequence']:
from matplotlib import pyplot as plt
plt.show(results['figure'])
if args['--plot-err']:
mumax = results['max_error_mus'][0, -1]
U = fom.solve(mumax)
URB = reductor.reconstruct(rom.solve(mumax))
fom.visualize(
(U, URB, U - URB),
legend=('Detailed Solution', 'Reduced Solution', 'Error'),
title='Maximum Error Solution',
separate_colorbars=True,
block=True)
def discretize_stationary_from_disk(parameter_file):
"""Generates stationary discretization only based on data 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::
L(u, w) = F(w)
with an operator L and a linear functional F with a parameter w given as system matrices and rhs vectors in
an affine decomposition on the hard disk.
Parameters
----------
parameterFile
String containing the path to the .ini parameter file.
Returns
-------
discretization
The |Discretization| that has been generated.
Example
-------
Following parameter file is suitable for a discrete elliptic problem with
L(u, w) = (f_1(w)*K1 + f_2(w)*K2+...)*u and F(w) = g_1(w)*L1+g_2(w)*L2+... 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. 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)
...
[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
...
"""
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 'rhs-vectors' in config.sections()
assert 'parameter' in config.sections()
system_mat = config.items('system-matrices')
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 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
# Create and return stationary discretization
return StationaryDiscretization(operator=system_lincombOperator, rhs=rhs_lincombOperator,
parameter_space=parameter_space, products=products)
def text_problem(text='pyMOR', font_name=None):
import numpy as np
from PIL import Image, ImageDraw, ImageFont
from tempfile import NamedTemporaryFile
font_list = [font_name] if font_name else [
'DejaVuSansMono.ttf', 'VeraMono.ttf', 'UbuntuMono-R.ttf', 'Arial.ttf'
]
font = None
for filename in font_list:
try:
font = ImageFont.truetype(
filename, 64) # load some font from file of given size
except (OSError, IOError):
pass
if font is None:
raise ValueError('Could not load TrueType font')
size = font.getsize(text) # compute width and height of rendered text
size = (size[0] + 20, size[1] + 20
) # add a border of 10 pixels around the text
def make_bitmap_function(
char_num
): # we need to genereate a BitmapFunction for each character
img = Image.new('L',
size) # create new Image object of given dimensions
d = ImageDraw.Draw(img) # create ImageDraw object for the given Image
# in order to position the character correctly, we first draw all characters from the first
# up to the wanted character
d.text((10, 10), text[:char_num + 1], font=font, fill=255)
# next we erase all previous character by drawing a black rectangle
if char_num > 0:
d.rectangle(
((0, 0), (font.getsize(text[:char_num])[0] + 10, size[1])),
fill=0,
outline=0)
# open a new temporary file
with NamedTemporaryFile(
suffix='.png'
) as f: # after leaving this 'with' block, the temporary
# file is automatically deleted
img.save(f, format='png')
return BitmapFunction(f.name,
bounding_box=[(0, 0), size],
range=[0., 1.])
# create BitmapFunctions for each character
dfs = [make_bitmap_function(n) for n in range(len(text))]
# create an indicator function for the background
background = ConstantFunction(1., 2) - LincombFunction(
dfs, np.ones(len(dfs)))
# form the linear combination
dfs = [background] + dfs
coefficients = [1] + [
ProjectionParameterFunctional('diffusion', (len(text), ), (i, ))
for i in range(len(text))
]
diffusion = LincombFunction(dfs, coefficients)
return StationaryProblem(domain=RectDomain(dfs[1].bounding_box,
bottom='neumann'),
neumann_data=ConstantFunction(-1., 2),
diffusion=diffusion,
parameter_space=CubicParameterSpace(
diffusion.parameter_type, 0.1, 1.))
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
}
def thermal_block_problem(num_blocks=(3, 3), parameter_range=(0.1, 1)):
"""Analytical description of a 2D 'thermal block' diffusion problem.
The problem is to solve the elliptic equation ::
- ∇ ⋅ [ d(x, μ) ∇ u(x, μ) ] = f(x, μ)
on the domain [0,1]^2 with Dirichlet zero boundary values. The domain is
partitioned into nx x ny blocks and the diffusion function d(x, μ) is
constant on each such block (i,j) with value μ_ij. ::
----------------------------
| | | |
| μ_11 | μ_12 | μ_13 |
| | | |
|---------------------------
| | | |
| μ_21 | μ_22 | μ_23 |
| | | |
----------------------------
Parameters
----------
num_blocks
The tuple `(nx, ny)`
parameter_range
A tuple `(μ_min, μ_max)`. Each |Parameter| component μ_ij is allowed
to lie in the interval [μ_min, μ_max].
"""
def parameter_functional_factory(ix, iy):
return ProjectionParameterFunctional(component_name='diffusion',
component_shape=(num_blocks[1], num_blocks[0]),
index=(num_blocks[1] - iy - 1, ix),
name=f'diffusion_{ix}_{iy}')
def diffusion_function_factory(ix, iy):
if ix + 1 < num_blocks[0]:
X = '(x[..., 0] >= ix * dx) * (x[..., 0] < (ix + 1) * dx)'
else:
X = '(x[..., 0] >= ix * dx)'
if iy + 1 < num_blocks[1]:
Y = '(x[..., 1] >= iy * dy) * (x[..., 1] < (iy + 1) * dy)'
else:
Y = '(x[..., 1] >= iy * dy)'
return ExpressionFunction(f'{X} * {Y} * 1.',
2, (), {}, {'ix': ix, 'iy': iy, 'dx': 1. / num_blocks[0], 'dy': 1. / num_blocks[1]},
name=f'diffusion_{ix}_{iy}')
return StationaryProblem(
domain=RectDomain(),
rhs=ConstantFunction(dim_domain=2, value=1.),
diffusion=LincombFunction([diffusion_function_factory(ix, iy)
for ix, iy in product(range(num_blocks[0]), range(num_blocks[1]))],
[parameter_functional_factory(ix, iy)
for ix, iy in product(range(num_blocks[0]), range(num_blocks[1]))],
name='diffusion'),
parameter_space=CubicParameterSpace({'diffusion': (num_blocks[1], num_blocks[0])}, *parameter_range),
name=f'ThermalBlock({num_blocks})'
)
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 norm(U):
return np.max(nonblocked_disc.h1_norm(U))
class Reconstructor(object):
def __init__(self, disc, RB):
