def fenics_vector_array_factory(length, space, seed):
V = FenicsVectorSpace(fenics_spaces[space])
U = V.zeros(length)
dim = V.dim
np.random.seed(seed)
for v, a in zip(U._list, np.random.random((length, dim))):
v.real_part.impl[:] = a
if np.random.randint(2):
UU = V.zeros(length)
for v, a in zip(UU._list, np.random.random((length, dim))):
v.real_part.impl[:] = a
for u, uu in zip(U._list, UU._list):
u.imag_part = uu.real_part
return U
def fenics_nonlinear_operator_factory():
import dolfin as df
from pymor.bindings.fenics import FenicsVectorSpace, FenicsOperator, FenicsMatrixOperator
class DirichletBoundary(df.SubDomain):
def inside(self, x, on_boundary):
return abs(x[0] - 1.0) < df.DOLFIN_EPS and on_boundary
mesh = df.UnitSquareMesh(10, 10)
V = df.FunctionSpace(mesh, "CG", 2)
g = df.Constant(1.)
c = df.Constant(1.)
db = DirichletBoundary()
bc = df.DirichletBC(V, g, db)
u = df.TrialFunction(V)
v = df.TestFunction(V)
w = df.Function(V)
f = df.Expression("x[0]*sin(x[1])", degree=2)
F = df.inner((1 + c*w**2)*df.grad(w), df.grad(v))*df.dx - f*v*df.dx
space = FenicsVectorSpace(V)
op = FenicsOperator(F, space, space, w, (bc,),
parameter_setter=lambda mu: c.assign(float(mu['c'])),
parameter_type={'c': ()},
solver_options={'inverse': {'type': 'newton', 'rtol': 1e-6}})
prod = FenicsMatrixOperator(df.assemble(u*v*df.dx), V, V)
return op, op.parse_parameter(42), op.source.random(), op.range.random(), prod, prod
def _fenics_vector_spaces(draw, np_data_list, compatible, count, dims):
ret = []
for d, ar in zip(dims, np_data_list):
assume(d > 1)
if d not in _FENICS_spaces:
_FENICS_spaces[d] = FenicsVectorSpace(df.FunctionSpace(df.UnitIntervalMesh(d - 1), 'Lagrange', 1))
ret.append((_FENICS_spaces[d], ar))
return ret
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
space = FenicsVectorSpace(V)
op = FenicsOperator(
F,
space,
space,
u, (bc, ),
parameter_setter=lambda mu: c.assign(mu['c'].item()),
parameters={'c': 1},
solver_options={'inverse': {
'type': 'newton',
'rtol': 1e-6
}})
rhs = VectorOperator(op.range.zeros())
fom = StationaryModel(op, rhs, visualizer=FenicsVisualizer(space))
return fom
def make_pymor_bindings(V, dx, ds, solver_options):
import pymor.basic as pmb
from pymor.bindings.fenics import FenicsVectorSpace, FenicsMatrixOperator
from pymor.algorithms.timestepping import ImplicitEulerTimeStepper
space = FenicsVectorSpace(V)
# Operators matrix
u = df.TrialFunction(V)
v = df.TestFunction(V)
mass_mat = [df.assemble(df.inner(u, v)*dx(i)) for i in domain_dict.values()]
diff_mat = [df.assemble(df.inner(df.grad(u), df.grad(v))*dx(i)) for i in domain_dict.values()]
robin_left_mat = df.assemble(u*v*ds(1))
source_mat = df.assemble(v*dx(domain_dict['die']))
# Function continues here with pymor bindings (see below)
def _discretize_fenics():
# assemble system matrices - FEniCS code
########################################
import dolfin as df
# discrete function space
mesh = df.UnitSquareMesh(GRID_INTERVALS, GRID_INTERVALS, 'crossed')
V = df.FunctionSpace(mesh, 'Lagrange', FENICS_ORDER)
u = df.TrialFunction(V)
v = df.TestFunction(V)
# data functions
bottom_diffusion = df.Expression('(x[0] > 0.45) * (x[0] < 0.55) * (x[1] < 0.7) * 1.',
element=df.FunctionSpace(mesh, 'DG', 0).ufl_element())
top_diffusion = df.Expression('(x[0] > 0.35) * (x[0] < 0.40) * (x[1] > 0.3) * 1. +'
'(x[0] > 0.60) * (x[0] < 0.65) * (x[1] > 0.3) * 1.',
element=df.FunctionSpace(mesh, 'DG', 0).ufl_element())
initial_data = df.Expression('(x[0] > 0.45) * (x[0] < 0.55) * (x[1] < 0.7) * 10.',
element=df.FunctionSpace(mesh, 'DG', 0).ufl_element())
neumann_data = df.Expression('(x[0] > 0.45) * (x[0] < 0.55) * 1000.',
element=df.FunctionSpace(mesh, 'DG', 0).ufl_element())
# assemble matrices and vectors
l2_mat = df.assemble(df.inner(u, v) * df.dx)
l2_0_mat = l2_mat.copy()
h1_mat = df.assemble(df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
h1_0_mat = h1_mat.copy()
mat0 = h1_mat.copy()
mat0.zero()
bottom_mat = df.assemble(bottom_diffusion * df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
top_mat = df.assemble(top_diffusion * df.inner(df.nabla_grad(u), df.nabla_grad(v)) * df.dx)
u0 = df.project(initial_data, V).vector()
f = df.assemble(neumann_data * v * df.ds)
# boundary treatment
def dirichlet_boundary(x, on_boundary):
tol = 1e-14
return on_boundary and (abs(x[0]) < tol or abs(x[0] - 1) < tol or abs(x[1] - 1) < tol)
bc = df.DirichletBC(V, df.Constant(0.), dirichlet_boundary)
bc.apply(l2_0_mat)
bc.apply(h1_0_mat)
bc.apply(mat0)
bc.zero(bottom_mat)
bc.zero(top_mat)
bc.apply(f)
bc.apply(u0)
# wrap everything as a pyMOR model
##################################
from pymor.bindings.fenics import FenicsVectorSpace, FenicsMatrixOperator, FenicsVisualizer
fom = InstationaryModel(
T=1.,
initial_data=FenicsVectorSpace(V).make_array([u0]),
operator=LincombOperator([FenicsMatrixOperator(mat0, V, V),
FenicsMatrixOperator(h1_0_mat, V, V),
FenicsMatrixOperator(bottom_mat, V, V),
FenicsMatrixOperator(top_mat, V, V)],
[1.,
1.,
100. - 1.,
ExpressionParameterFunctional('top[0] - 1.', {'top': 1})]),
rhs=VectorOperator(FenicsVectorSpace(V).make_array([f])),
mass=FenicsMatrixOperator(l2_0_mat, V, V, name='l2'),
products={'l2': FenicsMatrixOperator(l2_mat, V, V, name='l2'),
'l2_0': FenicsMatrixOperator(l2_0_mat, V, V, name='l2_0'),
'h1': FenicsMatrixOperator(h1_mat, V, V, name='h1'),
'h1_0_semi': FenicsMatrixOperator(h1_0_mat, V, V, name='h1_0_semi')},
time_stepper=ImplicitEulerTimeStepper(nt=NT),
visualizer=FenicsVisualizer(FenicsVectorSpace(V))
)
return fom
def _discretize_fenics():
# assemble system matrices - FEniCS code
########################################
import dolfin as df
mesh = df.UnitSquareMesh(GRID_INTERVALS, GRID_INTERVALS, 'crossed')
V = df.FunctionSpace(mesh, 'Lagrange', FENICS_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)
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
# define parameter functionals (same as in pymor.analyticalproblems.thermalblock)
parameter_functionals = [
ProjectionParameterFunctional(component_name='diffusion',
component_shape=(YBLOCKS, XBLOCKS),
index=(YBLOCKS - y - 1, x))
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')
# 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},
parameter_space=parameter_space,
visualizer=visualizer)
return fom
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 make_pymor_bindings(V, dx, ds, solver_options):
'''Assemble the Fenics operator and binds them to pymor.Operator with parameter separation
Returns the full order model (pymor.Model)'''
import pymor.basic as pmb
from pymor.bindings.fenics import FenicsVectorSpace, FenicsMatrixOperator
from pymor.algorithms.timestepping import ImplicitEulerTimeStepper
space = FenicsVectorSpace(V)
# Operators matrix
u = df.TrialFunction(V)
v = df.TestFunction(V)
mass_mat = [
df.assemble(df.inner(u, v) * dx(i)) for i in domain_dict.values()
]
diff_mat = [
df.assemble(df.inner(df.grad(u), df.grad(v)) * dx(i))
for i in domain_dict.values()
]
robin_left_mat = df.assemble(u * v * ds(1))
source_mat = df.assemble(v * dx(domain_dict['die']))
# Norms matrix
l2_mat = df.assemble(df.inner(u, v) * df.dx)
l2_0_mat = l2_mat.copy()
h1_mat = df.assemble(df.inner(df.grad(u), df.grad(v)) * dx)
h1_0_mat = h1_mat.copy()
# Operators
mass_op = [
FenicsMatrixOperator(M, V, V, solver_options=solver_options)
for M in mass_mat
]
diff_op = [
FenicsMatrixOperator(M, V, V, solver_options=solver_options)
for M in diff_mat
]
robin_left_op = FenicsMatrixOperator(robin_left_mat,
V,
V,
solver_options=solver_options)
source_op = pmb.VectorOperator(space.make_array([source_mat]))
# Param projection
project_lamb = [
pmb.ProjectionParameterFunctional(f'lamb_{dom}', 1, 0)
for dom in domain_dict.keys()
]
project_capa = [
pmb.ProjectionParameterFunctional(f'capa_{dom}', 1, 0)
for dom in domain_dict.keys()
]
# Separated operator
mass = pmb.LincombOperator(mass_op, project_capa)
op = pmb.LincombOperator(
[*diff_op, robin_left_op],
[*project_lamb,
pmb.ExpressionParameterFunctional('h[0]', {'h': 1})])
rhs = pmb.LincombOperator(
[source_op], [pmb.ExpressionParameterFunctional('phi[0]', {'phi': 1})])
end_time = 10 * 60
dt = 5
fom = InstationaryParametricMassModel(
T=end_time,
initial_data=space.make_array([df.project(df.Constant(0),
V).vector()]),
operator=op,
rhs=rhs,
mass=mass,
time_stepper=ImplicitEulerTimeStepper(end_time // dt),
num_values=None,
products={
'l2': FenicsMatrixOperator(l2_mat, V, V),
'l2_0': FenicsMatrixOperator(l2_0_mat, V, V),
'h1': FenicsMatrixOperator(h1_mat, V, V),
'h1_0_semi': FenicsMatrixOperator(h1_0_mat, V, V)
},
visualizer=None)
return fom