"""
This module implements the user-visible API for constructing
:class:`.FunctionSpace` and :class:`.MixedFunctionSpace` objects. The
API is functional, rather than object-based, to allow for simple
backwards-compatibility, argument checking, and dispatch.
"""
import ufl
import finat.ufl
from pyop2.utils import flatten
from firedrake import functionspaceimpl as impl
from firedrake.petsc import PETSc
import numbers
__all__ = ("MixedFunctionSpace", "FunctionSpace",
"VectorFunctionSpace", "TensorFunctionSpace", "RestrictedFunctionSpace")
@PETSc.Log.EventDecorator()
def make_scalar_element(mesh, family, degree, vfamily, vdegree, variant):
"""Build a scalar :class:`finat.ufl.finiteelement.FiniteElement`.
Parameters
----------
mesh :
The mesh to determine the cell from.
family :
The finite element family.
degree :
The degree of the finite element.
variant :
The variant of the finite element.
vfamily :
The finite element in the vertical dimension (extruded meshes
only).
vdegree :
The degree of the element in the vertical dimension (extruded
meshes only).
Notes
-----
The ``family`` argument may be an existing
:class:`finat.ufl.finiteelementbase.FiniteElementBase`, in which case all
other arguments are ignored and the element is returned immediately.
As a side effect, this function finalises the initialisation of
the provided mesh, by calling :meth:`.AbstractMeshTopology.init` (or
:meth:`.MeshGeometry.init`) as appropriate.
"""
topology = mesh.topology
cell = topology.ufl_cell()
if isinstance(family, finat.ufl.FiniteElementBase):
return family.reconstruct(cell=cell)
if isinstance(cell, ufl.TensorProductCell) \
and vfamily is not None and vdegree is not None:
la = finat.ufl.FiniteElement(family,
cell=cell.sub_cells()[0],
degree=degree, variant=variant)
# If second element was passed in, use it
lb = finat.ufl.FiniteElement(vfamily,
cell=ufl.interval,
degree=vdegree, variant=variant)
# Now make the TensorProductElement
return finat.ufl.TensorProductElement(la, lb)
else:
return finat.ufl.FiniteElement(family, cell=cell, degree=degree, variant=variant)
[docs]
@PETSc.Log.EventDecorator("CreateFunctionSpace")
def FunctionSpace(mesh, family, degree=None, name=None,
vfamily=None, vdegree=None, variant=None):
"""Create a :class:`.FunctionSpace`.
Parameters
----------
mesh :
The mesh to determine the cell from.
family :
The finite element family.
degree :
The degree of the finite element.
name:
An optional name for the function space.
vfamily :
The finite element in the vertical dimension (extruded meshes
only).
vdegree :
The degree of the element in the vertical dimension (extruded
meshes only).
variant :
The variant of the finite element.
Notes
-----
The ``family`` argument may be an existing
:class:`finat.ufl.finiteelementbase.FiniteElementBase`, in which case all other arguments
are ignored and the appropriate :class:`.FunctionSpace` is returned.
"""
element = make_scalar_element(mesh, family, degree, vfamily, vdegree, variant)
return impl.WithGeometry.make_function_space(mesh, element, name=name)
@PETSc.Log.EventDecorator()
def DualSpace(mesh, family, degree=None, name=None,
vfamily=None, vdegree=None, variant=None):
"""Create a :class:`.FunctionSpace`.
Parameters
----------
mesh :
The mesh to determine the cell from.
family :
The finite element family.
degree :
The degree of the finite element.
name :
An optional name for the function space.
vfamily:
The finite element in the vertical dimension (extruded meshes
only).
vdegree :
The degree of the element in the vertical dimension (extruded
meshes only).
variant :
The variant of the finite element.
Notes
-----
The ``family`` argument may be an existing
:class:`finat.ufl.finiteelementbase.FiniteElementBase`, in which case all
other arguments are ignored and the appropriate :class:`.FunctionSpace` is
returned.
"""
element = make_scalar_element(mesh, family, degree, vfamily, vdegree, variant)
return impl.FiredrakeDualSpace.make_function_space(mesh, element, name=name)
[docs]
@PETSc.Log.EventDecorator()
def VectorFunctionSpace(mesh, family, degree=None, dim=None,
name=None, vfamily=None, vdegree=None, variant=None):
"""Create a rank-1 :class:`.FunctionSpace`.
Parameters
----------
mesh :
The mesh to determine the cell from.
family :
The finite element family.
degree :
The degree of the finite element.
dim :
An optional number of degrees of freedom per function space
node (defaults to the geometric dimension of the mesh).
name :
An optional name for the function space.
vfamily :
The finite element in the vertical dimension (extruded meshes
only).
vdegree :
The degree of the element in the vertical dimension (extruded
meshes only).
variant :
The variant of the finite element.
Notes
-----
The ``family`` argument may be an existing
:class:`finat.ufl.finiteelementbase.FiniteElementBase`, in which case all other arguments
are ignored and the appropriate :class:`.FunctionSpace` is returned. In
this case, the provided element must have an empty
:attr:`finat.ufl.finiteelementbase.FiniteElementBase.value_shape`.
The element that you provide need be a scalar element (with empty
``value_shape``), however, it should not be an existing
:class:`finat.ufl.mixedelement.VectorElement`. If you already have an
existing :class:`finat.ufl.mixedelement.VectorElement`, you should
pass it to :class:`.FunctionSpace` directly instead.
"""
sub_element = make_scalar_element(mesh, family, degree, vfamily, vdegree, variant)
if dim is None:
dim = mesh.geometric_dimension()
if not isinstance(dim, numbers.Integral) and dim > 0:
raise ValueError(f"Can't make VectorFunctionSpace with dim={dim}")
element = finat.ufl.VectorElement(sub_element, dim=dim)
return FunctionSpace(mesh, element, name=name)
[docs]
@PETSc.Log.EventDecorator()
def TensorFunctionSpace(mesh, family, degree=None, shape=None,
symmetry=None, name=None, vfamily=None,
vdegree=None, variant=None):
"""Create a rank-2 FunctionSpace.
Parameters
----------
mesh :
The mesh to determine the cell from.
family :
The finite element family.
degree :
The degree of the finite element.
shape :
An optional shape for the tensor-valued degrees of freedom at
each function space node (defaults to a square tensor using the
geometric dimension of the mesh).
symmetry :
Optional symmetries in the tensor value.
name :
An optional name for the function space.
vfamily :
The finite element in the vertical dimension (extruded meshes
only).
vdegree :
The degree of the element in the vertical dimension (extruded
meshes only).
variant :
The variant of the finite element.
Notes
-----
The ``family`` argument may be an existing
:class:`finat.ufl.finiteelementbase.FiniteElementBase`, in which case all other arguments
are ignored and the appropriate `FunctionSpace` is
returned. In this case, the provided element must have an empty
:attr:`finat.ufl.finiteelementbase.FiniteElementBase.value_shape`.
The element that you provide must be a scalar element (with empty
``value_shape``). If you already have an existing
:class:`finat.ufl.mixedelement.TensorElement`, you should pass it to
`FunctionSpace` directly instead.
"""
sub_element = make_scalar_element(mesh, family, degree, vfamily, vdegree, variant)
shape = shape or (mesh.geometric_dimension(),) * 2
element = finat.ufl.TensorElement(sub_element, shape=shape, symmetry=symmetry)
return FunctionSpace(mesh, element, name=name)
[docs]
@PETSc.Log.EventDecorator()
def MixedFunctionSpace(spaces, name=None, mesh=None):
"""Create a MixedFunctionSpace.
Parameters
----------
spaces :
An iterable of constituent spaces, or a
:class:`finat.ufl.mixedelement.MixedElement`.
name :
An optional name for the mixed function space.
mesh :
An optional mesh. Must be provided if spaces is a
:class:`finat.ufl.mixedelement.MixedElement`, ignored otherwise.
"""
if isinstance(spaces, finat.ufl.FiniteElementBase):
# Build the spaces if we got a mixed element
assert type(spaces) is finat.ufl.MixedElement and mesh is not None
sub_elements = []
def rec(eles):
for ele in eles:
# Only want to recurse into MixedElements
if type(ele) is finat.ufl.MixedElement:
rec(ele.sub_elements)
else:
sub_elements.append(ele)
rec(spaces.sub_elements)
spaces = [FunctionSpace(mesh, element) for element in sub_elements]
# Check that function spaces are on the same mesh
meshes = [space.mesh() for space in spaces]
for i in range(1, len(meshes)):
if meshes[i] is not meshes[0]:
raise ValueError("All function spaces must be defined on the same mesh!")
try:
cls, = set(type(s) for s in spaces)
except ValueError:
# Neither primal nor dual
# We had not implemented something in between, so let's make it primal
cls = impl.WithGeometry
# Select mesh
mesh = meshes[0]
# Get topological spaces
spaces = tuple(s.topological for s in flatten(spaces))
# Error checking
for space in spaces:
if type(space) in (impl.FunctionSpace, impl.RealFunctionSpace, impl.RestrictedFunctionSpace):
continue
elif type(space) in (impl.ProxyFunctionSpace, impl.ProxyRestrictedFunctionSpace):
if space.component is not None:
raise ValueError("Can't make mixed space with %s" % space)
continue
else:
raise ValueError("Can't make mixed space with %s" % type(space))
new = impl.MixedFunctionSpace(spaces, name=name)
if mesh is not mesh.topology:
new = cls.create(new, mesh)
return new
[docs]
@PETSc.Log.EventDecorator("CreateFunctionSpace")
def RestrictedFunctionSpace(function_space, boundary_set=[], name=None):
"""Create a :class:`.RestrictedFunctionSpace`.
Parameters
----------
function_space :
FunctionSpace object to restrict
boundary_set :
A set of subdomains of the mesh in which Dirichlet boundary conditions
will be applied.
name :
An optional name for the function space.
"""
return impl.WithGeometry.create(impl.RestrictedFunctionSpace(function_space,
boundary_set=boundary_set,
name=name),
function_space.mesh())
