def __init__(self, mesh, element, name=None, dim=1, rank=0):
"""
:param mesh: :class:`Mesh` to build this space on
:param element: :class:`ufl.FiniteElementBase` to build this space from
:param name: user-defined name for this space
:param dim: vector space dimension of a :class:`.VectorFunctionSpace`
:param rank: rank of the space, not the value rank
"""
self._ufl_element = element
# Compute the FIAT version of the UFL element above
self.fiat_element = fiat_utils.fiat_from_ufl_element(element)
if isinstance(mesh, mesh_t.ExtrudedMesh):
# Set up some extrusion-specific things
# The bottom layer maps will come from element_dof_list
# dof_count is the total number of dofs in the extruded mesh
# Get the flattened version of the FIAT element
self.flattened_element = fiat_utils.FlattenedElement(self.fiat_element)
# Compute the number of DoFs per dimension on top/bottom and sides
entity_dofs = self.fiat_element.entity_dofs()
top_dim = mesh._plex.getDimension()
self._xtr_hdofs = [len(entity_dofs[(d, 0)][0]) for d in range(top_dim+1)]
self._xtr_vdofs = [len(entity_dofs[(d, 1)][0]) for d in range(top_dim+1)]
# Compute the dofs per column
self.dofs_per_column = eutils.compute_extruded_dofs(self.fiat_element,
self.flattened_element.entity_dofs(),
mesh._layers)
# Compute the offset for the extrusion process
self.offset = eutils.compute_offset(self.fiat_element.entity_dofs(),
self.flattened_element.entity_dofs(),
self.fiat_element.space_dimension())
# Compute the top and bottom masks to identify boundary dofs
#
# Sorting the keys of the closure entity dofs, the whole cell
# comes last [-1], before that the horizontal facet [-2], before
# that vertical facets [-3]. We need the horizontal facets here.
closure_dofs = self.fiat_element.entity_closure_dofs()
b_mask = closure_dofs[sorted(closure_dofs.keys())[-2]][0]
t_mask = closure_dofs[sorted(closure_dofs.keys())[-2]][1]
self.bt_masks = {}
self.bt_masks["topological"] = (b_mask, t_mask) # conversion to tuple
# Geometric facet dofs
facet_dofs = horiz_facet_support_dofs(self.fiat_element)
self.bt_masks["geometric"] = (facet_dofs[0], facet_dofs[1])
self.extruded = True
self._dofs_per_entity = self.dofs_per_column
else:
# If not extruded specific, set things to None/False, etc.
self.offset = None
self.bt_masks = None
self.dofs_per_column = np.zeros(1, np.int32)
self.extruded = False
entity_dofs = self.fiat_element.entity_dofs()
self._dofs_per_entity = [len(entity[0]) for d, entity in entity_dofs.iteritems()]
self.name = name
self._dim = dim
self._mesh = mesh
self._index = None
dm = PETSc.DMShell().create()
dm.setAttr('__fs__', weakref.ref(self))
dm.setPointSF(mesh._plex.getPointSF())
# Create the PetscSection mapping topological entities to DoFs
sec = mesh._plex.createSection([1], self._dofs_per_entity,
perm=mesh._plex_renumbering)
dm.setDefaultSection(sec)
self._global_numbering = sec
self._dm = dm
self._ises = None
self._halo = halo.Halo(dm)
# Compute entity class offsets
self.dof_classes = [0, 0, 0, 0]
for d in range(mesh._plex.getDimension()+1):
ndofs = self._dofs_per_entity[d]
for i in range(4):
self.dof_classes[i] += ndofs * mesh._entity_classes[d, i]
# Tell the DM about the layout of the global vector
from firedrake.function import Function
with Function(self).dat.vec_ro as v:
self._dm.setGlobalVector(v.duplicate())
self._node_count = self._global_numbering.getStorageSize()
self.cell_node_list = mesh.create_cell_node_list(self._global_numbering,
self.fiat_element)
if mesh._plex.getStratumSize("interior_facets", 1) > 0:
self.interior_facet_node_list = \
dmplex.get_facet_nodes(mesh.interior_facets.facet_cell,
self.cell_node_list)
else:
self.interior_facet_node_list = np.array([], dtype=np.int32)
if mesh._plex.getStratumSize("exterior_facets", 1) > 0:
self.exterior_facet_node_list = \
dmplex.get_facet_nodes(mesh.exterior_facets.facet_cell,
self.cell_node_list)
else:
self.exterior_facet_node_list = np.array([], dtype=np.int32)
# Note: this is the function space rank. The value rank may be different.
self.rank = rank
# Empty map caches. This is a sui generis cache
# implementation because of the need to support boundary
# conditions.
self._cell_node_map_cache = {}
self._exterior_facet_map_cache = {}
self._interior_facet_map_cache = {}
def __init__(self, mesh, layers, layer_height=None, extrusion_type='uniform', kernel=None, gdim=None):
# A cache of function spaces that have been built on this mesh
import firedrake.function as function
import firedrake.functionspace as functionspace
self._cache = {}
mesh.init()
self._old_mesh = mesh
if layers < 1:
raise RuntimeError("Must have at least one layer of extruded cells (not %d)" % layers)
# All internal logic works with layers of base mesh (not layers of cells)
self._layers = layers + 1
self.parent = mesh.parent
self.uid = mesh.uid
self.name = mesh.name
self._plex = mesh._plex
self._plex_renumbering = mesh._plex_renumbering
self._cell_numbering = mesh._cell_numbering
self._entity_classes = mesh._entity_classes
interior_f = self._old_mesh.interior_facets
self._interior_facets = _Facets(self, interior_f.classes,
"interior",
interior_f.facet_cell,
interior_f.local_facet_number)
exterior_f = self._old_mesh.exterior_facets
self._exterior_facets = _Facets(self, exterior_f.classes,
"exterior",
exterior_f.facet_cell,
exterior_f.local_facet_number,
exterior_f.markers,
unique_markers=exterior_f.unique_markers)
self.ufl_cell_element = ufl.FiniteElement("Lagrange",
domain=mesh.ufl_cell(),
degree=1)
self.ufl_interval_element = ufl.FiniteElement("Lagrange",
domain=ufl.Cell("interval", 1),
degree=1)
self.fiat_base_element = fiat_utils.fiat_from_ufl_element(self.ufl_cell_element)
self.fiat_vert_element = fiat_utils.fiat_from_ufl_element(self.ufl_interval_element)
fiat_element = FIAT.tensor_finite_element.TensorFiniteElement(self.fiat_base_element, self.fiat_vert_element)
if extrusion_type == "uniform":
# *must* add a new dimension
self._ufl_cell = ufl.OuterProductCell(mesh.ufl_cell(), ufl.Cell("interval", 1), gdim=mesh.ufl_cell().geometric_dimension() + 1)
elif extrusion_type in ("radial", "radial_hedgehog"):
# do not allow radial extrusion if tdim = gdim
if mesh.ufl_cell().geometric_dimension() == mesh.ufl_cell().topological_dimension():
raise RuntimeError("Cannot radially-extrude a mesh with equal geometric and topological dimension")
# otherwise, all is fine, so make cell
self._ufl_cell = ufl.OuterProductCell(mesh.ufl_cell(), ufl.Cell("interval", 1))
else:
# check for kernel
if kernel is None:
raise RuntimeError("If the custom extrusion_type is used, a kernel must be provided")
# otherwise, use the gdim that was passed in
if gdim is None:
raise RuntimeError("The geometric dimension of the mesh must be specified if a custom extrusion kernel is used")
self._ufl_cell = ufl.OuterProductCell(mesh.ufl_cell(), ufl.Cell("interval", 1), gdim=gdim)
self._ufl_domain = ufl.Domain(self.ufl_cell(), data=self)
flat_temp = fiat_utils.FlattenedElement(fiat_element)
# Calculated dofs_per_column from flattened_element and layers.
# The mirrored elements have to be counted only once.
# Then multiply by layers and layers - 1 accordingly.
self.dofs_per_column = eutils.compute_extruded_dofs(fiat_element, flat_temp.entity_dofs(),
layers)
# Compute Coordinates of the extruded mesh
if layer_height is None:
# Default to unit
layer_height = 1.0 / layers
if extrusion_type == 'radial_hedgehog':
hfamily = "DG"
else:
hfamily = mesh.coordinates.element().family()
hdegree = mesh.coordinates.element().degree()
self._coordinate_fs = functionspace.VectorFunctionSpace(self, hfamily,
hdegree,
vfamily="CG",
vdegree=1)
self.coordinates = function.Function(self._coordinate_fs)
self._ufl_domain = ufl.Domain(self.coordinates)
eutils.make_extruded_coords(self, layer_height, extrusion_type=extrusion_type,
kernel=kernel)
if extrusion_type == "radial_hedgehog":
fs = functionspace.VectorFunctionSpace(self, "CG", hdegree, vfamily="CG", vdegree=1)
self.radial_coordinates = function.Function(fs)
eutils.make_extruded_coords(self, layer_height, extrusion_type="radial",
output_coords=self.radial_coordinates)
# Build a new ufl element for this function space with the
# correct domain. This is necessary since this function space
# is in the cache and will be picked up by later
# VectorFunctionSpace construction.
self._coordinate_fs._ufl_element = self._coordinate_fs.ufl_element().reconstruct(domain=self.ufl_domain())
# HACK alert!
# Replace coordinate Function by one that has a real domain on it (but don't copy values)
self.coordinates = function.Function(self._coordinate_fs, val=self.coordinates.dat)
# Add subdomain_data to the measure objects we store with
# the mesh. These are weakrefs for consistency with the
# "global" measure objects
self._dx = ufl.Measure('cell', subdomain_data=weakref.ref(self.coordinates))
self._ds = ufl.Measure('exterior_facet', subdomain_data=weakref.ref(self.coordinates))
self._dS = ufl.Measure('interior_facet', subdomain_data=weakref.ref(self.coordinates))
self._ds_t = ufl.Measure('exterior_facet_top', subdomain_data=weakref.ref(self.coordinates))
self._ds_b = ufl.Measure('exterior_facet_bottom', subdomain_data=weakref.ref(self.coordinates))
self._ds_v = ufl.Measure('exterior_facet_vert', subdomain_data=weakref.ref(self.coordinates))
self._dS_h = ufl.Measure('interior_facet_horiz', subdomain_data=weakref.ref(self.coordinates))
self._dS_v = ufl.Measure('interior_facet_vert', subdomain_data=weakref.ref(self.coordinates))
# Set the subdomain_data on all the default measures to this
# coordinate field. We don't set the domain on the measure
# since this causes an uncollectable reference in the global
# space (dx is global). Furthermore, it's never used anyway.
for measure in [ufl.ds, ufl.dS, ufl.dx, ufl.ds_t, ufl.ds_b, ufl.ds_v, ufl.dS_h, ufl.dS_v]:
measure._subdomain_data = weakref.ref(self.coordinates)
def __init__(self, mesh, element, name=None, dim=1, rank=0):
"""
:param mesh: :class:`Mesh` to build this space on
:param element: :class:`ufl.FiniteElementBase` to build this space from
:param name: user-defined name for this space
:param dim: vector space dimension of a :class:`.VectorFunctionSpace`
:param rank: rank of the space, not the value rank
"""
self._ufl_element = element
# Compute the FIAT version of the UFL element above
self.fiat_element = fiat_utils.fiat_from_ufl_element(element)
if isinstance(mesh, mesh_t.ExtrudedMesh):
# Set up some extrusion-specific things
# The bottom layer maps will come from element_dof_list
# dof_count is the total number of dofs in the extruded mesh
# Get the flattened version of the FIAT element
self.flattened_element = fiat_utils.FlattenedElement(
self.fiat_element)
# Compute the number of DoFs per dimension on top/bottom and sides
entity_dofs = self.fiat_element.entity_dofs()
top_dim = mesh._plex.getDimension()
self._xtr_hdofs = [
len(entity_dofs[(d, 0)][0]) for d in range(top_dim + 1)
]
self._xtr_vdofs = [
len(entity_dofs[(d, 1)][0]) for d in range(top_dim + 1)
]
# Compute the dofs per column
self.dofs_per_column = eutils.compute_extruded_dofs(
self.fiat_element, self.flattened_element.entity_dofs(),
mesh._layers)
# Compute the offset for the extrusion process
self.offset = eutils.compute_offset(
self.fiat_element.entity_dofs(),
self.flattened_element.entity_dofs(),
self.fiat_element.space_dimension())
# Compute the top and bottom masks to identify boundary dofs
#
# Sorting the keys of the closure entity dofs, the whole cell
# comes last [-1], before that the horizontal facet [-2], before
# that vertical facets [-3]. We need the horizontal facets here.
closure_dofs = self.fiat_element.entity_closure_dofs()
b_mask = closure_dofs[sorted(closure_dofs.keys())[-2]][0]
t_mask = closure_dofs[sorted(closure_dofs.keys())[-2]][1]
self.bt_masks = (b_mask, t_mask) # conversion to tuple
self.extruded = True
self._dofs_per_entity = self.dofs_per_column
else:
# If not extruded specific, set things to None/False, etc.
self.offset = None
self.bt_masks = None
self.dofs_per_column = np.zeros(1, np.int32)
self.extruded = False
entity_dofs = self.fiat_element.entity_dofs()
self._dofs_per_entity = [
len(entity[0]) for d, entity in entity_dofs.iteritems()
]
self.name = name
self._dim = dim
self._mesh = mesh
self._index = None
dm = PETSc.DMShell().create()
dm.setAttr('__fs__', weakref.ref(self))
dm.setPointSF(mesh._plex.getPointSF())
# Create the PetscSection mapping topological entities to DoFs
sec = mesh._plex.createSection([1],
self._dofs_per_entity,
perm=mesh._plex_renumbering)
dm.setDefaultSection(sec)
self._global_numbering = sec
self._dm = dm
self._ises = None
self._halo = halo.Halo(dm)
# Compute entity class offsets
self.dof_classes = [0, 0, 0, 0]
for d in range(mesh._plex.getDimension() + 1):
ndofs = self._dofs_per_entity[d]
for i in range(4):
self.dof_classes[i] += ndofs * mesh._entity_classes[d, i]
# Tell the DM about the layout of the global vector
from firedrake.function import Function
with Function(self).dat.vec_ro as v:
self._dm.setGlobalVector(v.duplicate())
self._node_count = self._global_numbering.getStorageSize()
self.cell_node_list = mesh.create_cell_node_list(
self._global_numbering, self.fiat_element)
if mesh._plex.getStratumSize("interior_facets", 1) > 0:
self.interior_facet_node_list = \
dmplex.get_facet_nodes(mesh.interior_facets.facet_cell,
self.cell_node_list)
else:
self.interior_facet_node_list = np.array([], dtype=np.int32)
if mesh._plex.getStratumSize("exterior_facets", 1) > 0:
self.exterior_facet_node_list = \
dmplex.get_facet_nodes(mesh.exterior_facets.facet_cell,
self.cell_node_list)
else:
self.exterior_facet_node_list = np.array([], dtype=np.int32)
# Note: this is the function space rank. The value rank may be different.
self.rank = rank
# Empty map caches. This is a sui generis cache
# implementation because of the need to support boundary
# conditions.
self._cell_node_map_cache = {}
self._exterior_facet_map_cache = {}
self._interior_facet_map_cache = {}
def __init__(self,
mesh,
layers,
layer_height=None,
extrusion_type='uniform',
kernel=None,
gdim=None):
# A cache of function spaces that have been built on this mesh
import firedrake.function as function
import firedrake.functionspace as functionspace
self._cache = {}
mesh.init()
self._old_mesh = mesh
if layers < 1:
raise RuntimeError(
"Must have at least one layer of extruded cells (not %d)" %
layers)
# All internal logic works with layers of base mesh (not layers of cells)
self._layers = layers + 1
self.parent = mesh.parent
self.uid = mesh.uid
self.name = mesh.name
self._plex = mesh._plex
self._plex_renumbering = mesh._plex_renumbering
self._cell_numbering = mesh._cell_numbering
self._entity_classes = mesh._entity_classes
interior_f = self._old_mesh.interior_facets
self._interior_facets = _Facets(self, interior_f.classes, "interior",
interior_f.facet_cell,
interior_f.local_facet_number)
exterior_f = self._old_mesh.exterior_facets
self._exterior_facets = _Facets(
self,
exterior_f.classes,
"exterior",
exterior_f.facet_cell,
exterior_f.local_facet_number,
exterior_f.markers,
unique_markers=exterior_f.unique_markers)
self.ufl_cell_element = ufl.FiniteElement("Lagrange",
domain=mesh.ufl_cell(),
degree=1)
self.ufl_interval_element = ufl.FiniteElement("Lagrange",
domain=ufl.Cell(
"interval", 1),
degree=1)
self.fiat_base_element = fiat_utils.fiat_from_ufl_element(
self.ufl_cell_element)
self.fiat_vert_element = fiat_utils.fiat_from_ufl_element(
self.ufl_interval_element)
fiat_element = FIAT.tensor_finite_element.TensorFiniteElement(
self.fiat_base_element, self.fiat_vert_element)
if extrusion_type == "uniform":
# *must* add a new dimension
self._ufl_cell = ufl.OuterProductCell(
mesh.ufl_cell(),
ufl.Cell("interval", 1),
gdim=mesh.ufl_cell().geometric_dimension() + 1)
elif extrusion_type in ("radial", "radial_hedgehog"):
# do not allow radial extrusion if tdim = gdim
if mesh.ufl_cell().geometric_dimension() == mesh.ufl_cell(
).topological_dimension():
raise RuntimeError(
"Cannot radially-extrude a mesh with equal geometric and topological dimension"
)
# otherwise, all is fine, so make cell
self._ufl_cell = ufl.OuterProductCell(mesh.ufl_cell(),
ufl.Cell("interval", 1))
else:
# check for kernel
if kernel is None:
raise RuntimeError(
"If the custom extrusion_type is used, a kernel must be provided"
)
# otherwise, use the gdim that was passed in
if gdim is None:
raise RuntimeError(
"The geometric dimension of the mesh must be specified if a custom extrusion kernel is used"
)
self._ufl_cell = ufl.OuterProductCell(mesh.ufl_cell(),
ufl.Cell("interval", 1),
gdim=gdim)
self._ufl_domain = ufl.Domain(self.ufl_cell(), data=self)
flat_temp = fiat_utils.FlattenedElement(fiat_element)
# Calculated dofs_per_column from flattened_element and layers.
# The mirrored elements have to be counted only once.
# Then multiply by layers and layers - 1 accordingly.
self.dofs_per_column = eutils.compute_extruded_dofs(
fiat_element, flat_temp.entity_dofs(), layers)
# Compute Coordinates of the extruded mesh
if layer_height is None:
# Default to unit
layer_height = 1.0 / layers
if extrusion_type == 'radial_hedgehog':
hfamily = "DG"
else:
hfamily = mesh.coordinates.element().family()
hdegree = mesh.coordinates.element().degree()
self._coordinate_fs = functionspace.VectorFunctionSpace(self,
hfamily,
hdegree,
vfamily="CG",
vdegree=1)
self.coordinates = function.Function(self._coordinate_fs)
self._ufl_domain = ufl.Domain(self.coordinates)
eutils.make_extruded_coords(self,
layer_height,
extrusion_type=extrusion_type,
kernel=kernel)
if extrusion_type == "radial_hedgehog":
fs = functionspace.VectorFunctionSpace(self,
"CG",
hdegree,
vfamily="CG",
vdegree=1)
self.radial_coordinates = function.Function(fs)
eutils.make_extruded_coords(self,
layer_height,
extrusion_type="radial",
output_coords=self.radial_coordinates)
# Build a new ufl element for this function space with the
# correct domain. This is necessary since this function space
# is in the cache and will be picked up by later
# VectorFunctionSpace construction.
self._coordinate_fs._ufl_element = self._coordinate_fs.ufl_element(
).reconstruct(domain=self.ufl_domain())
# HACK alert!
# Replace coordinate Function by one that has a real domain on it (but don't copy values)
self.coordinates = function.Function(self._coordinate_fs,
val=self.coordinates.dat)
# Add subdomain_data to the measure objects we store with
# the mesh. These are weakrefs for consistency with the
# "global" measure objects
self._dx = ufl.Measure('cell',
subdomain_data=weakref.ref(self.coordinates))
self._ds = ufl.Measure('exterior_facet',
subdomain_data=weakref.ref(self.coordinates))
self._dS = ufl.Measure('interior_facet',
subdomain_data=weakref.ref(self.coordinates))
self._ds_t = ufl.Measure('exterior_facet_top',
subdomain_data=weakref.ref(self.coordinates))
self._ds_b = ufl.Measure('exterior_facet_bottom',
subdomain_data=weakref.ref(self.coordinates))
self._ds_v = ufl.Measure('exterior_facet_vert',
subdomain_data=weakref.ref(self.coordinates))
self._dS_h = ufl.Measure('interior_facet_horiz',
subdomain_data=weakref.ref(self.coordinates))
self._dS_v = ufl.Measure('interior_facet_vert',
subdomain_data=weakref.ref(self.coordinates))
# Set the subdomain_data on all the default measures to this
# coordinate field. We don't set the domain on the measure
# since this causes an uncollectable reference in the global
# space (dx is global). Furthermore, it's never used anyway.
for measure in [
ufl.ds, ufl.dS, ufl.dx, ufl.ds_t, ufl.ds_b, ufl.ds_v, ufl.dS_h,
ufl.dS_v
]:
measure._subdomain_data = weakref.ref(self.coordinates)