def __str__(self):
"Format as string for pretty printing."
qs = self.quadrature_scheme()
qs = "" if qs is None else "(%s)" % qs
v = self.variant()
v = "" if v is None else "(%s)" % v
return "<%s%s%s%s on a %s>" % (self._short_name, istr(
self.degree()), qs, v, self.cell())
def __str__(self):
"Format as string for pretty printing."
qs = self.quadrature_scheme()
qs = "" if qs is None else "(%s)" % qs
v = self.variant()
v = "" if v is None else "(%s)" % v
return "<%s%s%s%s on a %s>" % (self._short_name, istr(self.degree()),
qs, v, self.cell())
def canonical_element_description(family, cell, order, form_degree):
"""Given basic element information, return corresponding element information on canonical form.
Input: family, cell, (polynomial) order, form_degree
Output: family (canonical), short_name (for printing), order, value shape,
reference value shape, sobolev_space.
This is used by the FiniteElement constructor to ved input
data against the element list and aliases defined in ufl.
"""
# Get domain dimensions
if cell is not None:
tdim = cell.topological_dimension()
gdim = cell.geometric_dimension()
if isinstance(cell, Cell):
cellname = cell.cellname()
else:
cellname = None
else:
tdim = None
gdim = None
cellname = None
# Catch general FEEC notation "P" and "S"
if form_degree is not None and family in ("P", "S"):
family, order = feec_element(family, tdim, order, form_degree)
# Check whether this family is an alias for something else
while family in aliases:
if tdim is None:
error("Need dimension to handle element aliases.")
(family, order) = aliases[family](family, tdim, order, form_degree)
# Check that the element family exists
if family not in ufl_elements:
error('Unknown finite element "%s".' % family)
# Check that element data is valid (and also get common family
# name)
(family, short_name, value_rank, sobolev_space, mapping, krange, cellnames) = ufl_elements[family]
# Accept CG/DG on all kind of cells, but use Q/DQ on "product" cells
if cellname in set(cubes) - set(simplices) or isinstance(cell, TensorProductCell):
if family == "Lagrange":
family = "Q"
elif family == "Discontinuous Lagrange":
if order >= 1:
warning("Discontinuous Lagrange element requested on %s, creating DQ element." % cell.cellname())
family = "DQ"
# Validate cellname if a valid cell is specified
if not (cellname is None or cellname in cellnames):
error('Cellname "%s" invalid for "%s" finite element.' % (cellname, family))
# Validate order if specified
if order is not None:
if krange is None:
error('Order "%s" invalid for "%s" finite element, '
'should be None.' % (order, family))
kmin, kmax = krange
if not (kmin is None or (asarray(order) >= kmin).all()):
error('Order "%s" invalid for "%s" finite element.' %
(order, family))
if not (kmax is None or (asarray(order) <= kmax).all()):
error('Order "%s" invalid for "%s" finite element.' %
(istr(order), family))
# Override sobolev_space for piecewise constants (TODO: necessary?)
if order == 0:
sobolev_space = L2
if value_rank == 2:
# Tensor valued fundamental elements in HEin have this shape
if gdim is None or tdim is None:
error("Cannot infer shape of element without topological and geometric dimensions.")
reference_value_shape = (tdim, tdim)
value_shape = (gdim, gdim)
elif value_rank == 1:
# Vector valued fundamental elements in HDiv and HCurl have a shape
if gdim is None or tdim is None:
error("Cannot infer shape of element without topological and geometric dimensions.")
reference_value_shape = (tdim,)
value_shape = (gdim,)
elif value_rank == 0:
# All other elements are scalar values
reference_value_shape = ()
value_shape = ()
else:
error("Invalid value rank %d." % value_rank)
return family, short_name, order, value_shape, reference_value_shape, sobolev_space, mapping
def canonical_element_description(family, cell, order, form_degree):
"""Given basic element information, return corresponding element information on canonical form.
Input: family, cell, (polynomial) order, form_degree
Output: family (canonical), short_name (for printing), order, value shape,
reference value shape, sobolev_space.
This is used by the FiniteElement constructor to ved input
data against the element list and aliases defined in ufl.
"""
# Get domain dimensions
if cell is not None:
tdim = cell.topological_dimension()
gdim = cell.geometric_dimension()
if isinstance(cell, Cell):
cellname = cell.cellname()
else:
cellname = None
else:
tdim = None
gdim = None
cellname = None
# Catch general FEEC notation "P" and "S"
if form_degree is not None and family in ("P", "S"):
family, order = feec_element(family, tdim, order, form_degree)
if form_degree is not None and family in ("P L2", "S L2"):
family, order = feec_element_l2(family, tdim, order, form_degree)
# Check whether this family is an alias for something else
while family in aliases:
if tdim is None:
error("Need dimension to handle element aliases.")
(family, order) = aliases[family](family, tdim, order, form_degree)
# Check that the element family exists
if family not in ufl_elements:
error('Unknown finite element "%s".' % family)
# Check that element data is valid (and also get common family
# name)
(family, short_name, value_rank, sobolev_space, mapping, krange, cellnames) = ufl_elements[family]
# Accept CG/DG on all kind of cells, but use Q/DQ on "product" cells
if cellname in set(cubes) - set(simplices) or isinstance(cell, TensorProductCell):
if family == "Lagrange":
family = "Q"
elif family == "Discontinuous Lagrange":
if order >= 1:
warning("Discontinuous Lagrange element requested on %s, creating DQ element." % cell.cellname())
family = "DQ"
elif family == "Discontinuous Lagrange L2":
if order >= 1:
warning("Discontinuous Lagrange L2 element requested on %s, creating DQ L2 element." % cell.cellname())
family = "DQ L2"
# Validate cellname if a valid cell is specified
if not (cellname is None or cellname in cellnames):
error('Cellname "%s" invalid for "%s" finite element.' % (cellname, family))
# Validate order if specified
if order is not None:
if krange is None:
error('Order "%s" invalid for "%s" finite element, '
'should be None.' % (order, family))
kmin, kmax = krange
if not (kmin is None or (asarray(order) >= kmin).all()):
error('Order "%s" invalid for "%s" finite element.' %
(order, family))
if not (kmax is None or (asarray(order) <= kmax).all()):
error('Order "%s" invalid for "%s" finite element.' %
(istr(order), family))
# Override sobolev_space for piecewise constants (TODO: necessary?)
if order == 0:
sobolev_space = L2
if value_rank == 2:
# Tensor valued fundamental elements in HEin have this shape
if gdim is None or tdim is None:
error("Cannot infer shape of element without topological and geometric dimensions.")
reference_value_shape = (tdim, tdim)
value_shape = (gdim, gdim)
elif value_rank == 1:
# Vector valued fundamental elements in HDiv and HCurl have a shape
if gdim is None or tdim is None:
error("Cannot infer shape of element without topological and geometric dimensions.")
reference_value_shape = (tdim,)
value_shape = (gdim,)
elif value_rank == 0:
# All other elements are scalar values
reference_value_shape = ()
value_shape = ()
else:
error("Invalid value rank %d." % value_rank)
return family, short_name, order, value_shape, reference_value_shape, sobolev_space, mapping
def shortstr(self):
"Format as string for pretty printing."
return "%s%s(%s,%s)" % (self._short_name, istr(
self.degree()), istr(self.quadrature_scheme()), istr(
self.variant()))
def shortstr(self):
"Format as string for pretty printing."
return "%s%s(%s,%s)" % (self._short_name, istr(self.degree()),
istr(self.quadrature_scheme()), istr(self.variant()))