"""Doc."""
# Copyright (C) 2008-2016 Andrew T. T. McRae
#
# This file was originally part of UFL (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
#
# Modified by Massimiliano Leoni, 2016
# Modified by Matthew Scroggs, 2023
from finat.ufl.finiteelementbase import FiniteElementBase
from ufl.sobolevspace import L2, SobolevSpace
from ufl.sobolevspace import HCurl as HCurlSobolevSpace
from ufl.sobolevspace import HDiv as HDivSobolevSpace
[docs]class CallableSobolevSpace(SobolevSpace):
"""A Sobolev space that can be called to create HDiv and HCurl elements."""
def __init__(self, name, parents=None):
super().__init__(name, parents)
def __call__(self, element):
"""Syntax shortcut to create a HDivElement or HCurlElement."""
if self.name == "HDiv":
return HDivElement(element)
elif self.name == "HCurl":
return HCurlElement(element)
raise NotImplementedError(
"SobolevSpace has no call operator (only the specific HDiv and HCurl instances)."
)
HCurl = CallableSobolevSpace(HCurlSobolevSpace.name, HCurlSobolevSpace.parents)
HDiv = CallableSobolevSpace(HDivSobolevSpace.name, HDivSobolevSpace.parents)
[docs]class HDivElement(FiniteElementBase):
"""A div-conforming version of an outer product element, assuming this makes mathematical sense."""
__slots__ = ("_element", )
def __init__(self, element):
"""Doc."""
self._element = element
family = "TensorProductElement"
cell = element.cell
degree = element.degree()
quad_scheme = element.quadrature_scheme()
value_shape = (element.cell.geometric_dimension(),)
reference_value_shape = (element.cell.topological_dimension(),)
# Skipping TensorProductElement constructor! Bad code smell, refactor to avoid this non-inheritance somehow.
FiniteElementBase.__init__(self, family, cell, degree,
quad_scheme, value_shape, reference_value_shape)
def __repr__(self):
"""Doc."""
return f"HDivElement({repr(self._element)})"
[docs] def mapping(self):
"""Doc."""
return "contravariant Piola"
@property
def sobolev_space(self):
"""Return the underlying Sobolev space."""
return HDivSobolevSpace
[docs] def reconstruct(self, **kwargs):
"""Doc."""
return HDivElement(self._element.reconstruct(**kwargs))
[docs] def variant(self):
"""Doc."""
return self._element.variant()
def __str__(self):
"""Doc."""
return f"HDivElement({repr(self._element)})"
[docs] def shortstr(self):
"""Format as string for pretty printing."""
return f"HDivElement({self._element.shortstr()})"
@property
def embedded_subdegree(self):
"""Return embedded subdegree."""
return self._element.embedded_subdegree
@property
def embedded_superdegree(self):
"""Return embedded superdegree."""
return self._element.embedded_superdegree
[docs]class HCurlElement(FiniteElementBase):
"""A curl-conforming version of an outer product element, assuming this makes mathematical sense."""
__slots__ = ("_element",)
def __init__(self, element):
"""Doc."""
self._element = element
family = "TensorProductElement"
cell = element.cell
degree = element.degree()
quad_scheme = element.quadrature_scheme()
cell = element.cell
value_shape = (cell.geometric_dimension(),)
reference_value_shape = (cell.topological_dimension(),) # TODO: Is this right?
# Skipping TensorProductElement constructor! Bad code smell,
# refactor to avoid this non-inheritance somehow.
FiniteElementBase.__init__(self, family, cell, degree, quad_scheme,
value_shape, reference_value_shape)
def __repr__(self):
"""Doc."""
return f"HCurlElement({repr(self._element)})"
[docs] def mapping(self):
"""Doc."""
return "covariant Piola"
@property
def sobolev_space(self):
"""Return the underlying Sobolev space."""
return HCurlSobolevSpace
[docs] def reconstruct(self, **kwargs):
"""Doc."""
return HCurlElement(self._element.reconstruct(**kwargs))
[docs] def variant(self):
"""Doc."""
return self._element.variant()
def __str__(self):
"""Doc."""
return f"HCurlElement({repr(self._element)})"
[docs] def shortstr(self):
"""Format as string for pretty printing."""
return f"HCurlElement({self._element.shortstr()})"
@property
def embedded_subdegree(self):
"""Return embedded subdegree."""
return self._element.embedded_subdegree
@property
def embedded_superdegree(self):
"""Return embedded superdegree."""
return self._element.embedded_superdegree
[docs]class WithMapping(FiniteElementBase):
"""Specify an alternative mapping for the wrappee.
For example,
to use identity mapping instead of Piola map with an element E,
write
remapped = WithMapping(E, "identity")
"""
def __init__(self, wrapee, mapping):
"""Doc."""
if mapping == "symmetries":
raise ValueError("Can't change mapping to 'symmetries'")
self._mapping = mapping
self.wrapee = wrapee
def __getattr__(self, attr):
"""Doc."""
try:
return getattr(self.wrapee, attr)
except AttributeError:
raise AttributeError("'%s' object has no attribute '%s'" %
(type(self).__name__, attr))
def __repr__(self):
"""Doc."""
return f"WithMapping({repr(self.wrapee)}, '{self._mapping}')"
@property
def value_shape(self):
"""Doc."""
gdim = self.cell.geometric_dimension()
mapping = self.mapping()
if mapping in {"covariant Piola", "contravariant Piola"}:
return (gdim,)
elif mapping in {"double covariant Piola", "double contravariant Piola"}:
return (gdim, gdim)
else:
return self.wrapee.value_shape
@property
def reference_value_shape(self):
"""Doc."""
tdim = self.cell.topological_dimension()
mapping = self.mapping()
if mapping in {"covariant Piola", "contravariant Piola"}:
return (tdim,)
elif mapping in {"double covariant Piola", "double contravariant Piola"}:
return (tdim, tdim)
else:
return self.wrapee.reference_value_shape
[docs] def mapping(self):
"""Doc."""
return self._mapping
@property
def sobolev_space(self):
"""Return the underlying Sobolev space."""
if self.wrapee.mapping() == self.mapping():
return self.wrapee.sobolev_space
else:
return L2
[docs] def reconstruct(self, **kwargs):
"""Doc."""
mapping = kwargs.pop("mapping", self._mapping)
wrapee = self.wrapee.reconstruct(**kwargs)
return type(self)(wrapee, mapping)
[docs] def variant(self):
"""Doc."""
return self.wrapee.variant()
def __str__(self):
"""Doc."""
return f"WithMapping({repr(self.wrapee)}, {self._mapping})"
[docs] def shortstr(self):
"""Doc."""
return f"WithMapping({self.wrapee.shortstr()}, {self._mapping})"
@property
def embedded_subdegree(self):
"""Return embedded subdegree."""
return self._element.embedded_subdegree
@property
def embedded_superdegree(self):
"""Return embedded superdegree."""
return self._element.embedded_superdegree
