/usr/lib/python3/dist-packages/FIAT/hdivcurl.py is in python3-fiat 2017.2.0.0-2.
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#
# This file is part of FIAT.
#
# FIAT is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# FIAT is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with FIAT. If not, see <http://www.gnu.org/licenses/>.
from __future__ import absolute_import, print_function, division
import numpy
import types
from FIAT.tensor_product import TensorProductElement
from FIAT import functional
def Hdiv(element):
if not isinstance(element, TensorProductElement):
raise NotImplementedError
if element.A.get_formdegree() is None or element.B.get_formdegree() is None:
raise ValueError("form degree of sub-element was None (not set during initialisation), Hdiv cannot be done without this information")
formdegree = element.A.get_formdegree() + element.B.get_formdegree()
if formdegree != element.get_reference_element().get_spatial_dimension() - 1:
raise ValueError("Tried to use Hdiv on a non-(n-1)-form element")
newelement = TensorProductElement(element.A, element.B) # make a copy to return
# redefine value_shape()
def value_shape(self):
"Return the value shape of the finite element functions."
return (self.get_reference_element().get_spatial_dimension(),)
newelement.value_shape = types.MethodType(value_shape, newelement)
# store old _mapping
newelement._oldmapping = newelement._mapping
# redefine _mapping
newelement._mapping = "contravariant piola"
# store formdegree
newelement.formdegree = formdegree
# redefine tabulate
newelement.old_tabulate = newelement.tabulate
def tabulate(self, order, points, entity=None):
"""Return tabulated values of derivatives up to given order of
basis functions at given points."""
# don't duplicate what the old function does fine...
old_result = self.old_tabulate(order, points, entity)
new_result = {}
sd = self.get_reference_element().get_spatial_dimension()
for alpha in old_result.keys():
temp_old = old_result[alpha]
if self._oldmapping == "affine":
temp = numpy.zeros((temp_old.shape[0], sd, temp_old.shape[1]), dtype=temp_old.dtype)
# both constituents affine, i.e., they were 0 forms or n-forms.
# to sum to n-1, we must have "0-form on an interval" crossed
# with something discontinuous.
# look for the (continuous) 0-form, and put the value there
if self.A.get_formdegree() == 0:
# first element, so (-x, 0, ...)
# Sign flip to ensure that a positive value of the node
# means a vector field having a direction "to the left"
# relative to direction in which the nodes are placed on an
# edge in case of higher-order schemes.
# This is required for unstructured quadrilateral meshes.
temp[:, 0, :] = -temp_old[:, :]
elif self.B.get_formdegree() == 0:
# second element, so (..., 0, x)
temp[:, -1, :] = temp_old[:, :]
else:
raise Exception("Hdiv affine/affine form degrees broke")
elif self._oldmapping == "contravariant piola":
temp = numpy.zeros((temp_old.shape[0], sd, temp_old.shape[2]), dtype=temp_old.dtype)
Asd = self.A.get_reference_element().get_spatial_dimension()
# one component is affine, one is contravariant piola
# the affine one must be an n-form, hence discontinuous
# this component/these components get zeroed out
if element.A.mapping()[0] == "contravariant piola":
# first element, so (x1, ..., xn, 0, ...)
temp[:, :Asd, :] = temp_old[:, :, :]
elif element.B.mapping()[0] == "contravariant piola":
# second element, so (..., 0, x1, ..., xn)
temp[:, Asd:, :] = temp_old[:, :, :]
else:
raise ValueError("Hdiv contravariant piola couldn't find an existing ConPi subelement")
elif self._oldmapping == "covariant piola":
temp = numpy.zeros((temp_old.shape[0], sd, temp_old.shape[2]), dtype=temp_old.dtype)
# one component is affine, one is covariant piola
# the affine one must be an n-form, hence discontinuous
# this component/these components get zeroed out
# the remaining part gets perped
if element.A.mapping()[0] == "covariant piola":
Asd = self.A.get_reference_element().get_spatial_dimension()
if not Asd == 2:
raise ValueError("Must be 2d shape to automatically convert covariant to contravariant")
temp_perp = numpy.zeros(temp_old.shape, dtype=temp_old.dtype)
# first element, so (x2, -x1, 0, ...)
temp_perp[:, 0, :] = temp_old[:, 1, :]
temp_perp[:, 1, :] = -temp_old[:, 0, :]
temp[:, :Asd, :] = temp_perp[:, :, :]
elif element.B.mapping()[0] == "covariant piola":
Bsd = self.B.get_reference_element().get_spatial_dimension()
if not Bsd == 2:
raise ValueError("Must be 2d shape to automatically convert covariant to contravariant")
temp_perp = numpy.zeros(temp_old.shape, dtype=temp_old.dtype)
# second element, so (..., 0, x2, -x1)
temp_perp[:, 0, :] = temp_old[:, 1, :]
temp_perp[:, 1, :] = -temp_old[:, 0, :]
temp[:, Asd:, :] = temp_old[:, :, :]
else:
raise ValueError("Hdiv covariant piola couldn't find an existing CovPi subelement")
new_result[alpha] = temp
return new_result
newelement.tabulate = types.MethodType(tabulate, newelement)
# splat any PointEvaluation functionals.
# they become a nasty mix of internal and external component DOFs
if newelement._oldmapping == "affine":
oldnodes = newelement.dual.nodes
newnodes = []
for node in oldnodes:
if isinstance(node, functional.PointEvaluation):
newnodes.append(functional.Functional(None, None, None, {}, "Undefined"))
else:
newnodes.append(node)
newelement.dual.nodes = newnodes
return newelement
def Hcurl(element):
if not isinstance(element, TensorProductElement):
raise NotImplementedError
if element.A.get_formdegree() is None or element.B.get_formdegree() is None:
raise ValueError("form degree of sub-element was None (not set during initialisation), Hcurl cannot be done without this information")
formdegree = element.A.get_formdegree() + element.B.get_formdegree()
if not (formdegree == 1):
raise ValueError("Tried to use Hcurl on a non-1-form element")
newelement = TensorProductElement(element.A, element.B) # make a copy to return
# redefine value_shape()
def value_shape(self):
"Return the value shape of the finite element functions."
return (self.get_reference_element().get_spatial_dimension(),)
newelement.value_shape = types.MethodType(value_shape, newelement)
# store old _mapping
newelement._oldmapping = newelement._mapping
# redefine _mapping
newelement._mapping = "covariant piola"
# store formdegree
newelement.formdegree = formdegree
# redefine tabulate
newelement.old_tabulate = newelement.tabulate
def tabulate(self, order, points, entity=None):
"""Return tabulated values of derivatives up to given order of
basis functions at given points."""
# don't duplicate what the old function does fine...
old_result = self.old_tabulate(order, points, entity)
new_result = {}
sd = self.get_reference_element().get_spatial_dimension()
for alpha in old_result.keys():
temp_old = old_result[alpha]
if self._oldmapping == "affine":
temp = numpy.zeros((temp_old.shape[0], sd, temp_old.shape[1]), dtype=temp_old.dtype)
# both constituents affine, i.e., they were 0 forms or n-forms.
# to sum to 1, we must have "1-form on an interval" crossed with
# a bunch of 0-forms (continuous).
# look for the 1-form, and put the value in the other place
if self.A.get_formdegree() == 1:
# first element, so (x, 0, ...)
# No sign flip here, nor at the other branch, to ensure that
# a positive value of the node means a vector field having
# the same direction as the direction in which the nodes are
# placed on an edge in case of higher-order schemes.
# This is required for unstructured quadrilateral meshes.
temp[:, 0, :] = temp_old[:, :]
elif self.B.get_formdegree() == 1:
# second element, so (..., 0, x)
temp[:, -1, :] = temp_old[:, :]
else:
raise Exception("Hcurl affine/affine form degrees broke")
elif self._oldmapping == "covariant piola":
temp = numpy.zeros((temp_old.shape[0], sd, temp_old.shape[2]), dtype=temp_old.dtype)
Asd = self.A.get_reference_element().get_spatial_dimension()
# one component is affine, one is covariant piola
# the affine one must be an 0-form, hence continuous
# this component/these components get zeroed out
if element.A.mapping()[0] == "covariant piola":
# first element, so (x1, ..., xn, 0, ...)
temp[:, :Asd, :] = temp_old[:, :, :]
elif element.B.mapping()[0] == "covariant piola":
# second element, so (..., 0, x1, ..., xn)
temp[:, Asd:, :] = temp_old[:, :, :]
else:
raise ValueError("Hdiv contravariant piola couldn't find an existing ConPi subelement")
elif self._oldmapping == "contravariant piola":
temp = numpy.zeros((temp_old.shape[0], sd, temp_old.shape[2]), dtype=temp_old.dtype)
# one component is affine, one is contravariant piola
# the affine one must be an 0-form, hence continuous
# this component/these components get zeroed out
# the remaining part gets perped
if element.A.mapping()[0] == "contravariant piola":
Asd = self.A.get_reference_element().get_spatial_dimension()
if not Asd == 2:
raise ValueError("Must be 2d shape to automatically convert contravariant to covariant")
temp_perp = numpy.zeros(temp_old.shape, dtype=temp_old.dtype)
# first element, so (-x2, x1, 0, ...)
temp_perp[:, 0, :] = -temp_old[:, 1, :]
temp_perp[:, 1, :] = temp_old[:, 0, :]
temp[:, :Asd, :] = temp_perp[:, :, :]
elif element.B.mapping()[0] == "contravariant piola":
Bsd = self.B.get_reference_element().get_spatial_dimension()
if not Bsd == 2:
raise ValueError("Must be 2d shape to automatically convert contravariant to covariant")
temp_perp = numpy.zeros(temp_old.shape, dtype=temp_old.dtype)
# second element, so (..., 0, -x2, x1)
temp_perp[:, 0, :] = -temp_old[:, 1, :]
temp_perp[:, 1, :] = temp_old[:, 0, :]
temp[:, Asd:, :] = temp_old[:, :, :]
else:
raise ValueError("Hcurl contravariant piola couldn't find an existing CovPi subelement")
new_result[alpha] = temp
return new_result
newelement.tabulate = types.MethodType(tabulate, newelement)
# splat any PointEvaluation functionals.
# they become a nasty mix of internal and external component DOFs
if newelement._oldmapping == "affine":
oldnodes = newelement.dual.nodes
newnodes = []
for node in oldnodes:
if isinstance(node, functional.PointEvaluation):
newnodes.append(functional.Functional(None, None, None, {}, "Undefined"))
else:
newnodes.append(node)
newelement.dual.nodes = newnodes
return newelement
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