/usr/lib/python2.7/dist-packages/FIAT/hermite.py is in python-fiat 1.6.0-1.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 | # Copyright (C) 2008 Robert C. Kirby (Texas Tech University)
#
# 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 . import finite_element, polynomial_set, dual_set, functional
class CubicHermiteDualSet( dual_set.DualSet ):
"""The dual basis for Lagrange elements. This class works for
simplices of any dimension. Nodes are point evaluation at
equispaced points."""
def __init__( self, ref_el ):
entity_ids = {}
nodes = []
cur = 0
# make nodes by getting points
# need to do this dimension-by-dimension, facet-by-facet
top = ref_el.get_topology()
verts = ref_el.get_vertices()
sd = ref_el.get_spatial_dimension()
# get jet at each vertex
entity_ids[0] = {}
for v in sorted( top[0] ):
nodes.append( functional.PointEvaluation( ref_el, verts[v] ) )
pd = functional.PointDerivative
for i in range( sd ):
alpha = [0] * sd
alpha[i] = 1
nodes.append( pd( ref_el, verts[v], alpha ) )
entity_ids[0][v] = list(range(cur, cur+1+sd))
cur += sd + 1
# no edge dof
entity_ids[1] = {}
# face dof
# point evaluation at barycenter
entity_ids[2] = {}
for f in sorted( top[2] ):
pt = ref_el.make_points( 2, f, 3 )[0]
n = functional.PointEvaluation( ref_el, pt )
nodes.append( n )
entity_ids[2] = list(range(cur, cur+1))
cur += 1
for dim in range(3, sd+1):
entity_ids[dim] = {}
for facet in top[dim]:
entity_ids[dim][facet] = []
dual_set.DualSet.__init__( self, nodes, ref_el, entity_ids )
class CubicHermite( finite_element.FiniteElement ):
"""The Lagrange finite element. It is what it is."""
def __init__( self, ref_el ):
poly_set = polynomial_set.ONPolynomialSet( ref_el, 3 )
dual = CubicHermiteDualSet( ref_el )
finite_element.FiniteElement.__init__( self, poly_set, dual, 3 )
if __name__=="__main__":
from . import reference_element
T = reference_element.DefaultTetrahedron()
U = CubicHermite( T )
Ufs = U.get_nodal_basis()
pts = T.make_lattice( 3 )
print(pts)
print(list(Ufs.tabulate(pts).values())[0])
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