/usr/lib/python2.7/dist-packages/FIAT/argyris.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 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 | # 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
import numpy
class ArgyrisDualSet( dual_set.DualSet ):
def __init__( self, ref_el, degree ):
entity_ids = {}
nodes = []
cur = 0
top = ref_el.get_topology()
verts = ref_el.get_vertices()
sd = ref_el.get_spatial_dimension()
if sd != 2:
raise Exception("Illegal spatial dimension")
pe = functional.PointEvaluation
pd = functional.PointDerivative
pnd = functional.PointNormalDerivative
# get jet at each vertex
entity_ids[0] = {}
for v in sorted( top[0] ):
nodes.append( pe( ref_el, verts[v] ) )
# first derivatives
for i in range( sd ):
alpha = [0] * sd
alpha[i] = 1
nodes.append( pd( ref_el, verts[v], alpha ) )
# second derivatives
alphas = [ [2, 0], [0, 2], [1, 1] ]
for alpha in alphas:
nodes.append( pd( ref_el, verts[v], alpha ) )
entity_ids[0][v] = list(range(cur, cur+6))
cur += 6
# edge dof
entity_ids[1] = {}
for e in sorted( top[1] ):
# normal derivatives at degree - 4 points on each edge
ndpts = ref_el.make_points( 1, e, degree - 3 )
ndnds = [ pnd( ref_el, e, pt ) for pt in ndpts ]
nodes.extend( ndnds )
entity_ids[1][e] = list(range(cur, cur + len(ndpts)))
cur += len( ndpts )
# point value at degree-5 points on each edge
if degree > 5:
ptvalpts = ref_el.make_points( 1, e, degree - 4 )
ptvalnds = [ pe( ref_el, pt ) for pt in ptvalpts ]
nodes.extend( ptvalnds )
entity_ids[1][e] += list(range(cur, cur+len(ptvalpts)))
cur += len( ptvalpts )
# internal dof
entity_ids[2] = {}
if degree > 5:
internalpts = ref_el.make_points( 2, 0, degree - 3 )
internalnds = [ pe( ref_el, pt ) for pt in internalpts ]
nodes.extend( internalnds )
entity_ids[2][0] = list(range(cur, cur+len(internalpts)))
cur += len(internalpts)
dual_set.DualSet.__init__( self, nodes, ref_el, entity_ids )
class QuinticArgyrisDualSet( 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()
if sd != 2:
raise Exception("Illegal spatial dimension")
pd = functional.PointDerivative
# get jet at each vertex
entity_ids[0] = {}
for v in sorted( top[0] ):
nodes.append( functional.PointEvaluation( ref_el, verts[v] ) )
# first derivatives
for i in range( sd ):
alpha = [0] * sd
alpha[i] = 1
nodes.append( pd( ref_el, verts[v], alpha ) )
# second derivatives
alphas = [ [2, 0], [0, 2], [1, 1] ]
for alpha in alphas:
nodes.append( pd( ref_el, verts[v], alpha ) )
entity_ids[0][v] = list(range(cur, cur+6))
cur += 6
# edge dof -- normal at each edge midpoint
entity_ids[1] = {}
for e in sorted( top[1] ):
pt = ref_el.make_points( 1, e, 2 )[0]
n = functional.PointNormalDerivative( ref_el, e, pt )
nodes.append( n )
entity_ids[1][e] = [cur]
cur += 1
dual_set.DualSet.__init__( self, nodes, ref_el, entity_ids )
class Argyris( finite_element.FiniteElement ):
"""The Argyris finite element."""
def __init__( self, ref_el, degree ):
poly_set = polynomial_set.ONPolynomialSet( ref_el, degree )
dual = ArgyrisDualSet( ref_el, degree )
finite_element.FiniteElement.__init__( self, poly_set, dual, degree )
class QuinticArgyris( finite_element.FiniteElement ):
"""The Argyris finite element."""
def __init__( self, ref_el ):
poly_set = polynomial_set.ONPolynomialSet( ref_el, 5 )
dual = QuinticArgyrisDualSet( ref_el )
finite_element.FiniteElement.__init__( self, poly_set, dual, 5 )
if __name__=="__main__":
from . import reference_element
from . import lagrange
T = reference_element.DefaultTriangle()
for k in range(5, 11):
U = Argyris( T, k )
U2 = lagrange.Lagrange( T, k )
c = U.get_nodal_basis().get_coeffs()
sigma = numpy.linalg.svd( c, compute_uv = 0)
print("Argyris ", k, max(sigma) / min(sigma))
c = U2.get_nodal_basis().get_coeffs()
sigma = numpy.linalg.svd( c, compute_uv = 0)
print("Lagrange ", k, max(sigma) / min(sigma ))
print()
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