/usr/share/pyshared/FIAT/raviart_thomas.py is in python-fiat 1.0.0-1.
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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 | import expansions, polynomial_set, quadrature, reference_element, dual_set, \
quadrature, finite_element, functional
import numpy
def RTSpace( ref_el , deg ):
"""Constructs a basis for the the Raviart-Thomas space
(P_k)^d + P_k x"""
sd = ref_el.get_spatial_dimension()
vec_Pkp1 = polynomial_set.ONPolynomialSet( ref_el , deg+1 , (sd,) )
dimPkp1 = expansions.polynomial_dimension( ref_el , deg+1 )
dimPk = expansions.polynomial_dimension( ref_el , deg )
dimPkm1 = expansions.polynomial_dimension( ref_el , deg-1 )
vec_Pk_indices = reduce( lambda a,b: a+b , \
[ range(i*dimPkp1,i*dimPkp1+dimPk) \
for i in range(sd) ] )
vec_Pk_from_Pkp1 = vec_Pkp1.take( vec_Pk_indices )
Pkp1 = polynomial_set.ONPolynomialSet( ref_el , deg + 1 )
PkH = Pkp1.take( range(dimPkm1,dimPk) )
Q = quadrature.make_quadrature( ref_el , 2 * deg + 2 )
# have to work on this through "tabulate" interface
# first, tabulate PkH at quadrature points
Qpts = numpy.array( Q.get_points() )
Qwts = numpy.array( Q.get_weights() )
zero_index = tuple( [ 0 for i in range(sd) ] )
PkH_at_Qpts = PkH.tabulate( Qpts )[zero_index]
Pkp1_at_Qpts = Pkp1.tabulate( Qpts )[zero_index]
PkHx_coeffs = numpy.zeros( (PkH.get_num_members() , \
sd, \
Pkp1.get_num_members()) , "d" )
import time
t1 = time.time()
for i in range( PkH.get_num_members() ):
for j in range( sd ):
fooij = PkH_at_Qpts[i,:] * Qpts[:,j] * Qwts
PkHx_coeffs[i,j,:] = numpy.dot( Pkp1_at_Qpts , fooij )
PkHx = polynomial_set.PolynomialSet( ref_el , \
deg , \
deg + 1 , \
vec_Pkp1.get_expansion_set() , \
PkHx_coeffs , \
vec_Pkp1.get_dmats() )
return polynomial_set.polynomial_set_union_normalized( vec_Pk_from_Pkp1 , PkHx )
class RTDualSet( dual_set.DualSet ):
"""Dual basis for Raviart-Thomas elements consisting of point
evaluation of normals on facets of codimension 1 and internal
moments against polynomials"""
def __init__( self , ref_el , degree ):
entity_ids = {}
nodes = []
sd = ref_el.get_spatial_dimension()
t = ref_el.get_topology()
# codimension 1 facets
for i in range( len( t[sd-1] ) ):
pts_cur = ref_el.make_points( sd - 1 , i , sd + degree )
for j in range( len( pts_cur ) ):
pt_cur = pts_cur[j]
f = functional.PointScaledNormalEvaluation( ref_el , i , \
pt_cur )
nodes.append( f )
# internal nodes. Let's just use points at a lattice
if degree > 0:
cpe = functional.ComponentPointEvaluation
pts = ref_el.make_points( sd , 0 , degree + sd )
for d in range( sd ):
for i in range( len( pts ) ):
l_cur = cpe( ref_el , d , (sd,) , pts[i] )
nodes.append( l_cur )
# Q = quadrature.make_quadrature( ref_el , 2 * ( degree + 1 ) )
# qpts = Q.get_points()
# Pkm1 = polynomial_set.ONPolynomialSet( ref_el , degree - 1 )
# zero_index = tuple( [ 0 for i in range( sd ) ] )
# Pkm1_at_qpts = Pkm1.tabulate( qpts )[ zero_index ]
# for d in range( sd ):
# for i in range( Pkm1_at_qpts.shape[0] ):
# phi_cur = Pkm1_at_qpts[i,:]
# l_cur = functional.IntegralMoment( ref_el , Q , \
# phi_cur , (d,) , (sd,) )
# nodes.append( l_cur )
entity_ids = {}
# sets vertices (and in 3d, edges) to have no nodes
for i in range( sd - 1 ):
entity_ids[i] = {}
for j in range( len( t[i] ) ):
entity_ids[i][j] = []
cur = 0
# set codimension 1 (edges 2d, faces 3d) dof
pts_facet_0 = ref_el.make_points( sd - 1 , 0 , sd + degree )
pts_per_facet = len( pts_facet_0 )
entity_ids[sd-1] = {}
for i in range( len( t[sd-1] ) ):
entity_ids[sd-1][i] = range( cur , cur + pts_per_facet )
cur += pts_per_facet
# internal nodes, if applicable
entity_ids[sd] = {0: []}
if degree > 0:
num_internal_nodes = expansions.polynomial_dimension( ref_el , \
degree - 1 )
entity_ids[sd][0] = range( cur , cur + num_internal_nodes * sd )
dual_set.DualSet.__init__( self , nodes , ref_el , entity_ids )
class RaviartThomas( finite_element.FiniteElement ):
"""The Raviart-Thomas finite element"""
def __init__( self , ref_el , q ):
degree = q - 1
poly_set = RTSpace( ref_el , degree )
dual = RTDualSet( ref_el , degree )
finite_element.FiniteElement.__init__( self , poly_set , dual , degree,
mapping="contravariant piola")
return
if __name__=="__main__":
T = reference_element.UFCTriangle()
sd = T.get_spatial_dimension()
for k in range(6):
RT = RaviartThomas( T , k )
# RTfs = RT.get_nodal_basis()
# pts = T.make_lattice( 1 )
# print pts
# zero_index = tuple( [ 0 for i in range(sd) ] )
#
# RTvals = RTfs.tabulate( pts )[zero_index]
# print RTvals
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