def test_TFE_2Dx1D_vector_triangle_hdiv():
S = UFCTriangle()
T = UFCInterval()
RT1 = RaviartThomas(S, 1)
P1_DG = DiscontinuousLagrange(T, 1)
elt = Hdiv(TensorProductElement(RT1, P1_DG))
assert elt.value_shape() == (3, )
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tabA = RT1.tabulate(1, [(0.1, 0.2)])
tabB = P1_DG.tabulate(1, [(0.3, )])
for da, db in [[(0, 0), (0, )], [(1, 0), (0, )], [(0, 1), (0, )],
[(0, 0), (1, )]]:
dc = da + db
assert np.isclose(tab[dc][0][0][0], tabA[da][0][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][1][0][0], tabA[da][0][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][2][0][0], tabA[da][1][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][3][0][0], tabA[da][1][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][4][0][0], tabA[da][2][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][5][0][0], tabA[da][2][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][0][1][0], tabA[da][0][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][1][1][0], tabA[da][0][1][0] * tabB[db][1][0])
assert np.isclose(tab[dc][2][1][0], tabA[da][1][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][3][1][0], tabA[da][1][1][0] * tabB[db][1][0])
assert np.isclose(tab[dc][4][1][0], tabA[da][2][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][5][1][0], tabA[da][2][1][0] * tabB[db][1][0])
assert tab[dc][0][2][0] == 0.0
assert tab[dc][1][2][0] == 0.0
assert tab[dc][2][2][0] == 0.0
assert tab[dc][3][2][0] == 0.0
assert tab[dc][4][2][0] == 0.0
assert tab[dc][5][2][0] == 0.0
def test_TFE_2Dx1D_vector_triangle_hdiv_rotate():
S = UFCTriangle()
T = UFCInterval()
Ned1 = Nedelec(S, 1)
P1_DG = DiscontinuousLagrange(T, 1)
elt = Hdiv(TensorProductElement(Ned1, P1_DG))
assert elt.value_shape() == (3,)
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tabA = Ned1.tabulate(1, [(0.1, 0.2)])
tabB = P1_DG.tabulate(1, [(0.3,)])
for da, db in [[(0, 0), (0,)], [(1, 0), (0,)], [(0, 1), (0,)], [(0, 0), (1,)]]:
dc = da + db
assert np.isclose(tab[dc][0][0][0], tabA[da][0][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][1][0][0], tabA[da][0][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][2][0][0], tabA[da][1][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][3][0][0], tabA[da][1][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][4][0][0], tabA[da][2][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][5][0][0], tabA[da][2][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][0][1][0], -tabA[da][0][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][1][1][0], -tabA[da][0][0][0]*tabB[db][1][0])
assert np.isclose(tab[dc][2][1][0], -tabA[da][1][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][3][1][0], -tabA[da][1][0][0]*tabB[db][1][0])
assert np.isclose(tab[dc][4][1][0], -tabA[da][2][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][5][1][0], -tabA[da][2][0][0]*tabB[db][1][0])
assert tab[dc][0][2][0] == 0.0
assert tab[dc][1][2][0] == 0.0
assert tab[dc][2][2][0] == 0.0
assert tab[dc][3][2][0] == 0.0
assert tab[dc][4][2][0] == 0.0
assert tab[dc][5][2][0] == 0.0
def test_TFE_2Dx1D_scalar_quad():
T = UFCInterval()
P1 = Lagrange(T, 1)
P1_DG = DiscontinuousLagrange(T, 1)
elt = TensorProductElement(TensorProductElement(P1, P1_DG), P1)
assert elt.value_shape() == ()
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tA = P1.tabulate(1, [(0.1, )])
tB = P1_DG.tabulate(1, [(0.2, )])
tC = P1.tabulate(1, [(0.3, )])
for da, db, dc in [[(0, ), (0, ), (0, )], [(1, ), (0, ), (0, )],
[(0, ), (1, ), (0, )], [(0, ), (0, ), (1, )]]:
dd = da + db + dc
assert np.isclose(tab[dd][0][0],
tA[da][0][0] * tB[db][0][0] * tC[dc][0][0])
assert np.isclose(tab[dd][1][0],
tA[da][0][0] * tB[db][0][0] * tC[dc][1][0])
assert np.isclose(tab[dd][2][0],
tA[da][0][0] * tB[db][1][0] * tC[dc][0][0])
assert np.isclose(tab[dd][3][0],
tA[da][0][0] * tB[db][1][0] * tC[dc][1][0])
assert np.isclose(tab[dd][4][0],
tA[da][1][0] * tB[db][0][0] * tC[dc][0][0])
assert np.isclose(tab[dd][5][0],
tA[da][1][0] * tB[db][0][0] * tC[dc][1][0])
assert np.isclose(tab[dd][6][0],
tA[da][1][0] * tB[db][1][0] * tC[dc][0][0])
assert np.isclose(tab[dd][7][0],
tA[da][1][0] * tB[db][1][0] * tC[dc][1][0])
def test_TFE_1Dx1D_vector():
T = UFCInterval()
P1_DG = DiscontinuousLagrange(T, 1)
P2 = Lagrange(T, 2)
elt = TensorProductElement(P1_DG, P2)
hdiv_elt = Hdiv(elt)
hcurl_elt = Hcurl(elt)
assert hdiv_elt.value_shape() == (2,)
assert hcurl_elt.value_shape() == (2,)
tabA = P1_DG.tabulate(1, [(0.1,)])
tabB = P2.tabulate(1, [(0.2,)])
hdiv_tab = hdiv_elt.tabulate(1, [(0.1, 0.2)])
for da, db in [[(0,), (0,)], [(1,), (0,)], [(0,), (1,)]]:
dc = da + db
assert hdiv_tab[dc][0][0][0] == 0.0
assert hdiv_tab[dc][1][0][0] == 0.0
assert hdiv_tab[dc][2][0][0] == 0.0
assert hdiv_tab[dc][3][0][0] == 0.0
assert hdiv_tab[dc][4][0][0] == 0.0
assert hdiv_tab[dc][5][0][0] == 0.0
assert np.isclose(hdiv_tab[dc][0][1][0], tabA[da][0][0]*tabB[db][0][0])
assert np.isclose(hdiv_tab[dc][1][1][0], tabA[da][0][0]*tabB[db][1][0])
assert np.isclose(hdiv_tab[dc][2][1][0], tabA[da][0][0]*tabB[db][2][0])
assert np.isclose(hdiv_tab[dc][3][1][0], tabA[da][1][0]*tabB[db][0][0])
assert np.isclose(hdiv_tab[dc][4][1][0], tabA[da][1][0]*tabB[db][1][0])
assert np.isclose(hdiv_tab[dc][5][1][0], tabA[da][1][0]*tabB[db][2][0])
hcurl_tab = hcurl_elt.tabulate(1, [(0.1, 0.2)])
for da, db in [[(0,), (0,)], [(1,), (0,)], [(0,), (1,)]]:
dc = da + db
assert np.isclose(hcurl_tab[dc][0][0][0], tabA[da][0][0]*tabB[db][0][0])
assert np.isclose(hcurl_tab[dc][1][0][0], tabA[da][0][0]*tabB[db][1][0])
assert np.isclose(hcurl_tab[dc][2][0][0], tabA[da][0][0]*tabB[db][2][0])
assert np.isclose(hcurl_tab[dc][3][0][0], tabA[da][1][0]*tabB[db][0][0])
assert np.isclose(hcurl_tab[dc][4][0][0], tabA[da][1][0]*tabB[db][1][0])
assert np.isclose(hcurl_tab[dc][5][0][0], tabA[da][1][0]*tabB[db][2][0])
assert hcurl_tab[dc][0][1][0] == 0.0
assert hcurl_tab[dc][1][1][0] == 0.0
assert hcurl_tab[dc][2][1][0] == 0.0
assert hcurl_tab[dc][3][1][0] == 0.0
assert hcurl_tab[dc][4][1][0] == 0.0
assert hcurl_tab[dc][5][1][0] == 0.0
def test_TFE_1Dx1D_scalar():
T = UFCInterval()
P1_DG = DiscontinuousLagrange(T, 1)
P2 = Lagrange(T, 2)
elt = TensorProductElement(P1_DG, P2)
assert elt.value_shape() == ()
tab = elt.tabulate(1, [(0.1, 0.2)])
tabA = P1_DG.tabulate(1, [(0.1,)])
tabB = P2.tabulate(1, [(0.2,)])
for da, db in [[(0,), (0,)], [(1,), (0,)], [(0,), (1,)]]:
dc = da + db
assert np.isclose(tab[dc][0][0], tabA[da][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][1][0], tabA[da][0][0]*tabB[db][1][0])
assert np.isclose(tab[dc][2][0], tabA[da][0][0]*tabB[db][2][0])
assert np.isclose(tab[dc][3][0], tabA[da][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][4][0], tabA[da][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][5][0], tabA[da][1][0]*tabB[db][2][0])
def test_TFE_1Dx1D_scalar():
T = UFCInterval()
P1_DG = DiscontinuousLagrange(T, 1)
P2 = Lagrange(T, 2)
elt = TensorProductElement(P1_DG, P2)
assert elt.value_shape() == ()
tab = elt.tabulate(1, [(0.1, 0.2)])
tabA = P1_DG.tabulate(1, [(0.1, )])
tabB = P2.tabulate(1, [(0.2, )])
for da, db in [[(0, ), (0, )], [(1, ), (0, )], [(0, ), (1, )]]:
dc = da + db
assert np.isclose(tab[dc][0][0], tabA[da][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][1][0], tabA[da][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][2][0], tabA[da][0][0] * tabB[db][2][0])
assert np.isclose(tab[dc][3][0], tabA[da][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][4][0], tabA[da][1][0] * tabB[db][1][0])
assert np.isclose(tab[dc][5][0], tabA[da][1][0] * tabB[db][2][0])
def test_TFE_2Dx1D_vector_quad_hdiv():
T = UFCInterval()
P1 = Lagrange(T, 1)
P0 = DiscontinuousLagrange(T, 0)
P1_DG = DiscontinuousLagrange(T, 1)
P1P0 = Hdiv(TensorProductElement(P1, P0))
P0P1 = Hdiv(TensorProductElement(P0, P1))
horiz_elt = EnrichedElement(P1P0, P0P1)
elt = Hdiv(TensorProductElement(horiz_elt, P1_DG))
assert elt.value_shape() == (3,)
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tA = P1.tabulate(1, [(0.1,)])
tB = P0.tabulate(1, [(0.2,)])
tC = P0.tabulate(1, [(0.1,)])
tD = P1.tabulate(1, [(0.2,)])
tE = P1_DG.tabulate(1, [(0.3,)])
for da, db, dc in [[(0,), (0,), (0,)], [(1,), (0,), (0,)], [(0,), (1,), (0,)], [(0,), (0,), (1,)]]:
dd = da + db + dc
assert np.isclose(tab[dd][0][0][0], -tA[da][0][0]*tB[db][0][0]*tE[dc][0][0])
assert np.isclose(tab[dd][1][0][0], -tA[da][0][0]*tB[db][0][0]*tE[dc][1][0])
assert np.isclose(tab[dd][2][0][0], -tA[da][1][0]*tB[db][0][0]*tE[dc][0][0])
assert np.isclose(tab[dd][3][0][0], -tA[da][1][0]*tB[db][0][0]*tE[dc][1][0])
assert tab[dd][4][0][0] == 0.0
assert tab[dd][5][0][0] == 0.0
assert tab[dd][6][0][0] == 0.0
assert tab[dd][7][0][0] == 0.0
assert tab[dd][0][1][0] == 0.0
assert tab[dd][1][1][0] == 0.0
assert tab[dd][2][1][0] == 0.0
assert tab[dd][3][1][0] == 0.0
assert np.isclose(tab[dd][4][1][0], tC[da][0][0]*tD[db][0][0]*tE[dc][0][0])
assert np.isclose(tab[dd][5][1][0], tC[da][0][0]*tD[db][0][0]*tE[dc][1][0])
assert np.isclose(tab[dd][6][1][0], tC[da][0][0]*tD[db][1][0]*tE[dc][0][0])
assert np.isclose(tab[dd][7][1][0], tC[da][0][0]*tD[db][1][0]*tE[dc][1][0])
assert tab[dd][0][2][0] == 0.0
assert tab[dd][1][2][0] == 0.0
assert tab[dd][2][2][0] == 0.0
assert tab[dd][3][2][0] == 0.0
assert tab[dd][4][2][0] == 0.0
assert tab[dd][5][2][0] == 0.0
assert tab[dd][6][2][0] == 0.0
assert tab[dd][7][2][0] == 0.0
def test_TFE_2Dx1D_scalar_triangle_hdiv():
S = UFCTriangle()
T = UFCInterval()
P1_DG = DiscontinuousLagrange(S, 1)
P2 = Lagrange(T, 2)
elt = Hdiv(TensorProductElement(P1_DG, P2))
assert elt.value_shape() == (3, )
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tabA = P1_DG.tabulate(1, [(0.1, 0.2)])
tabB = P2.tabulate(1, [(0.3, )])
for da, db in [[(0, 0), (0, )], [(1, 0), (0, )], [(0, 1), (0, )],
[(0, 0), (1, )]]:
dc = da + db
assert tab[dc][0][0][0] == 0.0
assert tab[dc][1][0][0] == 0.0
assert tab[dc][2][0][0] == 0.0
assert tab[dc][3][0][0] == 0.0
assert tab[dc][4][0][0] == 0.0
assert tab[dc][5][0][0] == 0.0
assert tab[dc][6][0][0] == 0.0
assert tab[dc][7][0][0] == 0.0
assert tab[dc][8][0][0] == 0.0
assert tab[dc][0][1][0] == 0.0
assert tab[dc][1][1][0] == 0.0
assert tab[dc][2][1][0] == 0.0
assert tab[dc][3][1][0] == 0.0
assert tab[dc][4][1][0] == 0.0
assert tab[dc][5][1][0] == 0.0
assert tab[dc][6][1][0] == 0.0
assert tab[dc][7][1][0] == 0.0
assert tab[dc][8][1][0] == 0.0
assert np.isclose(tab[dc][0][2][0], tabA[da][0][0] * tabB[db][0][0])
assert np.isclose(tab[dc][1][2][0], tabA[da][0][0] * tabB[db][1][0])
assert np.isclose(tab[dc][2][2][0], tabA[da][0][0] * tabB[db][2][0])
assert np.isclose(tab[dc][3][2][0], tabA[da][1][0] * tabB[db][0][0])
assert np.isclose(tab[dc][4][2][0], tabA[da][1][0] * tabB[db][1][0])
assert np.isclose(tab[dc][5][2][0], tabA[da][1][0] * tabB[db][2][0])
assert np.isclose(tab[dc][6][2][0], tabA[da][2][0] * tabB[db][0][0])
assert np.isclose(tab[dc][7][2][0], tabA[da][2][0] * tabB[db][1][0])
assert np.isclose(tab[dc][8][2][0], tabA[da][2][0] * tabB[db][2][0])
def test_TFE_2Dx1D_scalar_quad():
T = UFCInterval()
P1 = Lagrange(T, 1)
P1_DG = DiscontinuousLagrange(T, 1)
elt = TensorProductElement(TensorProductElement(P1, P1_DG), P1)
assert elt.value_shape() == ()
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tA = P1.tabulate(1, [(0.1,)])
tB = P1_DG.tabulate(1, [(0.2,)])
tC = P1.tabulate(1, [(0.3,)])
for da, db, dc in [[(0,), (0,), (0,)], [(1,), (0,), (0,)], [(0,), (1,), (0,)], [(0,), (0,), (1,)]]:
dd = da + db + dc
assert np.isclose(tab[dd][0][0], tA[da][0][0]*tB[db][0][0]*tC[dc][0][0])
assert np.isclose(tab[dd][1][0], tA[da][0][0]*tB[db][0][0]*tC[dc][1][0])
assert np.isclose(tab[dd][2][0], tA[da][0][0]*tB[db][1][0]*tC[dc][0][0])
assert np.isclose(tab[dd][3][0], tA[da][0][0]*tB[db][1][0]*tC[dc][1][0])
assert np.isclose(tab[dd][4][0], tA[da][1][0]*tB[db][0][0]*tC[dc][0][0])
assert np.isclose(tab[dd][5][0], tA[da][1][0]*tB[db][0][0]*tC[dc][1][0])
assert np.isclose(tab[dd][6][0], tA[da][1][0]*tB[db][1][0]*tC[dc][0][0])
assert np.isclose(tab[dd][7][0], tA[da][1][0]*tB[db][1][0]*tC[dc][1][0])
def test_TFE_2Dx1D_scalar_triangle_hdiv():
S = UFCTriangle()
T = UFCInterval()
P1_DG = DiscontinuousLagrange(S, 1)
P2 = Lagrange(T, 2)
elt = Hdiv(TensorProductElement(P1_DG, P2))
assert elt.value_shape() == (3,)
tab = elt.tabulate(1, [(0.1, 0.2, 0.3)])
tabA = P1_DG.tabulate(1, [(0.1, 0.2)])
tabB = P2.tabulate(1, [(0.3,)])
for da, db in [[(0, 0), (0,)], [(1, 0), (0,)], [(0, 1), (0,)], [(0, 0), (1,)]]:
dc = da + db
assert tab[dc][0][0][0] == 0.0
assert tab[dc][1][0][0] == 0.0
assert tab[dc][2][0][0] == 0.0
assert tab[dc][3][0][0] == 0.0
assert tab[dc][4][0][0] == 0.0
assert tab[dc][5][0][0] == 0.0
assert tab[dc][6][0][0] == 0.0
assert tab[dc][7][0][0] == 0.0
assert tab[dc][8][0][0] == 0.0
assert tab[dc][0][1][0] == 0.0
assert tab[dc][1][1][0] == 0.0
assert tab[dc][2][1][0] == 0.0
assert tab[dc][3][1][0] == 0.0
assert tab[dc][4][1][0] == 0.0
assert tab[dc][5][1][0] == 0.0
assert tab[dc][6][1][0] == 0.0
assert tab[dc][7][1][0] == 0.0
assert tab[dc][8][1][0] == 0.0
assert np.isclose(tab[dc][0][2][0], tabA[da][0][0]*tabB[db][0][0])
assert np.isclose(tab[dc][1][2][0], tabA[da][0][0]*tabB[db][1][0])
assert np.isclose(tab[dc][2][2][0], tabA[da][0][0]*tabB[db][2][0])
assert np.isclose(tab[dc][3][2][0], tabA[da][1][0]*tabB[db][0][0])
assert np.isclose(tab[dc][4][2][0], tabA[da][1][0]*tabB[db][1][0])
assert np.isclose(tab[dc][5][2][0], tabA[da][1][0]*tabB[db][2][0])
assert np.isclose(tab[dc][6][2][0], tabA[da][2][0]*tabB[db][0][0])
assert np.isclose(tab[dc][7][2][0], tabA[da][2][0]*tabB[db][1][0])
assert np.isclose(tab[dc][8][2][0], tabA[da][2][0]*tabB[db][2][0])
def __init__(self, ref_el, degree):
sd = ref_el.get_spatial_dimension()
if sd in (0, 1):
raise ValueError(
"Cannot use this trace class on a %d-dimensional cell." % sd)
# Constructing facet element as a discontinuous Lagrange element
dglagrange = DiscontinuousLagrange(ufc_simplex(sd - 1), degree)
# Construct entity ids (assigning top. dim. and initializing as empty)
entity_dofs = {}
# Looping over dictionary of cell topology to construct the empty
# dictionary for entity ids of the trace element
topology = ref_el.get_topology()
for top_dim, entities in topology.items():
entity_dofs[top_dim] = {}
for entity in entities:
entity_dofs[top_dim][entity] = []
# Filling in entity ids and generating points for dual basis
nf = dglagrange.space_dimension()
points = []
num_facets = sd + 1
for f in range(num_facets):
entity_dofs[sd - 1][f] = range(f * nf, (f + 1) * nf)
for dof in dglagrange.dual_basis():
facet_point = list(dof.get_point_dict().keys())[0]
transform = ref_el.get_entity_transform(sd - 1, f)
points.append(tuple(transform(facet_point)))
# Setting up dual basis - only point evaluations
nodes = [PointEvaluation(ref_el, pt) for pt in points]
dual = dual_set.DualSet(nodes, ref_el, entity_dofs)
super(HDivTrace, self).__init__(ref_el, dual, dglagrange.get_order(),
dglagrange.get_formdegree(),
dglagrange.mapping()[0])
# Set up facet element
self.facet_element = dglagrange
# degree for quadrature rule
self.polydegree = degree
sys.path.insert(0, bsDir)
sys.path.insert(0, configDir)
if os.path.isdir(os.path.join(fiatDir,'FIAT')):
sys.path.insert(0, fiatDir)
import PETSc.FEM
from FIAT.reference_element import default_simplex
from FIAT.lagrange import Lagrange
from FIAT.discontinuous_lagrange import DiscontinuousLagrange
generator = PETSc.FEM.QuadratureGenerator()
generator.setup()
elements = []
if not (len(sys.argv)-2) % 5 == 0:
sys.exit('Incomplete set of arguments')
for n in range((len(sys.argv)-2) / 5):
dim = int(sys.argv[n*5+1])
order = int(sys.argv[n*5+2])
components = int(sys.argv[n*5+3])
numBlocks = int(sys.argv[n*5+4])
operator = sys.argv[n*5+5]
if order == 0:
element = DiscontinuousLagrange(default_simplex(dim), order)
else:
element = Lagrange(default_simplex(dim), order)
element.numComponents = components
elements.append(element)
filename = sys.argv[-1]
generator.quadDegree = max([e.order for e in elements])
generator.run(elements, numBlocks, operator, filename)