def get_line_element(V):
# Return the Line elements for Q, DQ, RTCF/E, NCF/E
from FIAT.reference_element import UFCInterval
from FIAT import gauss_legendre, gauss_lobatto_legendre, lagrange, discontinuous_lagrange
use_tensorproduct, N, ndim, sub_families, variant = tensor_product_space_query(
V)
assert use_tensorproduct
cell = UFCInterval()
if sub_families <= {"Q", "Lagrange"}:
if variant == "equispaced":
element = lagrange.Lagrange(cell, N)
else:
element = gauss_lobatto_legendre.GaussLobattoLegendre(cell, N)
element = [element] * ndim
elif sub_families <= {"DQ", "Discontinuous Lagrange"}:
if variant == "equispaced":
element = discontinuous_lagrange.DiscontinuousLagrange(cell, N)
else:
element = gauss_legendre.GaussLegendre(cell, N)
element = [element] * ndim
elif sub_families < {"RTCF", "NCF"}:
cg = gauss_lobatto_legendre.GaussLobattoLegendre(cell, N)
dg = gauss_legendre.GaussLegendre(cell, N - 1)
element = [cg] + [dg] * (ndim - 1)
elif sub_families < {"RTCE", "NCE"}:
cg = gauss_lobatto_legendre.GaussLobattoLegendre(cell, N)
dg = gauss_legendre.GaussLegendre(cell, N - 1)
element = [dg] + [cg] * (ndim - 1)
else:
raise ValueError("Don't know how to get line element for %s" %
V.ufl_element())
return element
def get_line_element(V):
# Return the corresponding Line element for CG / DG
from FIAT.reference_element import UFCInterval
from FIAT import gauss_legendre, gauss_lobatto_legendre, lagrange, discontinuous_lagrange
use_tensorproduct, N, family, variant = tensor_product_space_query(V)
assert use_tensorproduct
cell = UFCInterval()
if family <= {"Q", "Lagrange"}:
if variant == "equispaced":
element = lagrange.Lagrange(cell, N)
else:
element = gauss_lobatto_legendre.GaussLobattoLegendre(cell, N)
elif family <= {"DQ", "Discontinuous Lagrange"}:
if variant == "equispaced":
element = discontinuous_lagrange.DiscontinuousLagrange(cell, N)
else:
element = gauss_legendre.GaussLegendre(cell, N)
else:
raise ValueError("Don't know how to get line element for %r" % family)
return element
def BDFMSpace(ref_el, order):
sd = ref_el.get_spatial_dimension()
if sd != 2:
raise Exception("BDFM_k elements only valid for dim 2")
# Note that order will be 2.
# Linear vector valued space. Since the embedding degree of this element
# is 2, this is implemented by taking the quadratic space and selecting
# the linear polynomials.
vec_poly_set = polynomial_set.ONPolynomialSet(ref_el, order, (sd,))
# Linears are the first three polynomials in each dimension.
vec_poly_set = vec_poly_set.take([0, 1, 2, 6, 7, 8])
# Scalar quadratic Lagrange element.
lagrange_ele = lagrange.Lagrange(ref_el, order)
# Select the dofs associated with the edges.
edge_dofs_dict = lagrange_ele.dual.get_entity_ids()[sd - 1]
edge_dofs = numpy.array([(edge, dof)
for edge, dofs in list(edge_dofs_dict.items())
for dof in dofs])
tangent_polys = lagrange_ele.poly_set.take(edge_dofs[:, 1])
new_coeffs = numpy.zeros((tangent_polys.get_num_members(), sd, tangent_polys.coeffs.shape[-1]))
# Outer product of the tangent vectors with the quadratic edge polynomials.
for i, (edge, dof) in enumerate(edge_dofs):
tangent = ref_el.compute_edge_tangent(edge)
new_coeffs[i, :, :] = numpy.outer(tangent, tangent_polys.coeffs[i, :])
bubble_set = polynomial_set.PolynomialSet(ref_el,
order,
order,
vec_poly_set.get_expansion_set(),
new_coeffs,
vec_poly_set.get_dmats())
element_set = polynomial_set.polynomial_set_union_normalized(bubble_set, vec_poly_set)
return element_set