def __init__(self, ref_el, degree):
# Initialize containers for map: mesh_entity -> dof number and
# dual basis
entity_ids = {}
nodes = []
sd = ref_el.get_spatial_dimension()
t = ref_el.get_topology()
# Define each functional for the dual set
# 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
if degree > 1:
Q = quadrature.make_quadrature(ref_el, 2 * (degree + 1))
qpts = Q.get_points()
Nedel = nedelec.Nedelec(ref_el, degree - 1)
Nedfs = Nedel.get_nodal_basis()
zero_index = tuple([0 for i in range(sd)])
Ned_at_qpts = Nedfs.tabulate(qpts)[zero_index]
for i in range(len(Ned_at_qpts)):
phi_cur = Ned_at_qpts[i, :]
l_cur = functional.FrobeniusIntegralMoment(ref_el, Q, phi_cur)
nodes.append(l_cur)
# 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] = list(range(cur, cur + pts_per_facet))
cur += pts_per_facet
# internal nodes, if applicable
entity_ids[sd] = {0: []}
if degree > 1:
num_internal_nodes = len(Ned_at_qpts)
entity_ids[sd][0] = list(range(cur, cur + num_internal_nodes))
super().__init__(nodes, ref_el, entity_ids)
def __init__(self, ref_el, degree, variant, quad_deg):
# Initialize containers for map: mesh_entity -> dof number and
# dual basis
entity_ids = {}
nodes = []
sd = ref_el.get_spatial_dimension()
t = ref_el.get_topology()
if variant == "integral":
facet = ref_el.get_facet_element()
# Facet nodes are \int_F v\cdot n p ds where p \in P_{q-1}
# degree is q - 1
Q = quadrature.make_quadrature(facet, quad_deg)
Pq = polynomial_set.ONPolynomialSet(facet, degree)
Pq_at_qpts = Pq.tabulate(Q.get_points())[tuple([0] * (sd - 1))]
for f in range(len(t[sd - 1])):
for i in range(Pq_at_qpts.shape[0]):
phi = Pq_at_qpts[i, :]
nodes.append(
functional.IntegralMomentOfScaledNormalEvaluation(
ref_el, Q, phi, f))
# internal nodes
if degree > 1:
Q = quadrature.make_quadrature(ref_el, quad_deg)
qpts = Q.get_points()
Nedel = nedelec.Nedelec(ref_el, degree - 1, variant)
Nedfs = Nedel.get_nodal_basis()
zero_index = tuple([0 for i in range(sd)])
Ned_at_qpts = Nedfs.tabulate(qpts)[zero_index]
for i in range(len(Ned_at_qpts)):
phi_cur = Ned_at_qpts[i, :]
l_cur = functional.FrobeniusIntegralMoment(
ref_el, Q, phi_cur)
nodes.append(l_cur)
elif variant == "point":
# Define each functional for the dual set
# 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
if degree > 1:
Q = quadrature.make_quadrature(ref_el, 2 * (degree + 1))
qpts = Q.get_points()
Nedel = nedelec.Nedelec(ref_el, degree - 1, variant)
Nedfs = Nedel.get_nodal_basis()
zero_index = tuple([0 for i in range(sd)])
Ned_at_qpts = Nedfs.tabulate(qpts)[zero_index]
for i in range(len(Ned_at_qpts)):
phi_cur = Ned_at_qpts[i, :]
l_cur = functional.FrobeniusIntegralMoment(
ref_el, Q, phi_cur)
nodes.append(l_cur)
# 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] = list(range(cur, cur + pts_per_facet))
cur += pts_per_facet
# internal nodes, if applicable
entity_ids[sd] = {0: []}
if degree > 1:
num_internal_nodes = len(Ned_at_qpts)
entity_ids[sd][0] = list(range(cur, cur + num_internal_nodes))
super(BDMDualSet, self).__init__(nodes, ref_el, entity_ids)