def get_line_nodes(V):
# Return the Line nodes for Q, DQ, RTCF/E, NCF/E
from FIAT.reference_element import UFCInterval
from FIAT import quadrature
use_tensorproduct, N, ndim, sub_families, variant = tensor_product_space_query(
V)
assert use_tensorproduct
cell = UFCInterval()
if variant == "equispaced" and sub_families <= {
"Q", "DQ", "Lagrange", "Discontinuous Lagrange"
}:
return [cell.make_points(1, 0, N + 1)] * ndim
elif sub_families <= {"Q", "Lagrange"}:
rule = quadrature.GaussLobattoLegendreQuadratureLineRule(cell, N + 1)
return [rule.get_points()] * ndim
elif sub_families <= {"DQ", "Discontinuous Lagrange"}:
rule = quadrature.GaussLegendreQuadratureLineRule(cell, N + 1)
return [rule.get_points()] * ndim
elif sub_families < {"RTCF", "NCF"}:
cg = quadrature.GaussLobattoLegendreQuadratureLineRule(cell, N + 1)
dg = quadrature.GaussLegendreQuadratureLineRule(cell, N)
return [cg.get_points()] + [dg.get_points()] * (ndim - 1)
elif sub_families < {"RTCE", "NCE"}:
cg = quadrature.GaussLobattoLegendreQuadratureLineRule(cell, N + 1)
dg = quadrature.GaussLegendreQuadratureLineRule(cell, N)
return [dg.get_points()] + [cg.get_points()] * (ndim - 1)
else:
raise ValueError("Don't know how to get line nodes for %s" %
V.ufl_element())
def __init__(self, ref_el, degree):
entity_ids = {0: {0: [0], 1: [degree]}, 1: {0: list(range(1, degree))}}
lr = quadrature.GaussLobattoLegendreQuadratureLineRule(
ref_el, degree + 1)
nodes = [functional.PointEvaluation(ref_el, x) for x in lr.pts]
super().__init__(nodes, ref_el, entity_ids)
def __init__(self, ref_el, degree):
entity_ids = {0: {0: [0], 1: [degree]}, 1: {0: list(range(1, degree))}}
lr = quadrature.GaussLobattoLegendreQuadratureLineRule(
ref_el, degree + 1)
nodes = [functional.PointEvaluation(ref_el, x) for x in lr.pts]
entity_permutations = {}
entity_permutations[0] = {0: {0: [0]}, 1: {0: [0]}}
entity_permutations[1] = {0: make_entity_permutations(1, degree - 1)}
super(GaussLobattoLegendreDualSet,
self).__init__(nodes, ref_el, entity_ids, entity_permutations)
def get_line_nodes(V):
# Return the corresponding nodes in the Line for CG / DG
from FIAT.reference_element import UFCInterval
from FIAT import quadrature
use_tensorproduct, N, family, variant = tensor_product_space_query(V)
assert use_tensorproduct
cell = UFCInterval()
if variant == "equispaced":
return cell.make_points(1, 0, N + 1)
elif family <= {"Q", "Lagrange"}:
rule = quadrature.GaussLobattoLegendreQuadratureLineRule(cell, N + 1)
return rule.get_points()
elif family <= {"DQ", "Discontinuous Lagrange"}:
rule = quadrature.GaussLegendreQuadratureLineRule(cell, N + 1)
return rule.get_points()
else:
raise ValueError("Don't know how to get line nodes for %r" % family)
def get_nodes_1d(V):
# Return GLL nodes if V==CG or GL nodes if V==DG
from FIAT import quadrature
from FIAT.reference_element import DefaultLine
use_tensorproduct, N, family, variant = tensor_product_space_query(V)
assert use_tensorproduct
if family <= {"Q", "Lagrange"}:
if variant == "equispaced":
nodes = np.linspace(-1.0E0, 1.0E0, N+1)
else:
rule = quadrature.GaussLobattoLegendreQuadratureLineRule(DefaultLine(), N+1)
nodes = np.asarray(rule.get_points()).flatten()
elif family <= {"DQ", "Discontinuous Lagrange"}:
if variant == "equispaced":
nodes = np.arange(1, N+2)*(2.0E0/(N+2))-1.0E0
else:
rule = quadrature.GaussLegendreQuadratureLineRule(DefaultLine(), N+1)
nodes = np.asarray(rule.get_points()).flatten()
else:
raise ValueError("Don't know how to get nodes for %r" % family)
return nodes