import FIAT
import gem
from finat.fiat_elements import ScalarFiatElement, Lagrange, DiscontinuousLagrange
from finat.point_set import GaussLobattoLegendrePointSet, GaussLegendrePointSet
[docs]class GaussLobattoLegendre(Lagrange):
"""1D continuous element with nodes at the Gauss-Lobatto points."""
def __init__(self, cell, degree):
fiat_element = FIAT.GaussLobattoLegendre(cell, degree)
super(Lagrange, self).__init__(fiat_element)
[docs] def basis_evaluation(self, order, ps, entity=None, coordinate_mapping=None):
'''Return code for evaluating the element at known points on the
reference element.
:param order: return derivatives up to this order.
:param ps: the point set.
:param entity: the cell entity on which to tabulate.
'''
result = super(GaussLobattoLegendre, self).basis_evaluation(order, ps, entity)
cell_dimension = self.cell.get_dimension()
if entity is None or entity == (cell_dimension, 0): # on cell interior
space_dim = self.space_dimension()
if isinstance(ps, GaussLobattoLegendrePointSet) and len(ps.points) == space_dim:
# Bingo: evaluation points match node locations!
spatial_dim = self.cell.get_spatial_dimension()
q, = ps.indices
r, = self.get_indices()
result[(0,) * spatial_dim] = gem.ComponentTensor(gem.Delta(q, r), (r,))
return result
[docs]class GaussLegendre(DiscontinuousLagrange):
"""1D discontinuous element with nodes at the Gauss-Legendre points."""
def __init__(self, cell, degree):
fiat_element = FIAT.GaussLegendre(cell, degree)
super(DiscontinuousLagrange, self).__init__(fiat_element)
[docs] def basis_evaluation(self, order, ps, entity=None, coordinate_mapping=None):
'''Return code for evaluating the element at known points on the
reference element.
:param order: return derivatives up to this order.
:param ps: the point set.
:param entity: the cell entity on which to tabulate.
'''
result = super(GaussLegendre, self).basis_evaluation(order, ps, entity)
cell_dimension = self.cell.get_dimension()
if entity is None or entity == (cell_dimension, 0): # on cell interior
space_dim = self.space_dimension()
if isinstance(ps, GaussLegendrePointSet) and len(ps.points) == space_dim:
# Bingo: evaluation points match node locations!
spatial_dim = self.cell.get_spatial_dimension()
q, = ps.indices
r, = self.get_indices()
result[(0,) * spatial_dim] = gem.ComponentTensor(gem.Delta(q, r), (r,))
return result
[docs]class Legendre(ScalarFiatElement):
"""DG element with Legendre polynomials."""
def __init__(self, cell, degree):
fiat_element = FIAT.Legendre(cell, degree)
super(Legendre, self).__init__(fiat_element)
[docs]class IntegratedLegendre(ScalarFiatElement):
"""CG element with integrated Legendre polynomials."""
def __init__(self, cell, degree, variant=None):
fiat_element = FIAT.IntegratedLegendre(cell, degree, variant=variant)
super(IntegratedLegendre, self).__init__(fiat_element)
[docs]class FDMLagrange(ScalarFiatElement):
"""1D CG element with FDM shape functions and point evaluation BCs."""
def __init__(self, cell, degree):
fiat_element = FIAT.FDMLagrange(cell, degree)
super(FDMLagrange, self).__init__(fiat_element)
[docs]class FDMDiscontinuousLagrange(ScalarFiatElement):
"""1D DG element with derivatives of FDM shape functions with point evaluation Bcs."""
def __init__(self, cell, degree):
fiat_element = FIAT.FDMDiscontinuousLagrange(cell, degree)
super(FDMDiscontinuousLagrange, self).__init__(fiat_element)
[docs]class FDMQuadrature(ScalarFiatElement):
"""1D CG element with FDM shape functions and orthogonalized vertex modes."""
def __init__(self, cell, degree):
fiat_element = FIAT.FDMQuadrature(cell, degree)
super(FDMQuadrature, self).__init__(fiat_element)
[docs]class FDMBrokenH1(ScalarFiatElement):
"""1D Broken CG element with FDM shape functions."""
def __init__(self, cell, degree):
fiat_element = FIAT.FDMBrokenH1(cell, degree)
super(FDMBrokenH1, self).__init__(fiat_element)
[docs]class FDMBrokenL2(ScalarFiatElement):
"""1D DG element with derivatives of FDM shape functions."""
def __init__(self, cell, degree):
fiat_element = FIAT.FDMBrokenL2(cell, degree)
super(FDMBrokenL2, self).__init__(fiat_element)
[docs]class FDMHermite(ScalarFiatElement):
"""1D CG element with FDM shape functions, point evaluation BCs and derivative BCs."""
def __init__(self, cell, degree):
fiat_element = FIAT.FDMHermite(cell, degree)
super(FDMHermite, self).__init__(fiat_element)
