def test_quad_trace(degree):
"""Test the trace element defined on a quadrilateral cell"""
from FIAT import ufc_simplex, HDivTrace, make_quadrature
from FIAT.reference_element import TensorProductCell
tpc = TensorProductCell(ufc_simplex(1), ufc_simplex(1))
fiat_element = HDivTrace(tpc, (degree, degree))
facet_elements = fiat_element.dg_elements
quadrule = make_quadrature(ufc_simplex(1), degree + 1)
for i, entity in enumerate([((0, 1), 0), ((0, 1), 1), ((1, 0), 0),
((1, 0), 1)]):
entity_dim, _ = entity
element = facet_elements[entity_dim]
nf = element.space_dimension()
tab = fiat_element.tabulate(0, quadrule.pts,
entity)[(0, 0)][nf * i:nf * (i + 1)]
for test_degree in range(degree + 1):
coeffs = [
n(lambda x: x[0]**test_degree) for n in element.dual.nodes
]
integral = np.dot(coeffs, np.dot(tab, quadrule.wts))
reference = np.dot([x[0]**test_degree for x in quadrule.pts],
quadrule.wts)
assert np.allclose(integral, reference, rtol=1e-14)
def test_quad_trace(degree):
"""Test the trace element defined on a quadrilateral cell"""
from FIAT import ufc_simplex, HDivTrace, make_quadrature
from FIAT.reference_element import TensorProductCell
tpc = TensorProductCell(ufc_simplex(1), ufc_simplex(1))
fiat_element = HDivTrace(tpc, (degree, degree))
facet_elements = fiat_element.dg_elements
quadrule = make_quadrature(ufc_simplex(1), degree + 1)
for i, entity in enumerate([((0, 1), 0), ((0, 1), 1),
((1, 0), 0), ((1, 0), 1)]):
entity_dim, _ = entity
element = facet_elements[entity_dim]
nf = element.space_dimension()
tab = fiat_element.tabulate(0, quadrule.pts,
entity)[(0, 0)][nf*i:nf*(i+1)]
for test_degree in range(degree + 1):
coeffs = [n(lambda x: x[0]**test_degree)
for n in element.dual.nodes]
integral = np.dot(coeffs, np.dot(tab, quadrule.wts))
reference = np.dot([x[0]**test_degree
for x in quadrule.pts], quadrule.wts)
assert np.allclose(integral, reference, rtol=1e-14)
def test_cell_traceerror(dim, degree):
"""Ensure that the TraceError appears in all dict entries when deliberately
attempting to tabulate the cell of a trace element."""
from FIAT import ufc_simplex, HDivTrace, make_quadrature
from FIAT.hdiv_trace import TraceError
fiat_element = HDivTrace(ufc_simplex(dim), degree)
pts = make_quadrature(ufc_simplex(dim), 1).pts
tab = fiat_element.tabulate(0, pts, entity=(dim, 0))
for key in tab.keys():
assert isinstance(tab[key], TraceError)
def test_cell_traceerror(dim, degree):
"""Ensure that the TraceError appears in all dict entries when deliberately
attempting to tabulate the cell of a trace element."""
from FIAT import ufc_simplex, HDivTrace, make_quadrature
from FIAT.hdiv_trace import TraceError
fiat_element = HDivTrace(ufc_simplex(dim), degree)
pts = make_quadrature(ufc_simplex(dim), 1).pts
tab = fiat_element.tabulate(0, pts, entity=(dim, 0))
for key in tab.keys():
assert isinstance(tab[key], TraceError)
def test_gradient_traceerror(dim, order, degree):
"""Ensure that the TraceError appears in the appropriate dict entries when
attempting to tabulate certain orders of derivatives."""
from FIAT import ufc_simplex, HDivTrace, make_quadrature
from FIAT.hdiv_trace import TraceError
fiat_element = HDivTrace(ufc_simplex(dim), degree)
pts = make_quadrature(ufc_simplex(dim - 1), degree + 1).pts
for facet_id in range(dim + 1):
tab = fiat_element.tabulate(order, pts, entity=(dim - 1, facet_id))
for key in tab.keys():
if key != (0, ) * dim:
assert isinstance(tab[key], TraceError)
def test_gradient_traceerror(dim, order, degree):
"""Ensure that the TraceError appears in the appropriate dict entries when
attempting to tabulate certain orders of derivatives."""
from FIAT import ufc_simplex, HDivTrace, make_quadrature
from FIAT.hdiv_trace import TraceError
fiat_element = HDivTrace(ufc_simplex(dim), degree)
pts = make_quadrature(ufc_simplex(dim - 1), degree + 1).pts
for facet_id in range(dim + 1):
tab = fiat_element.tabulate(order, pts, entity=(dim - 1, facet_id))
for key in tab.keys():
if key != (0,)*dim:
assert isinstance(tab[key], TraceError)
def test_basis_values(dim, degree):
"""Ensure that integrating simple monomials produces the expected results
for each facet entity of the reference triangle and tetrahedron.
This test performs the trace tabulation in two ways:
(1) The entity is not specified, in which case the element uses
numerical tolerance to determine the facet id;
(2) The entity pair (dim, id) is provided, and the trace element
tabulates accordingly using the new tabulate API.
"""
from FIAT import ufc_simplex, HDivTrace, make_quadrature
ref_el = ufc_simplex(dim)
quadrule = make_quadrature(ufc_simplex(dim - 1), degree + 1)
fiat_element = HDivTrace(ref_el, degree)
facet_element = fiat_element.dg_elements[dim - 1]
nf = facet_element.space_dimension()
for facet_id in range(dim + 1):
# Tabulate without an entity pair given --- need to map to cell coordinates
cell_transform = ref_el.get_entity_transform(dim - 1, facet_id)
cell_points = np.array(list(map(cell_transform, quadrule.pts)))
ctab = fiat_element.tabulate(
0, cell_points)[(0, ) * dim][nf * facet_id:nf * (facet_id + 1)]
# Tabulate with entity pair provided
entity = (ref_el.get_spatial_dimension() - 1, facet_id)
etab = fiat_element.tabulate(0, quadrule.pts,
entity)[(0, ) * dim][nf * facet_id:nf *
(facet_id + 1)]
for test_degree in range(degree + 1):
coeffs = [
n(lambda x: x[0]**test_degree)
for n in facet_element.dual.nodes
]
cintegral = np.dot(coeffs, np.dot(ctab, quadrule.wts))
eintegral = np.dot(coeffs, np.dot(etab, quadrule.wts))
assert np.allclose(cintegral, eintegral, rtol=1e-14)
reference = np.dot([x[0]**test_degree for x in quadrule.pts],
quadrule.wts)
assert np.allclose(cintegral, reference, rtol=1e-14)
assert np.allclose(eintegral, reference, rtol=1e-14)
def test_basis_values(dim, degree):
"""Ensure that integrating simple monomials produces the expected results
for each facet entity of the reference triangle and tetrahedron.
This test performs the trace tabulation in two ways:
(1) The entity is not specified, in which case the element uses
numerical tolerance to determine the facet id;
(2) The entity pair (dim, id) is provided, and the trace element
tabulates accordingly using the new tabulate API.
"""
from FIAT import ufc_simplex, HDivTrace, make_quadrature
ref_el = ufc_simplex(dim)
quadrule = make_quadrature(ufc_simplex(dim - 1), degree + 1)
fiat_element = HDivTrace(ref_el, degree)
facet_element = fiat_element.dg_elements[dim - 1]
nf = facet_element.space_dimension()
for facet_id in range(dim + 1):
# Tabulate without an entity pair given --- need to map to cell coordinates
cell_transform = ref_el.get_entity_transform(dim - 1, facet_id)
cell_points = np.array(list(map(cell_transform, quadrule.pts)))
ctab = fiat_element.tabulate(0, cell_points)[(0,) * dim][nf*facet_id:nf*(facet_id + 1)]
# Tabulate with entity pair provided
entity = (ref_el.get_spatial_dimension() - 1, facet_id)
etab = fiat_element.tabulate(0, quadrule.pts,
entity)[(0,) * dim][nf*facet_id:nf*(facet_id + 1)]
for test_degree in range(degree + 1):
coeffs = [n(lambda x: x[0]**test_degree)
for n in facet_element.dual.nodes]
cintegral = np.dot(coeffs, np.dot(ctab, quadrule.wts))
eintegral = np.dot(coeffs, np.dot(etab, quadrule.wts))
assert np.allclose(cintegral, eintegral, rtol=1e-14)
reference = np.dot([x[0]**test_degree
for x in quadrule.pts], quadrule.wts)
assert np.allclose(cintegral, reference, rtol=1e-14)
assert np.allclose(eintegral, reference, rtol=1e-14)