def test_contains_h1():
h1_elements = [
# Standard Lagrange elements:
FiniteElement("CG", triangle, 1),
FiniteElement("CG", triangle, 2),
# Some special elements:
FiniteElement("HER", triangle),
FiniteElement("MTW", triangle),
# Tensor product elements:
TensorProductElement(FiniteElement("CG", interval, 1),
FiniteElement("CG", interval, 1)),
TensorProductElement(FiniteElement("CG", interval, 2),
FiniteElement("CG", interval, 2)),
# Enriched elements:
EnrichedElement(FiniteElement("CG", triangle, 2),
FiniteElement("B", triangle, 3))
]
for h1_element in h1_elements:
assert h1_element in H1
assert h1_element in H1dx1dy
assert h1_element in HDiv
assert h1_element in HCurl
assert h1_element in L2
assert h1_element in H0dx0dy
assert h1_element not in H2
assert h1_element not in H2dx2dy
def test_physically_mapped_facet():
mesh = Mesh(VectorElement("P", triangle, 1))
# set up variational problem
U = FiniteElement("Morley", mesh.ufl_cell(), 2)
V = FiniteElement("P", mesh.ufl_cell(), 1)
R = FiniteElement("P", mesh.ufl_cell(), 1)
Vv = VectorElement(BrokenElement(V))
Qhat = VectorElement(BrokenElement(V[facet]))
Vhat = VectorElement(V[facet])
Z = FunctionSpace(mesh, MixedElement(U, Vv, Qhat, Vhat, R))
z = Coefficient(Z)
u, d, qhat, dhat, lam = split(z)
s = FacetNormal(mesh)
trans = as_matrix([[1, 0], [0, 1]])
mat = trans*grad(grad(u))*trans + outer(d, d) * u
J = (u**2*dx +
u**3*dx +
u**4*dx +
inner(mat, mat)*dx +
inner(grad(d), grad(d))*dx +
dot(s, d)**2*ds)
L_match = inner(qhat, dhat - d)
L = J + inner(lam, inner(d, d)-1)*dx + (L_match('+') + L_match('-'))*dS + L_match*ds
compile_form(L)
def test_mixed_element_vector_element_form(cell_type, sign, order):
if cell_type == CellType.triangle or cell_type == CellType.quadrilateral:
mesh = create_unit_square(MPI.COMM_WORLD, 2, 2, cell_type)
else:
mesh = create_unit_cube(MPI.COMM_WORLD, 2, 2, 2, cell_type)
if cell_type == CellType.triangle:
U_el = MixedElement([VectorElement("Lagrange", ufl.triangle, order),
FiniteElement("N1curl", ufl.triangle, order)])
elif cell_type == CellType.quadrilateral:
U_el = MixedElement([VectorElement("Lagrange", ufl.quadrilateral, order),
FiniteElement("RTCE", ufl.quadrilateral, order)])
elif cell_type == CellType.tetrahedron:
U_el = MixedElement([VectorElement("Lagrange", ufl.tetrahedron, order),
FiniteElement("N1curl", ufl.tetrahedron, order)])
elif cell_type == CellType.hexahedron:
U_el = MixedElement([VectorElement("Lagrange", ufl.hexahedron, order),
FiniteElement("NCE", ufl.hexahedron, order)])
U = FunctionSpace(mesh, U_el)
u, p = ufl.TrialFunctions(U)
v, q = ufl.TestFunctions(U)
f = form(inner(u, v) * ufl.dx + inner(p, q)(sign) * ufl.dS)
A = dolfinx.fem.assemble_matrix(f)
A.assemble()
check_symmetry(A)
def initialize_data(self):
"""
Extract required objects for defining error control
forms. This will be stored, reused and in particular named.
"""
# Developer's note: The UFL-FFC-DOLFIN--PyDOLFIN toolchain for
# error control is quite fine-tuned. In particular, the order
# of coefficients in forms is (and almost must be) used for
# their assignment. This means that the order in which these
# coefficients are defined matters and should be considered
# fixed.
from ufl import FiniteElement, Coefficient
from ufl.algorithms.elementtransformations import tear, increase_order
# Primal trial element space
self._V = self.u.element()
# Primal test space == Dual trial space
Vhat = self.weak_residual.arguments()[0].element()
# Discontinuous version of primal trial element space
self._dV = tear(self._V)
# Extract domain and geometric dimension
domain, = self._V.domains()
gdim = domain.geometric_dimension()
# Coefficient representing improved dual
E = increase_order(Vhat)
self._Ez_h = Coefficient(E)
self.ec_names[id(self._Ez_h)] = "__improved_dual"
# Coefficient representing cell bubble function
B = FiniteElement("B", domain, gdim + 1)
self._b_T = Coefficient(B)
self.ec_names[id(self._b_T)] = "__cell_bubble"
# Coefficient representing strong cell residual
self._R_T = Coefficient(self._dV)
self.ec_names[id(self._R_T)] = "__cell_residual"
# Coefficient representing cell cone function
C = FiniteElement("DG", domain, gdim)
self._b_e = Coefficient(C)
self.ec_names[id(self._b_e)] = "__cell_cone"
# Coefficient representing strong facet residual
self._R_dT = Coefficient(self._dV)
self.ec_names[id(self._R_dT)] = "__facet_residual"
# Define discrete dual on primal test space
self._z_h = Coefficient(Vhat)
self.ec_names[id(self._z_h)] = "__discrete_dual_solution"
# Piecewise constants for assembling indicators
self._DG0 = FiniteElement("DG", domain, 0)
def test_mini():
m = Mesh(VectorElement('CG', triangle, 1))
P1 = FiniteElement('Lagrange', triangle, 1)
B = FiniteElement("Bubble", triangle, 3)
V = FunctionSpace(m, VectorElement(P1 + B))
u = TrialFunction(V)
v = TestFunction(V)
a = inner(grad(u), grad(v)) * dx
count_flops(a)
def lower_element_order(elem):
if isinstance(elem, VectorElement):
ndofs = elem.value_size()
baseelem = lower_element_order(elem.sub_elements()[0])
return VectorElement(baseelem, dim=ndofs)
elif isinstance(elem, MixedElement): # must come after because VectorElement is a subclass of MixedElement!
elemlist = elem.sub_elements()
newelemlist = []
for subelem in elemlist:
newelemlist.append(lower_element_order(subelem))
return newelemlist
if isinstance(elem, EnrichedElement):
elem1, elem2 = elem._elements
if (isinstance(elem1, HDivElement) and isinstance(elem2, HDivElement)):
elem1 = elem1._element
elem2 = elem2._element
elem1low = lower_element_order(elem1)
elem2low = lower_element_order(elem2)
return HDivElement(elem1low) + HDivElement(elem2low)
if (isinstance(elem1, HCurlElement) and isinstance(elem2, HCurlElement)):
elem1 = elem1._element
elem2 = elem2._element
elem1low = lower_element_order(elem1)
elem2low = lower_element_order(elem2)
return HCurlElement(elem1low) + HCurlElement(elem2low)
elif isinstance(elem, TensorProductElement):
elem1, elem2 = elem.sub_elements()
elem1low = lower_element_order(elem1)
elem2low = lower_element_order(elem2)
return TensorProductElement(elem1low, elem2low)
elif isinstance(elem, FiniteElement):
if elem.cell().cellname() == 'interval':
if elem.family() == 'Discontinuous Lagrange':
return FiniteElement("DG", interval, 0, variant='mgd')
elif elem.family() == 'Lagrange':
return FiniteElement("CG", interval, 1, variant='mgd')
elif elem.cell().cellname() == 'quadrilateral':
if elem.family() == 'Q':
return FiniteElement("Q", quadrilateral, 1, variant='mgd')
if elem.family() == 'DQ':
return FiniteElement("DQ", quadrilateral, 0, variant='mgd')
if elem.family() == 'RTCF':
return FiniteElement("RTCF", quadrilateral, 1, variant='mgd')
if elem.family() == 'RTCE':
return FiniteElement("RTCE", quadrilateral, 1, variant='mgd')
elif elem.cell().cellname() == 'hexahedron':
if elem.family() == 'Q':
return FiniteElement("Q", hexahedron, 1, variant='mgd')
if elem.family() == 'DQ':
return FiniteElement("DQ", hexahedron, 0, variant='mgd')
if elem.family() == 'NCF':
return FiniteElement("NCF", hexahedron, 1, variant='mgd')
if elem.family() == 'NCE':
return FiniteElement("NCE", hexahedron, 1, variant='mgd')
def test_contains_hdiv():
hdiv_elements = [
FiniteElement("RT", triangle, 1),
FiniteElement("BDM", triangle, 1),
FiniteElement("BDFM", triangle, 2),
# HDiv elements:
HDiv(
TensorProductElement(FiniteElement("DG", triangle, 1),
FiniteElement("CG", interval, 2))),
HDiv(
TensorProductElement(FiniteElement("RT", triangle, 1),
FiniteElement("DG", interval, 1))),
HDiv(
TensorProductElement(FiniteElement("N1curl", triangle, 1),
FiniteElement("DG", interval, 1)))
]
for hdiv_element in hdiv_elements:
assert hdiv_element in HDiv
assert hdiv_element in L2
assert hdiv_element in H0dx0dy
assert hdiv_element not in H1
assert hdiv_element not in H1dx1dy
assert hdiv_element not in HCurl
assert hdiv_element not in H2
assert hdiv_element not in H2dx2dy
def test_contains_hcurl():
hcurl_elements = [
FiniteElement("N1curl", triangle, 1),
FiniteElement("N2curl", triangle, 1),
]
for hcurl_element in hcurl_elements:
assert hcurl_element in HCurl
assert hcurl_element in L2
assert hcurl_element not in H1
assert hcurl_element not in HDiv
assert hcurl_element not in H2
def test_contains_h2():
h2_elements = [
FiniteElement("ARG", triangle, 1),
FiniteElement("MOR", triangle),
]
for h2_element in h2_elements:
assert h2_element in H2
assert h2_element in H1
assert h2_element in HDiv
assert h2_element in HCurl
assert h2_element in L2
def test_contains_hdiv():
hdiv_elements = [
FiniteElement("RT", triangle, 1),
FiniteElement("BDM", triangle, 1),
FiniteElement("BDFM", triangle, 2),
]
for hdiv_element in hdiv_elements:
assert hdiv_element in HDiv
assert hdiv_element in L2
assert hdiv_element not in H1
assert hdiv_element not in HCurl
assert hdiv_element not in H2
def test_global_dof_builder(mesh_factory):
func, args = mesh_factory
mesh = func(*args)
V = VectorElement("CG", mesh.ufl_cell(), 1)
Q = FiniteElement("CG", mesh.ufl_cell(), 1)
R = FiniteElement("R", mesh.ufl_cell(), 0)
W = FunctionSpace(mesh, MixedElement([Q, Q, Q, R]))
W = FunctionSpace(mesh, MixedElement([Q, Q, R, Q]))
W = FunctionSpace(mesh, V * R)
W = FunctionSpace(mesh, R * V)
assert (W)
def test_contains_h2():
h2_elements = [
FiniteElement("ARG", triangle, 5),
FiniteElement("MOR", triangle, 2),
]
for h2_element in h2_elements:
assert h2_element in H2
assert h2_element in H2dx2dy
assert h2_element in H1
assert h2_element in H1dx1dy
assert h2_element in HDiv
assert h2_element in HCurl
assert h2_element in L2
assert h2_element in H0dx0dy
def test_contains_l2():
l2_elements = [
FiniteElement("Real", triangle, 0),
FiniteElement("DG", triangle, 0),
FiniteElement("DG", triangle, 1),
FiniteElement("DG", triangle, 2),
FiniteElement("CR", triangle, 1),
]
for l2_element in l2_elements:
assert l2_element in L2
assert l2_element not in H1
assert l2_element not in HCurl
assert l2_element not in HDiv
assert l2_element not in H2
def test_extract_elements_and_extract_unique_elements(forms):
b = forms[2]
integrals = b.integrals_by_type("cell")
integrand = integrals[0].integrand()
element1 = FiniteElement("CG", triangle, 1)
element2 = FiniteElement("CG", triangle, 1)
v = TestFunction(element1)
u = TrialFunction(element2)
a = u * v * dx
assert extract_elements(a) == (element1, element2)
assert extract_unique_elements(a) == (element1, )
def test_taylor_hood_cube():
pytest.xfail("Problem with Mixed Function Spaces")
meshc = UnitCubeMesh(MPI.comm_world, 2, 2, 2)
meshf = UnitCubeMesh(MPI.comm_world, 3, 4, 5)
Ve = VectorElement("CG", meshc.ufl_cell(), 2)
Qe = FiniteElement("CG", meshc.ufl_cell(), 1)
Ze = MixedElement([Ve, Qe])
Zc = FunctionSpace(meshc, Ze)
Zf = FunctionSpace(meshf, Ze)
def z(x):
return np.row_stack((x[0] * x[1],
x[1] * x[2],
x[2] * x[0],
x[0] + 3.0 * x[1] + x[2]))
zc, zf = Function(Zc), Function(Zf)
zc.interpolate(z)
zf.interpolate(z)
mat = PETScDMCollection.create_transfer_matrix(Zc, Zf)
Zuc = Function(Zf)
mat.mult(zc.vector, Zuc.vector)
Zuc.vector.update_ghost_values()
diff = Function(Zf)
diff.assign(Zuc - zf)
assert diff.vector.norm("l2") < 1.0e-12
def test_contains_h1():
h1_elements = [
# Standard Lagrange elements:
FiniteElement("CG", triangle, 1),
FiniteElement("CG", triangle, 2),
# Some special elements:
FiniteElement("AW", triangle),
FiniteElement("HER", triangle),
FiniteElement("MTW", triangle),
]
for h1_element in h1_elements:
assert h1_element in H1
assert h1_element in HDiv
assert h1_element in HCurl
assert h1_element in L2
assert h1_element not in H2
def set_cell_sizes(self, domain):
"""Setup a fake coefficient for "cell sizes".
:arg domain: The domain of the integral.
This is required for scaling of derivative basis functions on
physically mapped elements (Argyris, Bell, etc...). We need a
measure of the mesh size around each vertex (hence this lives
in P1).
Should the domain have topological dimension 0 this does
nothing.
"""
if domain.ufl_cell().topological_dimension() > 0:
# Can't create P1 since only P0 is a valid finite element if
# topological_dimension is 0 and the concept of "cell size"
# is not useful for a vertex.
f = Coefficient(
FunctionSpace(domain, FiniteElement("P", domain.ufl_cell(),
1)))
funarg, expression = prepare_coefficient(
f,
"cell_sizes",
self.scalar_type,
interior_facet=self.interior_facet)
self.cell_sizes_arg = funarg
self._cell_sizes = expression
def test_save_and_checkpoint_timeseries(tempdir, encoding):
mesh = UnitSquareMesh(MPI.comm_world, 16, 16)
filename = os.path.join(tempdir, "u2_checkpoint.xdmf")
FE = FiniteElement("CG", mesh.ufl_cell(), 2)
V = FunctionSpace(mesh, FE)
times = [0.5, 0.2, 0.1]
u_out = [None] * len(times)
u_in = [None] * len(times)
p = 0.0
def expr_eval(values, x):
values[:, 0] = x[:, 0] * p
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file:
for i, p in enumerate(times):
u_out[i] = interpolate(expr_eval, V)
file.write_checkpoint(u_out[i], "u_out", p)
with XDMFFile(mesh.mpi_comm(), filename) as file:
for i, p in enumerate(times):
u_in[i] = file.read_checkpoint(V, "u_out", i)
for i, p in enumerate(times):
u_in[i].vector.axpy(-1.0, u_out[i].vector)
assert u_in[i].vector.norm() < 1.0e-12
# test reading last
with XDMFFile(mesh.mpi_comm(), filename) as file:
u_in_last = file.read_checkpoint(V, "u_out", -1)
u_out[-1].vector.axpy(-1.0, u_in_last.vector)
assert u_out[-1].vector.norm() < 1.0e-12
def test_taylor_hood_cube():
pytest.xfail("Problem with Mixed Function Spaces")
meshc = UnitCubeMesh(MPI.comm_world, 2, 2, 2)
meshf = UnitCubeMesh(MPI.comm_world, 3, 4, 5)
Ve = VectorElement("CG", meshc.ufl_cell(), 2)
Qe = FiniteElement("CG", meshc.ufl_cell(), 1)
Ze = MixedElement([Ve, Qe])
Zc = FunctionSpace(meshc, Ze)
Zf = FunctionSpace(meshf, Ze)
def z(values, x):
values[:, 0] = x[:, 0] * x[:, 1]
values[:, 1] = x[:, 1] * x[:, 2]
values[:, 2] = x[:, 2] * x[:, 0]
values[:, 3] = x[:, 0] + 3.0 * x[:, 1] + x[:, 2]
zc = interpolate(z, Zc)
zf = interpolate(z, Zf)
mat = PETScDMCollection.create_transfer_matrix(Zc, Zf)
Zuc = Function(Zf)
mat.mult(zc.vector, Zuc.vector)
Zuc.vector.update_ghost_values()
diff = Function(Zf)
diff.assign(Zuc - zf)
assert diff.vector.norm("l2") < 1.0e-12
def test_save_and_checkpoint_scalar(tempdir, encoding, fe_degree, fe_family,
mesh_tdim, mesh_n):
if invalid_fe(fe_family, fe_degree):
pytest.skip("Trivial finite element")
filename = os.path.join(tempdir, "u1_checkpoint.xdmf")
mesh = mesh_factory(mesh_tdim, mesh_n)
FE = FiniteElement(fe_family, mesh.ufl_cell(), fe_degree)
V = FunctionSpace(mesh, FE)
u_in = Function(V)
u_out = Function(V)
if has_petsc_complex:
def expr_eval(values, x):
values[:, 0] = x[:, 0] + 1.0j * x[:, 0]
u_out.interpolate(expr_eval)
else:
def expr_eval(values, x):
values[:, 0] = x[:, 0]
u_out.interpolate(expr_eval)
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file:
file.write_checkpoint(u_out, "u_out", 0)
with XDMFFile(mesh.mpi_comm(), filename) as file:
u_in = file.read_checkpoint(V, "u_out", 0)
u_in.vector.axpy(-1.0, u_out.vector)
assert u_in.vector.norm() < 1.0e-12
def test_tabulate_dofs(mesh_factory):
func, args = mesh_factory
mesh = func(*args)
W0 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
W1 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
W = FunctionSpace(mesh, W0 * W1)
L0 = W.sub(0)
L1 = W.sub(1)
L01 = L1.sub(0)
L11 = L1.sub(1)
for i, cell in enumerate(Cells(mesh)):
dofs0 = L0.dofmap().cell_dofs(cell.index())
dofs1 = L01.dofmap().cell_dofs(cell.index())
dofs2 = L11.dofmap().cell_dofs(cell.index())
dofs3 = L1.dofmap().cell_dofs(cell.index())
assert np.array_equal(dofs0, L0.dofmap().cell_dofs(i))
assert np.array_equal(dofs1, L01.dofmap().cell_dofs(i))
assert np.array_equal(dofs2, L11.dofmap().cell_dofs(i))
assert np.array_equal(dofs3, L1.dofmap().cell_dofs(i))
assert len(np.intersect1d(dofs0, dofs1)) == 0
assert len(np.intersect1d(dofs0, dofs2)) == 0
assert len(np.intersect1d(dofs1, dofs2)) == 0
assert np.array_equal(np.append(dofs1, dofs2), dofs3)
def mass_dg(cell, degree):
m = Mesh(VectorElement('Q', cell, 1))
V = FunctionSpace(m, FiniteElement('DQ', cell, degree, variant='spectral'))
u = TrialFunction(V)
v = TestFunction(V)
# In this case, the estimated quadrature degree will give the
# correct number of quadrature points by luck.
return u * v * dx
def main(args):
"Call evaluate basis derivatives for a range of different elements."
if "refs" in args:
print_refs()
return 0
# Change to temporary folder and copy form files
if not os.path.isdir("tmp"):
os.mkdir("tmp")
os.chdir("tmp")
values = {}
# Evaluate basis for single elements
print("\nComputing evaluate_basis_derivatives for single elements")
for element in single_elements:
for shape in element["shapes"]:
for order in element["orders"]:
ufl_element = FiniteElement(element["family"], shape, order)
print("Compiling element: ", str(ufl_element))
error = compile_element(ufl_element)
if error:
continue
print("Computing values")
values[repr(ufl_element)] = {}
for deriv_order in range(1, 4):
values[repr(ufl_element)][deriv_order] = compute_values(
ufl_element, deriv_order)
# Evaluate basis for single elements
print("\nComputing evaluate_basis_derivatives for mixed elements")
for ufl_element in mixed_elements:
print("Compiling element: ", str(ufl_element))
error = compile_element(ufl_element)
if error:
continue
print("Computing values")
values[repr(ufl_element)] = {}
for deriv_order in range(1, 4):
values[repr(ufl_element)][deriv_order] = compute_values(
ufl_element, deriv_order)
# Load or update reference values
os.chdir(os.pardir)
if os.path.isfile("reference.pickle"):
reference = pickle.load(open("reference.pickle", "r"))
else:
print("Unable to find reference values, storing current values.")
pickle.dump(values, open("reference.pickle", "w"))
return 0
# Check results
error = check_results(values, reference)
if not error:
# Remove temporary directory
shutil.rmtree("tmp")
return error
def test_tabulate_coord_periodic(mesh_factory):
class PeriodicBoundary2(SubDomain):
def inside(self, x, on_boundary):
return x[0] < np.finfo(float).eps
def map(self, x, y):
y[0] = x[0] - 1.0
y[1] = x[1]
# Create periodic boundary condition
periodic_boundary = PeriodicBoundary2()
func, args = mesh_factory
mesh = func(*args)
V = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
Q = VectorElement("Lagrange", mesh.ufl_cell(), 1)
W = V * Q
V = FunctionSpace(mesh, V, constrained_domain=periodic_boundary)
W = FunctionSpace(mesh, W, constrained_domain=periodic_boundary)
L0 = W.sub(0)
L1 = W.sub(1)
L01 = L1.sub(0)
L11 = L1.sub(1)
sdim = V.element().space_dimension()
coord0 = np.zeros((sdim, 2), dtype="d")
coord1 = np.zeros((sdim, 2), dtype="d")
coord2 = np.zeros((sdim, 2), dtype="d")
coord3 = np.zeros((sdim, 2), dtype="d")
for cell in Cells(mesh):
coord0 = V.element().tabulate_dof_coordinates(cell)
coord1 = L0.element().tabulate_dof_coordinates(cell)
coord2 = L01.element().tabulate_dof_coordinates(cell)
coord3 = L11.element().tabulate_dof_coordinates(cell)
coord4 = L1.element().tabulate_dof_coordinates(cell)
assert (coord0 == coord1).all()
assert (coord0 == coord2).all()
assert (coord0 == coord3).all()
assert (coord4[:sdim] == coord0).all()
assert (coord4[sdim:] == coord0).all()
def test_varying_continuity_elements():
P1DG_t = FiniteElement("DG", triangle, 1)
P1DG_i = FiniteElement("DG", interval, 1)
P1 = FiniteElement("CG", interval, 1)
P2 = FiniteElement("CG", interval, 2)
P3 = FiniteElement("CG", interval, 3)
RT1 = FiniteElement("RT", triangle, 1)
ARG = FiniteElement("ARG", triangle, 5)
# Tensor product elements
P1DGP2 = TensorProductElement(P1DG_t, P2)
P1P1DG = TensorProductElement(P1, P1DG_i)
P1DGP1 = TensorProductElement(P1DG_i, P1)
RT1DG1 = TensorProductElement(RT1, P1DG_i)
P2P3 = TensorProductElement(P2, P3)
ARGP3 = TensorProductElement(ARG, P3)
assert P1DGP2 in H1dz and P1DGP2 in L2
assert P1DGP2 not in H1dh
assert P1DGP1 in H1dy and P1DGP2 in L2
assert P1P1DG in H1dx and P1P1DG in L2
assert P1P1DG not in H1dx1dy
assert RT1DG1 in H000 and RT1DG1 in L2
assert P2P3 in H1dx1dy and P2P3 in H1
assert ARG in H2dx2dy
assert ARGP3 in H2dhH1dz
def test_expr():
from ufl import triangle, FiniteElement, TestFunction, TrialFunction, Coefficient
element = FiniteElement("CG", triangle, 1)
v = TestFunction(element)
u = TrialFunction(element)
f = Coefficient(element)
g = Coefficient(element)
expr = (f + g) * u.dx(0) * (g - 1) * v
return expr
def test_cell_error(cell, degree):
"""Test that tabulating the trace element deliberatly on the
cell triggers `gem.Failure` to raise the TraceError exception.
"""
trace_element = FiniteElement("HDiv Trace", cell, degree)
lambdar = TrialFunction(trace_element)
gammar = TestFunction(trace_element)
with pytest.raises(TraceError):
compile_form(lambdar * gammar * dx)
def test_compute_form_adjoint(self):
cell = triangle
element = FiniteElement('Lagrange', cell, 1)
u = TrialFunction(element)
v = TestFunction(element)
a = inner(grad(u), grad(v)) * dx
assert compute_form_adjoint(a) == conj(inner(grad(v), grad(u))) * dx
def test_automatic_simplification(self):
cell = triangle
element = FiniteElement("Lagrange", cell, 1)
v = TestFunction(element)
u = TrialFunction(element)
assert inner(u, v) == u * conj(v)
assert dot(u, v) == u * v
assert outer(u, v) == conj(u) * v
def test_gradient_error(cell, degree):
"""Test that tabulating gradient evaluations of the trace
element triggers `gem.Failure` to raise the TraceError
exception.
"""
trace_element = FiniteElement("HDiv Trace", cell, degree)
lambdar = TrialFunction(trace_element)
gammar = TestFunction(trace_element)
with pytest.raises(TraceError):
compile_form(inner(grad(lambdar('+')), grad(gammar('+'))) * dS)