def _make_identity(self, sh):
"Create a higher order identity tensor to represent dv/dv."
res = None
if sh == ():
# Scalar dv/dv is scalar
return FloatValue(1.0)
elif len(sh) == 1:
# Vector v makes dv/dv the identity matrix
return Identity(sh[0])
else:
# TODO: Add a type for this higher order identity?
# II[i0,i1,i2,j0,j1,j2] = 1 if all((i0==j0, i1==j1, i2==j2)) else 0
# Tensor v makes dv/dv some kind of higher rank identity tensor
ind1 = ()
ind2 = ()
for d in sh:
i, j = indices(2)
dij = Identity(d)[i, j]
if res is None:
res = dij
else:
res *= dij
ind1 += (i, )
ind2 += (j, )
fp = as_tensor(res, ind1 + ind2)
return fp
def facet_area(self, o):
if self._preserve_types[o._ufl_typecode_]:
return o
domain = o.ufl_domain()
tdim = domain.topological_dimension()
if not domain.is_piecewise_linear_simplex_domain():
# Don't lower for non-affine cells, instead leave it to
# form compiler
warning("Only know how to compute the facet area of an affine cell.")
return o
# Area of "facet" of interval (i.e. "area" of a vertex) is defined as 1.0
if tdim == 1:
return FloatValue(1.0)
r = self.facet_jacobian_determinant(FacetJacobianDeterminant(domain))
r0 = ReferenceFacetVolume(domain)
return abs(r * r0)
def _simplify_abs_cellorientation(o, self, in_abs):
if not in_abs:
return o
# Cell orientation is +-1
return FloatValue(1)