def jacobian_at(self, point):
ps = PointSingleton(point)
expr = Jacobian(self.mt.terminal.ufl_domain())
assert ps.expression.shape == (
expr.ufl_domain().topological_dimension(), )
if self.mt.restriction == '+':
expr = PositiveRestricted(expr)
elif self.mt.restriction == '-':
expr = NegativeRestricted(expr)
config = {"point_set": PointSingleton(point)}
config.update(self.config)
context = PointSetContext(**config)
expr = self.preprocess(expr, context)
return map_expr_dag(context.translator, expr)
def translate_cellorigin(terminal, mt, ctx):
domain = terminal.ufl_domain()
coords = SpatialCoordinate(domain)
expression = construct_modified_terminal(mt, coords)
point_set = PointSingleton((0.0,) * domain.topological_dimension())
config = {name: getattr(ctx, name)
for name in ["ufl_cell", "precision", "index_cache"]}
config.update(interface=ctx, point_set=point_set)
context = PointSetContext(**config)
return context.translator(expression)
def detJ_at(self, point):
expr = JacobianDeterminant(self.mt.terminal.ufl_domain())
if self.mt.restriction == '+':
expr = PositiveRestricted(expr)
elif self.mt.restriction == '-':
expr = NegativeRestricted(expr)
config = {"point_set": PointSingleton(point)}
config.update(self.config)
context = PointSetContext(**config)
expr = self.preprocess(expr, context)
return map_expr_dag(context.translator, expr)
def physical_edge_lengths(self):
expr = ufl.classes.CellEdgeVectors(self.mt.terminal.ufl_domain())
if self.mt.restriction == '+':
expr = PositiveRestricted(expr)
elif self.mt.restriction == '-':
expr = NegativeRestricted(expr)
expr = ufl.as_vector([ufl.sqrt(ufl.dot(expr[i, :], expr[i, :])) for i in range(3)])
expr = preprocess_expression(expr)
config = {"point_set": PointSingleton([1/3, 1/3])}
config.update(self.config)
context = PointSetContext(**config)
return map_expr_dag(context.translator, expr)
def factor_point_set(product_cell, product_dim, point_set):
"""Factors a point set for the product element into a point sets for
each subelement.
:arg product_cell: a TensorProductCell
:arg product_dim: entity dimension for the product cell
:arg point_set: point set for the product element
"""
assert len(product_cell.cells) == len(product_dim)
point_dims = [
cell.construct_subelement(dim).get_spatial_dimension()
for cell, dim in zip(product_cell.cells, product_dim)
]
if isinstance(point_set, TensorPointSet):
# Just give the factors asserting matching dimensions.
assert len(point_set.factors) == len(point_dims)
assert all(ps.dimension == dim
for ps, dim in zip(point_set.factors, point_dims))
return point_set.factors
# Split the point coordinates along the point dimensions
# required by the subelements.
assert point_set.dimension == sum(point_dims)
slices = TensorProductCell._split_slices(point_dims)
if isinstance(point_set, PointSingleton):
return [PointSingleton(point_set.point[s]) for s in slices]
elif isinstance(point_set, PointSet):
# Use the same point index for the new point sets.
result = []
for s in slices:
ps = PointSet(point_set.points[:, s])
ps.indices = point_set.indices
result.append(ps)
return result
raise NotImplementedError("How to tabulate TensorProductElement on %s?" %
(type(point_set).__name__, ))
