def parametrization_derivative(actx: ArrayContext,
dcoll: DiscretizationCollection,
dd) -> MultiVector:
r"""Computes the product of forward metric derivatives spanning the
tangent space with topological dimension *dim*.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
Defaults to the base volume discretization.
:returns: a :class:`pymbolic.geometric_algebra.MultiVector` containing
the product of metric derivatives.
"""
if dd is None:
dd = DD_VOLUME
dim = dcoll.discr_from_dd(dd).dim
if dim == 0:
from pymbolic.geometric_algebra import get_euclidean_space
return MultiVector(_signed_face_ones(actx, dcoll, dd),
space=get_euclidean_space(dcoll.ambient_dim))
from pytools import product
return product(
forward_metric_derivative_mv(actx, dcoll, rst_axis, dd)
for rst_axis in range(dim))
def parametrization_derivative(ambient_dim, dim=None, dd=None):
if dim is None:
dim = ambient_dim
if dim == 0:
from pymbolic.geometric_algebra import get_euclidean_space
return MultiVector(_SignedFaceOnes(dd),
space=get_euclidean_space(ambient_dim))
from pytools import product
return product(
forward_metric_derivative_mv(ambient_dim, rst_axis, dd)
for rst_axis in range(dim))