diff --git a/grudge/geometry/metrics.py b/grudge/geometry/metrics.py
index 40eb0306bd114c369c289826b981ce159ab5a062..16881e60b50079b2a62c5a46f07315ba54ea6881 100644
--- a/grudge/geometry/metrics.py
+++ b/grudge/geometry/metrics.py
@@ -178,7 +178,7 @@ def forward_metric_derivative_mv(
def forward_metric_derivative_mat(
- actx: ArrayContext, dcoll: DiscretizationCollection, dim=None, dd=None
+ actx: ArrayContext, dcoll: DiscretizationCollection, dd=None
) -> np.ndarray:
r"""Computes the forward metric derivative matrix, also commonly
called the Jacobian matrix, with entries defined as the
@@ -195,8 +195,6 @@ def forward_metric_derivative_mat(
Note that, in the case of immersed manifolds, `J` is not necessarily
a square matrix.
- :arg dim: an integer denoting the spatial dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.dim`.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
Defaults to the base volume discretization.
:returns: a matrix containing the evaluated forward metric derivatives
@@ -204,8 +202,10 @@ def forward_metric_derivative_mat(
"""
ambient_dim = dcoll.ambient_dim
- if dim is None:
- dim = dcoll.dim
+ if dd is None:
+ dd = DD_VOLUME
+
+ dim = dcoll.discr_from_dd(dd).dim
result = np.zeros((ambient_dim, dim), dtype=object)
for j in range(dim):
@@ -215,7 +215,7 @@ def forward_metric_derivative_mat(
def first_fundamental_form(actx: ArrayContext, dcoll: DiscretizationCollection,
- dim=None, dd=None) -> np.ndarray:
+ dd=None) -> np.ndarray:
r"""Computes the first fundamental form using the Jacobian matrix:
.. math::
@@ -233,37 +233,35 @@ def first_fundamental_form(actx: ArrayContext, dcoll: DiscretizationCollection,
:math:`x(u, v)` defines a parameterized region. Here, :math:`J` is the
corresponding Jacobian matrix.
- :arg dim: an integer denoting the spatial dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.dim`.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
Defaults to the base volume discretization.
:returns: a matrix containing coefficients of the first fundamental
form.
"""
- if dim is None:
- dim = dcoll.ambient_dim - 1
+ if dd is None:
+ dd = DD_VOLUME
- mder = forward_metric_derivative_mat(actx, dcoll, dim=dim, dd=dd)
+ mder = forward_metric_derivative_mat(actx, dcoll, dd=dd)
return mder.T.dot(mder)
def inverse_metric_derivative_mat(
- actx: ArrayContext, dcoll: DiscretizationCollection, dim=None, dd=None
+ actx: ArrayContext, dcoll: DiscretizationCollection, dd=None
) -> np.ndarray:
r"""Computes the inverse metric derivative matrix, which is
the inverse of the Jacobian (forward metric derivative) matrix.
- :arg dim: an integer denoting the spatial dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.dim`.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
Defaults to the base volume discretization.
:returns: a matrix containing the evaluated inverse metric derivatives.
"""
ambient_dim = dcoll.ambient_dim
- if dim is None:
- dim = dcoll.dim
+ if dd is None:
+ dd = DD_VOLUME
+
+ dim = dcoll.discr_from_dd(dd).dim
result = np.zeros((ambient_dim, dim), dtype=object)
for i in range(dim):
@@ -276,7 +274,7 @@ def inverse_metric_derivative_mat(
def inverse_first_fundamental_form(
- actx: ArrayContext, dcoll: DiscretizationCollection, dim=None, dd=None
+ actx: ArrayContext, dcoll: DiscretizationCollection, dd=None
) -> np.ndarray:
r"""Computes the inverse of the first fundamental form:
@@ -292,21 +290,21 @@ def inverse_first_fundamental_form(
where :math:`E, F, G` are coefficients of the first fundamental form.
- :arg dim: an integer denoting the spatial dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.dim`.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
Defaults to the base volume discretization.
:returns: a matrix containing coefficients of the inverse of the
first fundamental form.
"""
- if dim is None:
- dim = dcoll.dim
+ if dd is None:
+ dd = DD_VOLUME
+
+ dim = dcoll.discr_from_dd(dd).dim
if dcoll.ambient_dim == dim:
- inv_mder = inverse_metric_derivative_mat(actx, dcoll, dim=dim, dd=dd)
+ inv_mder = inverse_metric_derivative_mat(actx, dcoll, dd=dd)
inv_form1 = inv_mder.dot(inv_mder.T)
else:
- form1 = first_fundamental_form(actx, dcoll, dim=dim, dd=dd)
+ form1 = first_fundamental_form(actx, dcoll, dd=dd)
if dim == 1:
inv_form1 = 1.0 / form1
@@ -317,7 +315,7 @@ def inverse_first_fundamental_form(
make_obj_array([-F, E])]
)
else:
- raise ValueError("%dD surfaces not supported" % dim)
+ raise ValueError(f"{dim}D surfaces not supported" % dim)
return inv_form1
@@ -399,7 +397,7 @@ def inverse_surface_metric_derivative(
actx, dcoll, rst_axis, xyz_axis, dd=dd
)
else:
- inv_form1 = inverse_first_fundamental_form(actx, dcoll, dim=dim, dd=dd)
+ inv_form1 = inverse_first_fundamental_form(actx, dcoll, dd=dd)
imd = sum(
inv_form1[rst_axis, d]*forward_metric_nth_derivative(
actx, dcoll, xyz_axis, d, dd=dd
@@ -434,18 +432,20 @@ def _signed_face_ones(
def parametrization_derivative(
- actx: ArrayContext, dcoll: DiscretizationCollection, dim, dd
+ actx: ArrayContext, dcoll: DiscretizationCollection, dd
) -> MultiVector:
r"""Computes the product of forward metric derivatives spanning the
tangent space with topological dimension *dim*.
- :arg dim: an integer denoting the spatial dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.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
@@ -463,12 +463,10 @@ def parametrization_derivative(
def pseudoscalar(actx: ArrayContext, dcoll: DiscretizationCollection,
- dim=None, dd=None) -> MultiVector:
+ dd=None) -> MultiVector:
r"""Computes the field of pseudoscalars for the domain/discretization
identified by *dd*.
- :arg dim: an integer denoting the spatial dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.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` of
@@ -477,33 +475,31 @@ def pseudoscalar(actx: ArrayContext, dcoll: DiscretizationCollection,
if dd is None:
dd = DD_VOLUME
- if dim is None:
- dim = dcoll.discr_from_dd(dd).dim
-
- return parametrization_derivative(
- actx, dcoll, dim, dd
- ).project_max_grade()
+ return parametrization_derivative(actx, dcoll, dd).project_max_grade()
def area_element(
- actx: ArrayContext, dcoll: DiscretizationCollection, dim=None, dd=None
+ actx: ArrayContext, dcoll: DiscretizationCollection, dd=None
) -> DOFArray:
r"""Computes the scale factor used to transform integrals from reference
to global space.
- :arg dim: an integer denoting the spatial dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.dim`.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
Defaults to the base volume discretization.
:returns: a :class:`~meshmode.dof_array.DOFArray` containing the transformed
volumes for each element.
"""
+ if dd is None:
+ dd = DD_VOLUME
+
+ dim = dcoll.discr_from_dd(dd).dim
+
@memoize_in(dcoll, (area_element, dd,
"area_elements_adim%s_gdim%s"
% (dcoll.ambient_dim, dim)))
def _area_elements():
return actx.np.sqrt(
- pseudoscalar(actx, dcoll, dim=dim, dd=dd).norm_squared()
+ pseudoscalar(actx, dcoll, dd=dd).norm_squared()
)
return _area_elements()
@@ -523,13 +519,11 @@ def rel_mv_normal(
import grudge.dof_desc as dof_desc
dd = dof_desc.as_dofdesc(dd)
- dim = dcoll.discr_from_dd(dd).dim
# NOTE: Don't be tempted to add a sign here. As it is, it produces
# exterior normals for positively oriented curves.
- pder = pseudoscalar(actx, dcoll, dim=dim, dd=dd) \
- / area_element(actx, dcoll, dim=dim, dd=dd)
+ pder = pseudoscalar(actx, dcoll, dd=dd) / area_element(actx, dcoll, dd=dd)
# Dorst Section 3.7.2
return pder << pder.I.inv()
@@ -611,7 +605,7 @@ def normal(actx: ArrayContext, dcoll: DiscretizationCollection, dd):
# {{{ Curvature computations
def second_fundamental_form(
- actx: ArrayContext, dcoll: DiscretizationCollection, dim=None, dd=None
+ actx: ArrayContext, dcoll: DiscretizationCollection, dd=None
) -> np.ndarray:
r"""Computes the second fundamental form:
@@ -625,15 +619,14 @@ def second_fundamental_form(
where :math:`n` is the surface normal, :math:`x(u, v)` defines a parameterized
surface, and :math:`u,v` are coordinates on the parameterized surface.
- :arg dim: an integer denoting the surface dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.ambient_dim` - 1.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
:returns: a rank-2 object array describing second fundamental form.
"""
- if dim is None:
- dim = dcoll.ambient_dim - 1
+ if dd is None:
+ dd = DD_VOLUME
+ dim = dcoll.discr_from_dd(dd).dim
normal = rel_mv_normal(actx, dcoll, dd=dd).as_vector(dtype=object)
if dim == 1:
@@ -660,7 +653,7 @@ def second_fundamental_form(
def shape_operator(actx: ArrayContext, dcoll: DiscretizationCollection,
- dim=None, dd=None) -> np.ndarray:
+ dd=None) -> np.ndarray:
r"""Computes the shape operator (also called the curvature tensor) containing
second order derivatives:
@@ -674,23 +667,18 @@ def shape_operator(actx: ArrayContext, dcoll: DiscretizationCollection,
where :math:`x(u, v)` defines a parameterized surface, and :math:`u,v` are
coordinates on the parameterized surface.
- :arg dim: an integer denoting the surface dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.ambient_dim` - 1.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
:returns: a rank-2 object array describing the shape operator.
"""
- if dim is None:
- dim = dcoll.ambient_dim - 1
-
- inv_form1 = inverse_first_fundamental_form(actx, dcoll, dim=dim, dd=dd)
- form2 = second_fundamental_form(actx, dcoll, dim=dim, dd=dd)
+ inv_form1 = inverse_first_fundamental_form(actx, dcoll, dd=dd)
+ form2 = second_fundamental_form(actx, dcoll, dd=dd)
return -form2.dot(inv_form1)
def summed_curvature(actx: ArrayContext, dcoll: DiscretizationCollection,
- dim=None, dd=None) -> DOFArray:
+ dd=None) -> DOFArray:
r"""Computes the sum of the principal curvatures:
.. math::
@@ -701,15 +689,15 @@ def summed_curvature(actx: ArrayContext, dcoll: DiscretizationCollection,
coordinates on the parameterized surface, and :math:`C(x)` is the shape
operator.
- :arg dim: an integer denoting the surface dimension. Defaults to the
- :attr:`grudge.DiscretizationCollection.ambient_dim` - 1.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc`, or a value convertible to one.
:returns: a :class:`~meshmode.dof_array.DOFArray` containing the summed
curvature at each nodal coordinate.
"""
- if dim is None:
- dim = dcoll.ambient_dim - 1
+ if dd is None:
+ dd = DD_VOLUME
+
+ dim = dcoll.ambient_dim - 1
if dcoll.ambient_dim == 1:
return 0.0
@@ -717,7 +705,7 @@ def summed_curvature(actx: ArrayContext, dcoll: DiscretizationCollection,
if dcoll.ambient_dim == dim:
return 0.0
- return np.trace(shape_operator(actx, dcoll, dim=dim, dd=dd))
+ return np.trace(shape_operator(actx, dcoll, dd=dd))
# }}}
diff --git a/test/test_grudge.py b/test/test_grudge.py
index 913511e1d6f7f4b40c0db3e811beccec4f1e0a7e..41a52edf22e30f4121350ed3575c825ebc5018ae 100644
--- a/test/test_grudge.py
+++ b/test/test_grudge.py
@@ -362,7 +362,6 @@ def test_face_normal_surface(actx_factory, mesh_name):
df = dof_desc.as_dofdesc(FACE_RESTR_INTERIOR)
ambient_dim = mesh.ambient_dim
- dim = mesh.dim
surf_normal = op.project(
dcoll, dv, df,
@@ -377,8 +376,7 @@ def test_face_normal_surface(actx_factory, mesh_name):
from grudge.geometry import pseudoscalar, area_element
# NOTE: there's only one face tangent in 3d
face_tangent = (
- pseudoscalar(actx, dcoll, dim=dim-1, dd=df)
- / area_element(actx, dcoll, dim=dim-1, dd=df)
+ pseudoscalar(actx, dcoll, dd=df) / area_element(actx, dcoll, dd=df)
).as_vector(dtype=object)
# }}}
@@ -591,7 +589,6 @@ def test_surface_divergence_theorem(actx_factory, mesh_name, visualize=False):
dq = dd.with_discr_tag(qtag)
df = dof_desc.as_dofdesc(FACE_RESTR_ALL)
ambient_dim = dcoll.ambient_dim
- dim = dcoll.dim
# variables
f_num = f(thaw(op.nodes(dcoll, dd=dd), actx))
@@ -599,7 +596,7 @@ def test_surface_divergence_theorem(actx_factory, mesh_name, visualize=False):
from grudge.geometry import normal, summed_curvature
- kappa = summed_curvature(actx, dcoll, dim=dim, dd=dq)
+ kappa = summed_curvature(actx, dcoll, dd=dq)
normal = normal(actx, dcoll, dd=dq)
face_normal = thaw(op.normal(dcoll, df), actx)
face_f = op.project(dcoll, dd, df, f_num)