def face_jacobian(self, where):
bdry_discr = self.get_discr(where)
((a, ), (b, )) = parametrization_derivative(self._setup_actx,
bdry_discr)
return freeze((a**2 + b**2)**0.5)
def normal(self, where):
bdry_discr = self.get_discr(where)
((a, ), (b, )) = parametrization_derivative(self._setup_actx,
bdry_discr)
nrm = 1 / (a**2 + b**2)**0.5
return freeze(flat_obj_array(b * nrm, -a * nrm))
def normal(self, dd):
surface_discr = self.discr_from_dd(dd)
actx = surface_discr._setup_actx
return freeze(
bind(self,
sym.normal(dd, surface_discr.ambient_dim, surface_discr.dim),
local_only=True)
(array_context=actx))
def inverse_parametrization_derivative(self):
[a, b], [c, d] = thaw(self._setup_actx,
self.parametrization_derivative())
result = np.zeros((2, 2), dtype=object)
det = a * d - b * c
result[0, 0] = d / det
result[0, 1] = -b / det
result[1, 0] = -c / det
result[1, 1] = a / det
return freeze(result)
def normal(dcoll, dd):
"""Get unit normal to specified surface discretization, *dd*.
:arg dd: a :class:`~grudge.dof_desc.DOFDesc` as the surface discretization.
:returns: an object array of :class:`~meshmode.dof_array.DOFArray`.
"""
surface_discr = dcoll.discr_from_dd(dd)
actx = surface_discr._setup_actx
return freeze(
bind(dcoll,
sym.normal(dd, surface_discr.ambient_dim, surface_discr.dim),
local_only=True)(array_context=actx))
def vol_jacobian(self):
[a, b], [c, d] = thaw(self._setup_actx,
self.parametrization_derivative())
return freeze(a * d - b * c)
def parametrization_derivative(self):
return freeze(
parametrization_derivative(self._setup_actx, self.volume_discr))