def get_ref_stiffness_transpose_mat(out_grp, in_grp):
if in_grp == out_grp:
from meshmode.discretization.poly_element import \
mass_matrix, diff_matrices
mmat = mass_matrix(out_grp)
return actx.freeze(
actx.from_numpy(
np.asarray(
[dmat.T @ mmat.T for dmat in diff_matrices(out_grp)])))
from modepy import vandermonde
basis = out_grp.basis_obj()
vand = vandermonde(basis.functions, out_grp.unit_nodes)
grad_vand = vandermonde(basis.gradients, in_grp.unit_nodes)
vand_inv_t = np.linalg.inv(vand).T
if not isinstance(grad_vand, tuple):
# NOTE: special case for 1d
grad_vand = (grad_vand, )
weights = in_grp.quadrature_rule().weights
return actx.freeze(
actx.from_numpy(
np.einsum("c,bz,acz->abc", weights, vand_inv_t,
grad_vand).copy() # contigify the array
))
def matrix(out_element_group, in_element_group):
if out_element_group == in_element_group:
from meshmode.discretization.poly_element import mass_matrix
return mass_matrix(in_element_group)
from modepy import vandermonde
basis = out_element_group.basis_obj()
vand = vandermonde(basis.functions, out_element_group.unit_nodes)
o_vand = vandermonde(basis.functions, in_element_group.unit_nodes)
vand_inv_t = np.linalg.inv(vand).T
weights = in_element_group.quadrature_rule().weights
return np.einsum("j,ik,jk->ij", weights, vand_inv_t, o_vand)
def get_ref_mass_mat(out_grp, in_grp):
if out_grp == in_grp:
from meshmode.discretization.poly_element import mass_matrix
return actx.freeze(
actx.from_numpy(np.asarray(mass_matrix(out_grp), order="C")))
from modepy import vandermonde
basis = out_grp.basis_obj()
vand = vandermonde(basis.functions, out_grp.unit_nodes)
o_vand = vandermonde(basis.functions, in_grp.unit_nodes)
vand_inv_t = np.linalg.inv(vand).T
weights = in_grp.quadrature_rule().weights
return actx.freeze(
actx.from_numpy(
np.asarray(np.einsum("j,ik,jk->ij", weights, vand_inv_t,
o_vand),
order="C")))
def matrices(out_elem_grp, in_elem_grp):
if in_elem_grp == out_elem_grp:
assert in_elem_grp.is_orthonormal_basis()
from meshmode.discretization.poly_element import (mass_matrix,
diff_matrices)
mmat = mass_matrix(in_elem_grp)
return [dmat.T.dot(mmat.T) for dmat in diff_matrices(in_elem_grp)]
from modepy import vandermonde
basis = out_elem_grp.basis_obj()
vand = vandermonde(basis.functions, out_elem_grp.unit_nodes)
grad_vand = vandermonde(basis.gradients, in_elem_grp.unit_nodes)
vand_inv_t = np.linalg.inv(vand).T
if not isinstance(grad_vand, tuple):
# NOTE: special case for 1d
grad_vand = (grad_vand, )
weights = in_elem_grp.quadrature_rule().weights
return np.einsum("c,bz,acz->abc", weights, vand_inv_t, grad_vand)