def test_nodal_face_mass_matrix(dim, order=3):
from modepy.tools import unit_vertices
all_verts = unit_vertices(dim).T
basis = mp.simplex_onb(dim, order)
np.set_printoptions(linewidth=200)
from modepy.matrices import nodal_face_mass_matrix
volume_nodes = mp.warp_and_blend_nodes(dim, order)
face_nodes = mp.warp_and_blend_nodes(dim - 1, order)
for iface in range(dim + 1):
verts = np.hstack([all_verts[:, :iface], all_verts[:, iface + 1:]])
fmm = nodal_face_mass_matrix(basis, volume_nodes, face_nodes, order,
verts)
fmm2 = nodal_face_mass_matrix(basis, volume_nodes, face_nodes,
order + 1, verts)
assert la.norm(fmm - fmm2, np.inf) < 1e-11
fmm[np.abs(fmm) < 1e-13] = 0
print(fmm)
nnz = np.sum(np.abs(fmm) > 0)
print(nnz)
print(
mp.mass_matrix(
mp.simplex_onb(dim - 1, order),
mp.warp_and_blend_nodes(dim - 1, order),
))
def mass_matrix(self):
assert self.is_orthogonal_basis()
import modepy as mp
return mp.mass_matrix(
self.basis(),
self.unit_nodes)
def mass_matrix(grp: InterpolatoryElementGroupBase) -> np.ndarray:
if not isinstance(grp, InterpolatoryElementGroupBase):
raise NoninterpolatoryElementGroupError(
f"cannot construct mass matrix on '{type(grp).__name__}'")
assert grp.is_orthonormal_basis()
return mp.mass_matrix(grp.basis_obj().functions, grp.unit_nodes)
def test_deprecated_nodal_face_mass_matrix(dims, order=3):
# FIXME DEPRECATED remove along with nodal_face_mass_matrix (>=2022)
vol_shape = mp.Simplex(dims)
vol_space = mp.space_for_shape(vol_shape, order)
vertices = mp.unit_vertices_for_shape(vol_shape)
volume_nodes = mp.edge_clustered_nodes_for_space(vol_space, vol_shape)
volume_basis = mp.basis_for_space(vol_space, vol_shape)
from modepy.matrices import nodal_face_mass_matrix
for face in mp.faces_for_shape(vol_shape):
face_space = mp.space_for_shape(face, order)
face_nodes = mp.edge_clustered_nodes_for_space(face_space, face)
face_vertices = vertices[:, face.volume_vertex_indices]
fmm = nodal_face_mass_matrix(
volume_basis.functions, volume_nodes,
face_nodes, order, face_vertices)
fmm2 = nodal_face_mass_matrix(
volume_basis.functions,
volume_nodes, face_nodes, order+1, face_vertices)
error = la.norm(fmm - fmm2, np.inf) / la.norm(fmm2, np.inf)
logger.info("fmm error: %.5e", error)
assert error < 5e-11, f"error {error:.5e} on face {face.face_index}"
fmm[np.abs(fmm) < 1e-13] = 0
nnz = np.sum(fmm > 0)
logger.info("fmm: nnz %d\n%s", nnz, fmm)
logger.info("mass matrix:\n%s", mp.mass_matrix(
mp.basis_for_space(face_space, face).functions,
mp.edge_clustered_nodes_for_space(face_space, face)))
def mass_matrix(self):
assert self.is_orthogonal_basis()
import modepy as mp
return mp.mass_matrix(
self.basis(),
self.unit_nodes)
def test_nodal_face_mass_matrix(dim, order=3):
from modepy.tools import unit_vertices
all_verts = unit_vertices(dim).T
basis = mp.simplex_onb(dim, order)
np.set_printoptions(linewidth=200)
from modepy.matrices import nodal_face_mass_matrix
volume_nodes = mp.warp_and_blend_nodes(dim, order)
face_nodes = mp.warp_and_blend_nodes(dim-1, order)
for iface in range(dim+1):
verts = np.hstack([all_verts[:, :iface], all_verts[:, iface+1:]])
fmm = nodal_face_mass_matrix(basis, volume_nodes, face_nodes, order,
verts)
fmm2 = nodal_face_mass_matrix(basis, volume_nodes, face_nodes, order+1,
verts)
assert la.norm(fmm-fmm2, np.inf) < 1e-11
fmm[np.abs(fmm) < 1e-13] = 0
print(fmm)
nnz = np.sum(np.abs(fmm) > 0)
print(nnz)
print(mp.mass_matrix(
mp.simplex_onb(dim-1, order),
mp.warp_and_blend_nodes(dim-1, order), ))
def test_nodal_mass_matrix_for_face(dims, shape_cls, order=3):
vol_shape = shape_cls(dims)
vol_space = mp.space_for_shape(vol_shape, order)
volume_nodes = mp.edge_clustered_nodes_for_space(vol_space, vol_shape)
volume_basis = mp.basis_for_space(vol_space, vol_shape)
from modepy.matrices import (nodal_mass_matrix_for_face,
nodal_quad_mass_matrix_for_face)
for face in mp.faces_for_shape(vol_shape):
face_space = mp.space_for_shape(face, order)
face_basis = mp.basis_for_space(face_space, face)
face_nodes = mp.edge_clustered_nodes_for_space(face_space, face)
face_quad = mp.quadrature_for_space(mp.space_for_shape(face, 2*order), face)
face_quad2 = mp.quadrature_for_space(
mp.space_for_shape(face, 2*order+2), face)
fmm = nodal_mass_matrix_for_face(
face, face_quad, face_basis.functions, volume_basis.functions,
volume_nodes, face_nodes)
fmm2 = nodal_quad_mass_matrix_for_face(
face, face_quad2, volume_basis.functions, volume_nodes)
for f_face in face_basis.functions:
fval_nodal = f_face(face_nodes)
fval_quad = f_face(face_quad2.nodes)
assert (
la.norm(fmm@fval_nodal - fmm2@fval_quad, np.inf)
/ la.norm(fval_quad)) < 3e-15
fmm[np.abs(fmm) < 1e-13] = 0
nnz = np.sum(fmm > 0)
logger.info("fmm: nnz %d\n%s", nnz, fmm)
logger.info("mass matrix:\n%s",
mp.mass_matrix(face_basis.functions, face_nodes))
def weights(self):
return np.dot(
mp.mass_matrix(self.basis(), self.unit_nodes),
np.ones(len(self.basis())))
def quadrature_rule(self):
basis_fcts = self._basis.functions
nodes = self._nodes
mass_matrix = mp.mass_matrix(basis_fcts, nodes)
weights = np.dot(mass_matrix, np.ones(len(basis_fcts)))
return mp.Quadrature(nodes, weights, exact_to=self.order)
def weights(self):
return np.dot(mp.mass_matrix(self.basis(), self.unit_nodes),
np.ones(len(self.basis())))