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# Copyright (C) 2023 Jorgen Dokken and Matthew Scroggs
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
from mpi4py import MPI
import numpy as np
import pytest
import basix.ufl
import dolfinx
import ufl
@pytest.mark.parametrize("degree", range(1, 4))
def test_default(degree):
msh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)
CG2_vect = dolfinx.fem.functionspace(msh, ("Lagrange", 1))
Qe = basix.ufl.quadrature_element(msh.topology.cell_name(), degree=degree)
Quad = dolfinx.fem.functionspace(msh, Qe)
u = dolfinx.fem.Function(Quad)
v = ufl.TrialFunction(CG2_vect)
dx_m = ufl.Measure(
"dx", domain=msh, metadata={"quadrature_degree": 1, "quadrature_scheme": "default"}
)
ds = ufl.Measure("ds", domain=msh)
residual = u * v * dx_m
vol = dolfinx.fem.form(residual)
residual = v * ds
surf = dolfinx.fem.form(residual)
residual = u * v * dx_m + v * ds
vol_surf = dolfinx.fem.form(residual)
vol_v = dolfinx.fem.assemble_vector(vol)
sur_v = dolfinx.fem.assemble_vector(surf)
vol_surf = dolfinx.fem.assemble_vector(vol_surf)
assert np.allclose(vol_v.array + sur_v.array, vol_surf.array)
def test_points_and_weights():
msh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)
CG2_vect = dolfinx.fem.functionspace(msh, ("Lagrange", 1))
Qe = basix.ufl.quadrature_element(
msh.topology.cell_name(),
value_shape=(),
points=np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1 / 3, 1 / 3]]),
weights=np.array([0.2, 0.2, 0.2, 0.4]),
)
Quad = dolfinx.fem.functionspace(msh, Qe)
u = dolfinx.fem.Function(Quad)
v = ufl.TrialFunction(CG2_vect)
dx_m = ufl.Measure(
"dx", domain=msh, metadata={"quadrature_degree": 1, "quadrature_scheme": "default"}
)
ds = ufl.Measure("ds", domain=msh)
residual = u * v * dx_m
vol = dolfinx.fem.form(residual)
residual = v * ds
surf = dolfinx.fem.form(residual)
residual = u * v * dx_m + v * ds
vol_surf = dolfinx.fem.form(residual)
vol_v = dolfinx.fem.assemble_vector(vol)
sur_v = dolfinx.fem.assemble_vector(surf)
vol_surf = dolfinx.fem.assemble_vector(vol_surf)
assert np.allclose(vol_v.array + sur_v.array, vol_surf.array)
@pytest.mark.parametrize("degree", range(1, 5))
def test_interpolation(degree):
msh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)
e = basix.ufl.quadrature_element(msh.topology.cell_name(), degree=degree)
space = dolfinx.fem.functionspace(msh, e)
p4 = dolfinx.fem.functionspace(msh, ("Lagrange", 4))
f_p4 = dolfinx.fem.Function(p4)
f_p4.interpolate(lambda x: x[0] ** 4)
f = dolfinx.fem.Function(space)
f.interpolate(lambda x: x[0] ** 4)
diff = dolfinx.fem.form(ufl.inner(f - f_p4, f - f_p4) * ufl.dx)
error = dolfinx.fem.assemble_scalar(diff)
assert np.isclose(error, 0)
@pytest.mark.parametrize("degree", range(1, 5))
def test_interpolation_blocked(degree):
msh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)
e = basix.ufl.quadrature_element(msh.topology.cell_name(), value_shape=(2,), degree=degree)
space = dolfinx.fem.functionspace(msh, e)
p4 = dolfinx.fem.functionspace(msh, ("Lagrange", 4, (2,)))
f_p4 = dolfinx.fem.Function(p4)
f_p4.interpolate(lambda x: ([x[1] ** 4, x[0] ** 3]))
f = dolfinx.fem.Function(space)
f.interpolate(lambda x: ([x[1] ** 4, x[0] ** 3]))
diff = dolfinx.fem.form(ufl.inner(f - f_p4, f - f_p4) * ufl.dx)
error = dolfinx.fem.assemble_scalar(diff)
assert np.isclose(error, 0)
def extract_diagonal(mat):
num_rows = mat._cpp_object.index_map(0).size_local
num_cols = mat._cpp_object.index_map(1).size_local
assert num_rows == num_cols, "Matrix must be square"
bs = mat.block_size[0]
diag = np.empty(num_rows * bs, dtype=mat.data.dtype)
for row, (start, end) in enumerate(zip(mat.indptr[:-1], mat.indptr[1:])):
for i in range(start, end):
if mat.indices[i] == row:
for block in range(bs):
diag[bs * row + block] = mat.data[bs**2 * i + (bs + 1) * block]
return diag
@pytest.mark.parametrize("degree", range(1, 4))
@pytest.mark.parametrize("shape", [(), (1,), (2,), (3,), (4,), (2, 2), (3, 3)])
def test_vector_element(shape, degree):
"""
Compare assembly into a vector with quadrature elements with the diagonal of
an assembled mass matrix with the same quadrature element.
"""
msh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)
dx_m = ufl.Measure(
"dx",
domain=msh,
metadata={"quadrature_degree": degree, "quadrature_scheme": "default"},
)
Qe = basix.ufl.quadrature_element(
msh.topology.cell_name(), value_shape=shape, scheme="default", degree=degree
)
Quad = dolfinx.fem.functionspace(msh, Qe)
q_ = ufl.TestFunction(Quad)
dq = ufl.TrialFunction(Quad)
one = dolfinx.fem.Function(Quad)
one.x.array[:] = 1.0
mass_L_form = dolfinx.fem.form(ufl.inner(one, q_) * dx_m)
mass_v = dolfinx.fem.assemble_vector(mass_L_form)
mass_v.scatter_reverse(dolfinx.la.InsertMode.add)
mass_v.scatter_forward()
mass_a_form = dolfinx.fem.form(ufl.inner(dq, q_) * dx_m)
mass_A = dolfinx.fem.assemble_matrix(mass_a_form)
mass_A.scatter_reverse()
num_owned_dofs = Quad.dofmap.index_map.size_local * Quad.dofmap.index_map_bs
assert np.allclose(extract_diagonal(mass_A), mass_v.array[:num_owned_dofs])
@pytest.mark.parametrize("degree", range(1, 4))
def test_quadrature_assembly(degree):
"""
Test quadrature element against assembly with spatial coordinate and a fixed quadrature rule
"""
msh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 5, 7)
dx_m = ufl.Measure(
"dx",
domain=msh,
metadata={"quadrature_degree": degree, "quadrature_scheme": "default"},
)
Qe = basix.ufl.quadrature_element(
msh.topology.cell_name(), value_shape=(), scheme="default", degree=degree
)
Quad = dolfinx.fem.functionspace(msh, Qe)
V = dolfinx.fem.functionspace(msh, ("Lagrange", 1))
v = ufl.TestFunction(V)
def f(x):
return 1 + x[0] + x[1] ** degree
q = dolfinx.fem.Function(Quad)
q.interpolate(f)
L = ufl.inner(q, v) * dx_m
b = dolfinx.fem.assemble_vector(dolfinx.fem.form(L))
b.scatter_reverse(dolfinx.la.InsertMode.add)
b.scatter_forward()
x = ufl.SpatialCoordinate(msh)
L_ref = ufl.inner(f(x), v) * dx_m
b_ref = dolfinx.fem.assemble_vector(dolfinx.fem.form(L_ref))
b_ref.scatter_reverse(dolfinx.la.InsertMode.add)
b_ref.scatter_forward()
np.testing.assert_allclose(b.array, b_ref.array)
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