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# Copyright (C) 2021 Matthew W. Scroggs and Jack Hale
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
"""Test that matrices are symmetric."""
from mpi4py import MPI
import numpy as np
import pytest
import basix
import dolfinx
import ufl
from basix.ufl import element, mixed_element
from dolfinx.fem import form, functionspace
from dolfinx.mesh import CellType, create_unit_cube, create_unit_square
from ufl import grad, inner
def check_symmetry(A, tol):
Ad = A.to_dense()
assert np.allclose(Ad, Ad.T, atol=tol)
def run_symmetry_test(cell_type, e, form_f):
dtype = np.float64
if cell_type == CellType.triangle or cell_type == CellType.quadrilateral:
mesh = create_unit_square(MPI.COMM_WORLD, 2, 2, cell_type, dtype=dtype)
else:
mesh = create_unit_cube(MPI.COMM_WORLD, 2, 2, 2, cell_type, dtype=dtype)
space = functionspace(mesh, e)
u = ufl.TrialFunction(space)
v = ufl.TestFunction(space)
f = form(form_f(u, v), dtype=dtype)
A = dolfinx.fem.assemble_matrix(f)
A.scatter_reverse()
tol = np.sqrt(np.finfo(dtype).eps)
check_symmetry(A, tol)
parametrize_elements = pytest.mark.parametrize(
"cell_type, family",
[
(CellType.triangle, "Lagrange"),
(CellType.triangle, "N1curl"),
(CellType.triangle, "RT"),
(CellType.triangle, "Regge"),
(CellType.quadrilateral, "Lagrange"),
(CellType.quadrilateral, "RTCE"),
(CellType.quadrilateral, "RTCF"),
(CellType.tetrahedron, "Lagrange"),
(CellType.tetrahedron, "N1curl"),
(CellType.tetrahedron, "RT"),
(CellType.tetrahedron, "Regge"),
(CellType.hexahedron, "Lagrange"),
(CellType.hexahedron, "NCE"),
(CellType.hexahedron, "NCF"),
],
)
parametrize_lagrange_elements = pytest.mark.parametrize(
"cell_type, family",
[
(CellType.triangle, "Lagrange"),
(CellType.quadrilateral, "Lagrange"),
(CellType.tetrahedron, "Lagrange"),
(CellType.hexahedron, "Lagrange"),
],
)
@pytest.mark.skip_in_parallel
@parametrize_elements
@pytest.mark.parametrize("order", range(1, 2))
def test_mass_matrix_dx(cell_type, family, order):
run_symmetry_test(cell_type, (family, order), lambda u, v: inner(u, v) * ufl.dx)
@pytest.mark.skip_in_parallel
@parametrize_lagrange_elements
@pytest.mark.parametrize("order", range(1, 2))
def test_stiffness_matrix_dx(cell_type, family, order):
run_symmetry_test(cell_type, (family, order), lambda u, v: inner(grad(u), grad(v)) * ufl.dx)
@pytest.mark.skip_in_parallel
@parametrize_elements
@pytest.mark.parametrize("order", range(1, 2))
def test_mass_matrix_ds(cell_type, family, order):
run_symmetry_test(cell_type, (family, order), lambda u, v: inner(u, v) * ufl.ds)
@pytest.mark.skip_in_parallel
@parametrize_lagrange_elements
@pytest.mark.parametrize("order", range(1, 2))
def test_stiffness_matrix_ds(cell_type, family, order):
run_symmetry_test(cell_type, (family, order), lambda u, v: inner(grad(u), grad(v)) * ufl.ds)
@pytest.mark.skip_in_parallel
@parametrize_elements
@pytest.mark.parametrize("order", range(1, 2))
@pytest.mark.parametrize("sign", ["+", "-"])
def test_mass_matrix_dS(cell_type, family, order, sign):
run_symmetry_test(cell_type, (family, order), lambda u, v: inner(u, v)(sign) * ufl.dS)
@pytest.mark.skip_in_parallel
@parametrize_lagrange_elements
@pytest.mark.parametrize("order", range(1, 2))
@pytest.mark.parametrize("sign", ["+", "-"])
def test_stiffness_matrix_dS(cell_type, family, order, sign):
run_symmetry_test(
cell_type, (family, order), lambda u, v: inner(grad(u), grad(v))(sign) * ufl.dS
)
@pytest.mark.skip_in_parallel
@pytest.mark.parametrize(
"cell_type",
[CellType.triangle, CellType.quadrilateral, CellType.tetrahedron, CellType.hexahedron],
)
@pytest.mark.parametrize("sign", ["+", "-"])
@pytest.mark.parametrize("order", range(1, 2))
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_mixed_element_form(cell_type, sign, order, dtype):
if cell_type == CellType.triangle or cell_type == CellType.quadrilateral:
mesh = create_unit_square(MPI.COMM_WORLD, 2, 2, cell_type, dtype=dtype)
else:
mesh = create_unit_cube(MPI.COMM_WORLD, 2, 2, 2, cell_type, dtype=dtype)
U_el = mixed_element(
[
element(basix.ElementFamily.P, cell_type.name, order, dtype=dtype),
element(basix.ElementFamily.N1E, cell_type.name, order, dtype=dtype),
]
)
U = functionspace(mesh, U_el)
u, p = ufl.TrialFunctions(U)
v, q = ufl.TestFunctions(U)
f = form(inner(u, v) * ufl.dx + inner(p, q)(sign) * ufl.dS, dtype=dtype)
A = dolfinx.fem.assemble_matrix(f)
A.scatter_reverse()
tol = np.sqrt(np.finfo(dtype).eps)
check_symmetry(A, tol)
@pytest.mark.skip_in_parallel
@pytest.mark.parametrize("cell_type", [CellType.triangle, CellType.quadrilateral])
@pytest.mark.parametrize("sign", ["+", "-"])
@pytest.mark.parametrize("order", range(1, 2))
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_mixed_element_vector_element_form(cell_type, sign, order, dtype):
if cell_type == CellType.triangle or cell_type == CellType.quadrilateral:
mesh = create_unit_square(MPI.COMM_WORLD, 2, 2, cell_type, dtype=dtype)
else:
mesh = create_unit_cube(MPI.COMM_WORLD, 2, 2, 2, cell_type, dtype=dtype)
U_el = mixed_element(
[
element(
basix.ElementFamily.P,
cell_type.name,
order,
shape=(mesh.geometry.dim,),
dtype=dtype,
),
element(basix.ElementFamily.N1E, cell_type.name, order, dtype=dtype),
]
)
U = functionspace(mesh, U_el)
u, p = ufl.TrialFunctions(U)
v, q = ufl.TestFunctions(U)
f = form(inner(u, v) * ufl.dx + inner(p, q)(sign) * ufl.dS, dtype=dtype)
A = dolfinx.fem.assemble_matrix(f)
A.scatter_reverse()
tol = np.sqrt(np.finfo(dtype).eps)
check_symmetry(A, tol)
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