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# Copyright (C) 2015-2022 Garth N. Wells, Jørgen S. Dokken
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
"""Unit tests for the DiscreteOperator class"""
from mpi4py import MPI
import numpy as np
import pytest
import ufl
from basix.ufl import element
from dolfinx import default_real_type
from dolfinx.fem import Expression, Function, assemble_scalar, form, functionspace
from dolfinx.mesh import CellType, GhostMode, create_mesh, create_unit_cube, create_unit_square
@pytest.mark.petsc4py
class TestPETScDiscreteOperators:
@pytest.mark.skip_in_parallel
@pytest.mark.parametrize(
"mesh",
[
create_unit_square(MPI.COMM_WORLD, 11, 6, ghost_mode=GhostMode.none),
create_unit_square(MPI.COMM_WORLD, 11, 6, ghost_mode=GhostMode.shared_facet),
create_unit_cube(MPI.COMM_WORLD, 4, 3, 7, ghost_mode=GhostMode.none),
create_unit_cube(MPI.COMM_WORLD, 4, 3, 7, ghost_mode=GhostMode.shared_facet),
],
)
def test_gradient_petsc(self, mesh):
"""Test discrete gradient computation for lowest order elements."""
from petsc4py import PETSc
from dolfinx.fem.petsc import discrete_gradient
V = functionspace(mesh, ("Lagrange", 1))
W = functionspace(mesh, ("Nedelec 1st kind H(curl)", 1))
G = discrete_gradient(V, W)
assert G.getRefCount() == 1
num_edges = mesh.topology.index_map(1).size_global
m, n = G.getSize()
assert m == num_edges
assert n == mesh.topology.index_map(0).size_global
G.assemble()
assert np.isclose(G.norm(PETSc.NormType.FROBENIUS), np.sqrt(2.0 * num_edges))
G.destroy()
@pytest.mark.parametrize("p", range(1, 4))
@pytest.mark.parametrize("q", range(1, 4))
@pytest.mark.parametrize(
"cell_type",
[CellType.quadrilateral, CellType.triangle, CellType.tetrahedron, CellType.hexahedron],
)
def test_gradient_interpolation_petsc(self, cell_type, p, q):
"""Test discrete gradient computation with verification using Expression."""
from dolfinx.fem.petsc import discrete_gradient
comm = MPI.COMM_WORLD
if cell_type == CellType.triangle:
mesh = create_unit_square(
comm, 11, 6, ghost_mode=GhostMode.none, cell_type=cell_type, dtype=default_real_type
)
family0 = "Lagrange"
family1 = "Nedelec 1st kind H(curl)"
elif cell_type == CellType.quadrilateral:
mesh = create_unit_square(
comm, 11, 6, ghost_mode=GhostMode.none, cell_type=cell_type, dtype=default_real_type
)
family0 = "Q"
family1 = "RTCE"
elif cell_type == CellType.hexahedron:
mesh = create_unit_cube(
comm,
3,
3,
2,
ghost_mode=GhostMode.none,
cell_type=cell_type,
dtype=default_real_type,
)
family0 = "Q"
family1 = "NCE"
elif cell_type == CellType.tetrahedron:
mesh = create_unit_cube(
comm,
3,
2,
2,
ghost_mode=GhostMode.none,
cell_type=cell_type,
dtype=default_real_type,
)
family0 = "Lagrange"
family1 = "Nedelec 1st kind H(curl)"
V = functionspace(mesh, (family0, p))
W = functionspace(mesh, (family1, q))
G = discrete_gradient(V, W)
G.assemble()
u = Function(V)
u.interpolate(lambda x: 2 * x[0] ** p + 3 * x[1] ** p)
grad_u = Expression(ufl.grad(u), W.element.interpolation_points())
w_expr = Function(W)
w_expr.interpolate(grad_u)
# Compute global matrix vector product
w = Function(W)
G.mult(u.x.petsc_vec, w.x.petsc_vec)
w.x.scatter_forward()
atol = 100 * np.finfo(default_real_type).resolution
assert np.allclose(w_expr.x.array, w.x.array, atol=atol)
G.destroy()
@pytest.mark.parametrize("p", range(1, 4))
@pytest.mark.parametrize("q", range(1, 4))
@pytest.mark.parametrize("from_lagrange", [True, False])
@pytest.mark.parametrize(
"cell_type",
[CellType.quadrilateral, CellType.triangle, CellType.tetrahedron, CellType.hexahedron],
)
def test_interpolation_matrix_petsc(self, cell_type, p, q, from_lagrange):
"""Test that discrete interpolation matrix yields the same result as interpolation."""
from dolfinx.fem.petsc import interpolation_matrix
comm = MPI.COMM_WORLD
if cell_type == CellType.triangle:
mesh = create_unit_square(comm, 7, 5, ghost_mode=GhostMode.none, cell_type=cell_type)
lagrange = "Lagrange" if from_lagrange else "DG"
nedelec = "Nedelec 1st kind H(curl)"
elif cell_type == CellType.quadrilateral:
mesh = create_unit_square(comm, 11, 6, ghost_mode=GhostMode.none, cell_type=cell_type)
lagrange = "Q" if from_lagrange else "DQ"
nedelec = "RTCE"
elif cell_type == CellType.hexahedron:
mesh = create_unit_cube(comm, 3, 2, 1, ghost_mode=GhostMode.none, cell_type=cell_type)
lagrange = "Q" if from_lagrange else "DQ"
nedelec = "NCE"
elif cell_type == CellType.tetrahedron:
mesh = create_unit_cube(comm, 3, 2, 2, ghost_mode=GhostMode.none, cell_type=cell_type)
lagrange = "Lagrange" if from_lagrange else "DG"
nedelec = "Nedelec 1st kind H(curl)"
v_el = element(
lagrange, mesh.basix_cell(), p, shape=(mesh.geometry.dim,), dtype=default_real_type
)
s_el = element(nedelec, mesh.basix_cell(), q, dtype=default_real_type)
if from_lagrange:
el0 = v_el
el1 = s_el
else:
el0 = s_el
el1 = v_el
V = functionspace(mesh, el0)
W = functionspace(mesh, el1)
G = interpolation_matrix(V, W)
G.assemble()
u = Function(V)
def f(x):
if mesh.geometry.dim == 2:
return (x[1] ** p, x[0] ** p)
else:
return (x[0] ** p, x[2] ** p, x[1] ** p)
u.interpolate(f)
w_vec = Function(W)
w_vec.interpolate(u)
# Compute global matrix vector product
w = Function(W)
G.mult(u.x.petsc_vec, w.x.petsc_vec)
w.x.scatter_forward()
atol = 100 * np.finfo(default_real_type).resolution
assert np.allclose(w_vec.x.array, w.x.array, atol=atol)
G.destroy()
@pytest.mark.skip_in_parallel
def test_nonaffine_discrete_operator_petsc(self):
"""Check that discrete operator is consistent with normal
interpolation between non-matching maps on non-affine geometries"""
from dolfinx.fem.petsc import interpolation_matrix
points = np.array(
[
[0, 0, 0],
[1, 0, 0],
[0, 2, 0],
[1, 2, 0],
[0, 0, 3],
[1, 0, 3],
[0, 2, 3],
[1, 2, 3],
[0.5, 0, 0],
[0, 1, 0],
[0, 0, 1.5],
[1, 1, 0],
[1, 0, 1.5],
[0.5, 2, 0],
[0, 2, 1.5],
[1, 2, 1.5],
[0.5, 0, 3],
[0, 1, 3],
[1, 1, 3],
[0.5, 2, 3],
[0.5, 1, 0],
[0.5, -0.1, 1.5],
[0, 1, 1.5],
[1, 1, 1.5],
[0.5, 2, 1.5],
[0.5, 1, 3],
[0.5, 1, 1.5],
],
dtype=default_real_type,
)
cells = np.array([range(len(points))], dtype=np.int32)
cell_type = CellType.hexahedron
domain = ufl.Mesh(
element("Lagrange", cell_type.name, 2, shape=(3,), dtype=default_real_type)
)
mesh = create_mesh(MPI.COMM_WORLD, cells, points, domain)
gdim = mesh.geometry.dim
W = functionspace(mesh, ("DG", 1, (gdim,)))
V = functionspace(mesh, ("NCE", 4))
w, v = Function(W), Function(V)
w.interpolate(lambda x: x)
v.interpolate(w)
G = interpolation_matrix(W, V)
G.assemble()
# Compute global matrix vector product
v_vec = Function(V)
G.mult(w.x.petsc_vec, v_vec.x.petsc_vec)
v_vec.x.scatter_forward()
atol = 10 * np.finfo(default_real_type).resolution
assert np.allclose(v_vec.x.array, v.x.array, atol=atol)
s = assemble_scalar(form(ufl.inner(w - v, w - v) * ufl.dx))
assert np.isclose(s, 0, atol=atol)
G.destroy()
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