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|
# Copyright (C) 2024 Matthew W. Scroggs Garth N. Wells
#
# 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
import basix.ufl
import ufl
from dolfinx import default_real_type, la
from dolfinx.fem import (
Function,
apply_lifting,
assemble_matrix,
assemble_scalar,
assemble_vector,
dirichletbc,
form,
functionspace,
locate_dofs_topological,
)
from dolfinx.mesh import CellType, create_unit_cube, create_unit_square, exterior_facet_indices
from ufl import SpatialCoordinate, TestFunction, TrialFunction, div, dx, grad, inner
def run_scalar_test(V, degree, dtype, cg_solver, rtol=None):
mesh = V.mesh
u, v = TrialFunction(V), TestFunction(V)
a = inner(grad(u), grad(v)) * dx
# Get quadrature degree for bilinear form integrand (ignores effect of non-affine map)
a = inner(grad(u), grad(v)) * dx(metadata={"quadrature_degree": -1})
a.integrals()[0].metadata()["quadrature_degree"] = (
ufl.algorithms.estimate_total_polynomial_degree(a)
)
a = form(a, dtype=dtype)
# Source term
x = SpatialCoordinate(mesh)
u_exact = x[1] ** degree
f = -div(grad(u_exact))
# Set quadrature degree for linear form integrand (ignores effect of non-affine map)
L = inner(f, v) * dx(metadata={"quadrature_degree": -1})
L.integrals()[0].metadata()["quadrature_degree"] = (
ufl.algorithms.estimate_total_polynomial_degree(L)
)
L = form(L, dtype=dtype)
u_bc = Function(V, dtype=dtype)
u_bc.interpolate(lambda x: x[1] ** degree)
# Create Dirichlet boundary condition
facetdim = mesh.topology.dim - 1
mesh.topology.create_connectivity(facetdim, mesh.topology.dim)
bndry_facets = exterior_facet_indices(mesh.topology)
bdofs = locate_dofs_topological(V, facetdim, bndry_facets)
bc = dirichletbc(u_bc, bdofs)
b = assemble_vector(L)
apply_lifting(b.array, [a], bcs=[[bc]])
b.scatter_reverse(la.InsertMode.add)
bc.set(b.array)
a = form(a, dtype=dtype)
A = assemble_matrix(a, bcs=[bc])
A.scatter_reverse()
uh = Function(V, dtype=dtype)
cg_solver(mesh.comm, A, b, uh.x, rtol=rtol)
uh.x.scatter_forward()
M = (u_exact - uh) ** 2 * dx
M = form(M, dtype=dtype)
error = mesh.comm.allreduce(assemble_scalar(M), op=MPI.SUM)
eps = np.sqrt(np.finfo(dtype).eps)
assert np.isclose(error, 0, atol=eps)
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
@pytest.mark.parametrize("degree", range(1, 6))
def test_basix_element_wrapper(degree, dtype, cg_solver):
ufl_element = basix.ufl.element(
basix.ElementFamily.P,
basix.CellType.triangle,
degree,
basix.LagrangeVariant.gll_isaac,
dtype=dtype,
)
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, dtype=dtype)
V = functionspace(mesh, ufl_element)
run_scalar_test(V, degree, dtype, cg_solver)
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_custom_element_triangle_degree1(dtype, cg_solver):
wcoeffs = np.eye(3)
z = np.zeros((0, 2))
x = [
[np.array([[0.0, 0.0]]), np.array([[1.0, 0.0]]), np.array([[0.0, 1.0]])],
[z, z, z],
[z],
[],
]
z = np.zeros((0, 1, 0, 1))
M = [[np.array([[[[1.0]]]]), np.array([[[[1.0]]]]), np.array([[[[1.0]]]])], [z, z, z], [z], []]
ufl_element = basix.ufl.custom_element(
basix.CellType.triangle,
[],
wcoeffs,
x,
M,
0,
basix.MapType.identity,
basix.SobolevSpace.H1,
False,
1,
1,
dtype=dtype,
)
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, dtype=dtype)
V = functionspace(mesh, ufl_element)
run_scalar_test(V, 1, dtype, cg_solver)
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_custom_element_triangle_degree4(dtype, cg_solver):
wcoeffs = np.eye(15)
x = [
[np.array([[0.0, 0.0]]), np.array([[1.0, 0.0]]), np.array([[0.0, 1.0]])],
[
np.array([[0.75, 0.25], [0.5, 0.5], [0.25, 0.75]]),
np.array([[0.0, 0.25], [0.0, 0.5], [0.0, 0.75]]),
np.array([[0.25, 0.0], [0.5, 0.0], [0.75, 0.0]]),
],
[np.array([[0.25, 0.25], [0.5, 0.25], [0.25, 0.5]])],
[],
]
id = np.array([[[[1.0], [0.0], [0.0]]], [[[0.0], [1.0], [0.0]]], [[[0.0], [0.0], [1.0]]]])
M = [
[np.array([[[[1.0]]]]), np.array([[[[1.0]]]]), np.array([[[[1.0]]]])],
[id, id, id],
[id],
[],
]
ufl_element = basix.ufl.custom_element(
basix.CellType.triangle,
[],
wcoeffs,
x,
M,
0,
basix.MapType.identity,
basix.SobolevSpace.H1,
False,
4,
4,
dtype=dtype,
)
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, dtype=dtype)
V = functionspace(mesh, ufl_element)
run_scalar_test(V, 4, dtype, cg_solver)
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_custom_element_triangle_degree4_integral(dtype, cg_solver):
pts, wts = basix.make_quadrature(basix.CellType.interval, 10)
tab = basix.create_element(
basix.ElementFamily.P, basix.CellType.interval, 2, dtype=default_real_type
).tabulate(0, pts)[0, :, :, 0]
wcoeffs = np.eye(15)
x = [
[np.array([[0.0, 0.0]]), np.array([[1.0, 0.0]]), np.array([[0.0, 1.0]])],
[
np.array([[1.0 - p[0], p[0]] for p in pts]),
np.array([[0.0, p[0]] for p in pts]),
np.array([[p[0], 0.0] for p in pts]),
],
[np.array([[0.25, 0.25], [0.5, 0.25], [0.25, 0.5]])],
[],
]
assert pts.shape[0] != 3
quadrature_mat = np.zeros([3, 1, pts.shape[0], 1])
for dof in range(3):
for p in range(pts.shape[0]):
quadrature_mat[dof, 0, p, 0] = wts[p] * tab[p, dof]
M = [
[np.array([[[[1.0]]]]), np.array([[[[1.0]]]]), np.array([[[[1.0]]]])],
[quadrature_mat, quadrature_mat, quadrature_mat],
[np.array([[[[1.0], [0.0], [0.0]]], [[[0.0], [1.0], [0.0]]], [[[0.0], [0.0], [1.0]]]])],
[],
]
ufl_element = basix.ufl.custom_element(
basix.CellType.triangle,
[],
wcoeffs,
x,
M,
0,
basix.MapType.identity,
basix.SobolevSpace.H1,
False,
4,
4,
dtype=dtype,
)
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, dtype=dtype)
V = functionspace(mesh, ufl_element)
run_scalar_test(V, 4, dtype, cg_solver, rtol=1e-5)
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
def test_custom_element_quadrilateral_degree1(dtype, cg_solver):
wcoeffs = np.eye(4)
z = np.zeros((0, 2))
x = [
[
np.array([[0.0, 0.0]]),
np.array([[1.0, 0.0]]),
np.array([[0.0, 1.0]]),
np.array([[1.0, 1.0]]),
],
[z, z, z, z],
[z],
[],
]
z = np.zeros((0, 1, 0, 1))
M = [
[
np.array([[[[1.0]]]]),
np.array([[[[1.0]]]]),
np.array([[[[1.0]]]]),
np.array([[[[1.0]]]]),
],
[z, z, z, z],
[z],
[],
]
ufl_element = basix.ufl.custom_element(
basix.CellType.quadrilateral,
[],
wcoeffs,
x,
M,
0,
basix.MapType.identity,
basix.SobolevSpace.H1,
False,
1,
1,
dtype=dtype,
)
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, CellType.quadrilateral, dtype=dtype)
V = functionspace(mesh, ufl_element)
run_scalar_test(V, 1, dtype, cg_solver)
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
@pytest.mark.parametrize(
"cell_type",
[CellType.triangle, CellType.quadrilateral, CellType.tetrahedron, CellType.hexahedron],
)
@pytest.mark.parametrize(
"element_family",
[
basix.ElementFamily.N1E,
basix.ElementFamily.N2E,
basix.ElementFamily.RT,
basix.ElementFamily.BDM,
],
)
def test_vector_copy_degree1(cell_type, element_family, dtype):
if cell_type in [CellType.triangle, CellType.quadrilateral]:
tdim = 2
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, cell_type, dtype=dtype)
else:
tdim = 3
mesh = create_unit_cube(MPI.COMM_WORLD, 5, 5, 5, cell_type, dtype=dtype)
def func(x):
return x[:tdim]
e1 = basix.ufl.element(element_family, getattr(basix.CellType, cell_type.name), 1, dtype=dtype)
e2 = basix.ufl.custom_element(
e1._element.cell_type,
e1._element.value_shape,
e1._element.wcoeffs,
e1._element.x,
e1._element.M,
0,
e1._element.map_type,
e1._element.sobolev_space,
e1._element.discontinuous,
e1._element.embedded_subdegree,
e1._element.embedded_superdegree,
dtype=dtype,
)
space1 = functionspace(mesh, e1)
space2 = functionspace(mesh, e2)
f1 = Function(space1, dtype=dtype)
f2 = Function(space2, dtype=dtype)
f1.interpolate(func)
f2.interpolate(func)
diff = f1 - f2
error = assemble_scalar(form(ufl.inner(diff, diff) * ufl.dx, dtype=dtype))
assert np.isclose(error, 0)
@pytest.mark.parametrize("dtype", [np.float32, np.float64])
@pytest.mark.parametrize(
"cell_type",
[CellType.triangle, CellType.quadrilateral, CellType.tetrahedron, CellType.hexahedron],
)
@pytest.mark.parametrize("element_family", [basix.ElementFamily.P, basix.ElementFamily.serendipity])
def test_scalar_copy_degree1(cell_type, element_family, dtype):
if element_family == basix.ElementFamily.serendipity and cell_type in [
CellType.triangle,
CellType.tetrahedron,
]:
pytest.xfail("Serendipity elements cannot be created on simplices")
if cell_type in [CellType.triangle, CellType.quadrilateral]:
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, cell_type, dtype=dtype)
else:
mesh = create_unit_cube(MPI.COMM_WORLD, 5, 5, 5, cell_type, dtype=dtype)
def func(x):
return x[0]
e1 = basix.ufl.element(element_family, getattr(basix.CellType, cell_type.name), 1, dtype=dtype)
e2 = basix.ufl.custom_element(
e1._element.cell_type,
e1._element.value_shape,
e1._element.wcoeffs,
e1._element.x,
e1._element.M,
0,
e1._element.map_type,
e1._element.sobolev_space,
e1._element.discontinuous,
e1._element.embedded_subdegree,
e1._element.embedded_superdegree,
dtype=dtype,
)
space1 = functionspace(mesh, e1)
space2 = functionspace(mesh, e2)
f1 = Function(space1, dtype=dtype)
f2 = Function(space2, dtype=dtype)
f1.interpolate(func)
f2.interpolate(func)
diff = f1 - f2
error = assemble_scalar(form(ufl.inner(diff, diff) * ufl.dx, dtype=dtype))
assert np.isclose(error, 0)
|
