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from mpi4py import MPI
from petsc4py import PETSc
import dolfinx
import dolfinx.fem.petsc
import ufl
import numpy as np
import scifem
import pytest
@pytest.mark.parametrize("L", [0.1, 0.2, 0.3])
@pytest.mark.parametrize("H", [1.3, 0.8, 0.2])
@pytest.mark.parametrize(
"cell_type", [dolfinx.mesh.CellType.triangle, dolfinx.mesh.CellType.quadrilateral]
)
@pytest.mark.parametrize("dtype", [np.float64, np.float32])
def test_real_function_space_mass(L, H, cell_type, dtype):
"""
Check that real space mass matrix is the same as assembling the volume of the mesh
"""
mesh = dolfinx.mesh.create_rectangle(
MPI.COMM_WORLD, [[0.0, 0.0], [L, H]], [7, 9], cell_type, dtype=dtype
)
V = scifem.create_real_functionspace(mesh)
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(u, v) * ufl.dx
A = dolfinx.fem.assemble_matrix(dolfinx.fem.form(a, dtype=dtype), bcs=[])
A.scatter_reverse()
tol = 100 * np.finfo(dtype).eps
cell_map = mesh.topology.index_map(mesh.topology.dim)
if cell_map.size_local + cell_map.num_ghosts > 0:
assert len(A.data) == 1
if cell_map.local_range[0] == 0:
assert np.isclose(A.data[0], L * H, atol=tol)
else:
assert len(A.data) == 0
assert len(V.dofmap.list.flatten()) == 0
assert V.dofmap.index_map.size_local == 0
assert V.dofmap.index_map.num_ghosts == 1
@pytest.mark.parametrize("dtype", [np.float64, np.float32])
@pytest.mark.parametrize(
"cell_type", [dolfinx.mesh.CellType.tetrahedron, dolfinx.mesh.CellType.hexahedron]
)
def test_real_function_space_vector(cell_type, dtype):
"""
Test that assembling against a real space test function is equivalent to assembling a vector
"""
mesh = dolfinx.mesh.create_unit_cube(MPI.COMM_WORLD, 2, 3, 5, cell_type, dtype=dtype)
V = dolfinx.fem.functionspace(mesh, ("Lagrange", 3))
v = ufl.TrialFunction(V)
R = scifem.create_real_functionspace(mesh)
u = ufl.TestFunction(R)
a_R = ufl.inner(u, v) * ufl.dx
form_rhs = dolfinx.fem.form(a_R, dtype=dtype)
A_R = dolfinx.fem.assemble_matrix(form_rhs, bcs=[])
A_R.scatter_reverse()
L = ufl.inner(ufl.constantvalue.IntValue(1), v) * ufl.dx
form_lhs = dolfinx.fem.form(L, dtype=dtype)
b = dolfinx.fem.assemble_vector(form_lhs)
b.scatter_reverse(dolfinx.la.InsertMode.add)
b.scatter_forward()
row_map = A_R.index_map(0)
num_local_rows = row_map.size_local
num_dofs = V.dofmap.index_map.size_local * V.dofmap.index_map_bs
tol = 100 * np.finfo(dtype).eps
if MPI.COMM_WORLD.rank == 0:
assert num_local_rows == 1
num_dofs_global = V.dofmap.index_map.size_global * V.dofmap.index_map_bs
assert A_R.indptr[1] - A_R.indptr[0] == num_dofs_global
np.testing.assert_allclose(A_R.indices, np.arange(num_dofs_global))
np.testing.assert_allclose(b.array[:num_dofs], A_R.data[:num_dofs], atol=tol)
else:
assert num_local_rows == 0
@pytest.mark.parametrize("dtype", [(PETSc.RealType, PETSc.ScalarType)])
@pytest.mark.parametrize("tensor", [0, 1, 2])
@pytest.mark.parametrize("degree", range(1, 5))
def test_singular_poisson(tensor, degree, dtype):
M = 9
rtype, stype = dtype
mesh = dolfinx.mesh.create_unit_square(
MPI.COMM_WORLD, M, M, dolfinx.mesh.CellType.triangle, dtype=rtype
)
if tensor == 0:
value_shape = ()
elif tensor == 1:
value_shape = (2,)
else:
value_shape = (3, 2)
V = dolfinx.fem.functionspace(mesh, ("Lagrange", degree, value_shape))
R = scifem.create_real_functionspace(mesh, value_shape)
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
c = ufl.TrialFunction(R)
d = ufl.TestFunction(R)
x = ufl.SpatialCoordinate(mesh)
pol = x[0] ** degree - 2 * x[1] ** degree
# Compute average value of polynomial to make mean 0
C = mesh.comm.allreduce(
dolfinx.fem.assemble_scalar(dolfinx.fem.form(pol * ufl.dx, dtype=stype)), op=MPI.SUM
)
u_scalar = pol - dolfinx.fem.Constant(mesh, stype(C))
if tensor == 0:
u_ex = u_scalar
zero = dolfinx.fem.Constant(mesh, stype(0.0))
elif tensor == 1:
u_ex = ufl.as_vector([u_scalar, -u_scalar])
zero = dolfinx.fem.Constant(mesh, stype((0.0, 0.0)))
else:
u_ex = ufl.as_tensor(
[
[u_scalar, 2 * u_scalar],
[3 * u_scalar, -u_scalar],
[u_scalar, 2 * u_scalar],
]
)
zero = dolfinx.fem.Constant(mesh, stype(((0.0, 0.0), (0.0, 0.0), (0.0, 0.0))))
dx = ufl.Measure("dx", domain=mesh)
f = -ufl.div(ufl.grad(u_ex))
n = ufl.FacetNormal(mesh)
g = ufl.dot(ufl.grad(u_ex), n)
a00 = ufl.inner(ufl.grad(u), ufl.grad(v)) * dx
a01 = ufl.inner(c, v) * dx
a10 = ufl.inner(u, d) * dx
L0 = ufl.inner(f, v) * dx + ufl.inner(g, v) * ufl.ds
L1 = ufl.inner(zero, d) * dx
a = dolfinx.fem.form([[a00, a01], [a10, None]], dtype=stype)
L = dolfinx.fem.form([L0, L1], dtype=stype)
new_assemble_mode = False
try:
A = dolfinx.fem.petsc.assemble_matrix_block(a)
except AttributeError:
new_assemble_mode = True
A = dolfinx.fem.petsc.assemble_matrix(a, kind="mpi")
A.assemble()
if new_assemble_mode:
b = dolfinx.fem.petsc.create_vector(dolfinx.fem.extract_function_spaces(L), kind="mpi")
else:
b = dolfinx.fem.petsc.create_vector_block(L)
with b.localForm() as loc:
loc.set(0)
if new_assemble_mode:
dolfinx.fem.petsc.assemble_vector(b, L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
b.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
else:
dolfinx.fem.petsc.assemble_vector_block(b, L, a, bcs=[])
ksp = PETSc.KSP().create(mesh.comm)
ksp.setOperators(A)
ksp.setType("preonly")
pc = ksp.getPC()
pc.setType("lu")
pc.setFactorSolverType("mumps")
if new_assemble_mode:
x = dolfinx.fem.petsc.create_vector(dolfinx.fem.extract_function_spaces(L), kind="mpi")
else:
x = dolfinx.fem.petsc.create_vector_block(L)
ksp.solve(b, x)
x.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
uh = dolfinx.fem.Function(V)
rh = dolfinx.fem.Function(R)
if new_assemble_mode:
dolfinx.fem.petsc.assign(x, [uh, rh])
else:
x_local = dolfinx.cpp.la.petsc.get_local_vectors(
x,
[
(V.dofmap.index_map, V.dofmap.index_map_bs),
(R.dofmap.index_map, R.dofmap.index_map_bs),
],
)
uh.x.array[: len(x_local[0])] = x_local[0]
uh.x.scatter_forward()
b.destroy()
x.destroy()
A.destroy()
ksp.destroy()
error = dolfinx.fem.form(ufl.inner(u_ex - uh, u_ex - uh) * dx, dtype=stype)
e_local = dolfinx.fem.assemble_scalar(error)
tol = 1e4 * np.finfo(stype).eps
e_global = np.sqrt(mesh.comm.allreduce(e_local, op=MPI.SUM))
assert np.isclose(e_global, 0, atol=tol)
@pytest.mark.parametrize("ftype, stype", [(np.float32, np.complex64), (np.float64, np.complex128)])
def test_complex_real_space(ftype, stype):
mesh = dolfinx.mesh.create_unit_interval(MPI.COMM_WORLD, 13, dtype=ftype)
val = (2 + 3j, -4 + 5j)
value_shape = (2,)
R = scifem.create_real_functionspace(mesh, value_shape=value_shape)
u = dolfinx.fem.Function(R, dtype=stype)
u.x.array[0] = val[0]
u.x.array[1] = val[1]
u.x.scatter_forward()
V = dolfinx.fem.functionspace(mesh, ("Lagrange", 1, value_shape))
v = ufl.TestFunction(V)
L = ufl.inner(u, v) * ufl.dx
b = dolfinx.fem.assemble_vector(dolfinx.fem.form(L, dtype=stype))
b.scatter_reverse(dolfinx.la.InsertMode.add)
b.scatter_forward()
const = dolfinx.fem.Constant(mesh, stype(val))
L_const = ufl.inner(const, v) * ufl.dx
b_const = dolfinx.fem.assemble_vector(dolfinx.fem.form(L_const, dtype=stype))
b_const.scatter_reverse(dolfinx.la.InsertMode.add)
b_const.scatter_forward()
tol = 100 * np.finfo(stype).eps
np.testing.assert_allclose(b.array, b_const.array, atol=tol)
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