def test_interpolate_subset(order, dim, affine):
if dim == 2:
ct = CellType.triangle if affine else CellType.quadrilateral
mesh = create_unit_square(MPI.COMM_WORLD, 3, 4, ct)
elif dim == 3:
ct = CellType.tetrahedron if affine else CellType.hexahedron
mesh = create_unit_cube(MPI.COMM_WORLD, 3, 2, 2, ct)
V = FunctionSpace(mesh, ("DG", order))
u = Function(V)
cells = locate_entities(mesh, mesh.topology.dim,
lambda x: x[1] <= 0.5 + 1e-10)
num_local_cells = mesh.topology.index_map(mesh.topology.dim).size_local
cells_local = cells[cells < num_local_cells]
x = ufl.SpatialCoordinate(mesh)
f = x[1]**order
expr = Expression(f, V.element.interpolation_points)
u.interpolate(expr, cells_local)
mt = MeshTags(mesh, mesh.topology.dim, cells_local,
np.ones(cells_local.size, dtype=np.int32))
dx = ufl.Measure("dx", domain=mesh, subdomain_data=mt)
assert np.isclose(
np.abs(form(assemble_scalar(form(ufl.inner(u - f, u - f) * dx(1))))),
0)
integral = mesh.comm.allreduce(assemble_scalar(form(u * dx)), op=MPI.SUM)
assert np.isclose(integral, 1 / (order + 1) * 0.5**(order + 1), 0)
def plot_streamlines():
# Plotting streamlines
# ====================
# In this section we illustrate how to visualize streamlines in 3D
mesh = create_unit_cube(MPI.COMM_WORLD, 4, 4, 4, CellType.hexahedron)
V = VectorFunctionSpace(mesh, ("Discontinuous Lagrange", 2))
u = Function(V, dtype=np.float64)
u.interpolate(lambda x: np.vstack((-(x[1] - 0.5), x[0] - 0.5, np.zeros(x.shape[1]))))
cells, types, x = plot.create_vtk_mesh(V)
num_dofs = x.shape[0]
values = np.zeros((num_dofs, 3), dtype=np.float64)
values[:, :mesh.geometry.dim] = u.x.array.reshape(num_dofs, V.dofmap.index_map_bs)
# Create a point cloud of glyphs
grid = pyvista.UnstructuredGrid(cells, types, x)
grid["vectors"] = values
grid.set_active_vectors("vectors")
glyphs = grid.glyph(orient="vectors", factor=0.1)
streamlines = grid.streamlines(vectors="vectors", return_source=False, source_radius=1, n_points=150)
# Create Create plotter
plotter = pyvista.Plotter()
plotter.add_text("Streamlines.", position="upper_edge", font_size=20, color="black")
plotter.add_mesh(grid, style="wireframe")
plotter.add_mesh(glyphs)
plotter.add_mesh(streamlines.tube(radius=0.001))
plotter.view_xy()
if pyvista.OFF_SCREEN:
plotter.screenshot(f"streamlines_{MPI.COMM_WORLD.rank}.png",
transparent_background=transparent, window_size=[figsize, figsize])
else:
plotter.show()
def test_mixed_element_interpolation():
mesh = create_unit_cube(MPI.COMM_WORLD, 3, 3, 3)
el = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
V = FunctionSpace(mesh, ufl.MixedElement([el, el]))
u = Function(V)
with pytest.raises(RuntimeError):
u.interpolate(lambda x: np.ones(2, x.shape[1]))
def test_assemble_derivatives():
"""This test checks the original_coefficient_positions, which may change
under differentiation (some coefficients and constants are
eliminated)"""
mesh = create_unit_square(MPI.COMM_WORLD, 12, 12)
Q = FunctionSpace(mesh, ("Lagrange", 1))
u = Function(Q)
v = ufl.TestFunction(Q)
du = ufl.TrialFunction(Q)
b = Function(Q)
c1 = Constant(mesh, np.array([[1.0, 0.0], [3.0, 4.0]], PETSc.ScalarType))
c2 = Constant(mesh, PETSc.ScalarType(2.0))
b.x.array[:] = 2.0
# derivative eliminates 'u' and 'c1'
L = ufl.inner(c1, c1) * v * dx + c2 * b * inner(u, v) * dx
a = form(derivative(L, u, du))
A1 = assemble_matrix(a)
A1.assemble()
a = form(c2 * b * inner(du, v) * dx)
A2 = assemble_matrix(a)
A2.assemble()
assert (A1 - A2).norm() == pytest.approx(0.0, rel=1e-12, abs=1e-12)
def run_vector_test(V, poly_order):
"""Test that interpolation is correct in a scalar valued space."""
random.seed(12)
tdim = V.mesh.topology.dim
if tdim == 1:
def f(x):
return x[0]**poly_order
elif tdim == 2:
def f(x):
return (x[1]**min(poly_order, 1), 2 * x[0]**poly_order)
else:
def f(x):
return (x[1]**min(poly_order, 1), 2 * x[0]**poly_order,
3 * x[2]**min(poly_order, 2))
v = Function(V)
v.interpolate(f)
points = [random_point_in_cell(V.mesh) for count in range(5)]
cells = [0 for count in range(5)]
values = v.eval(points, cells)
for p, val in zip(points, values):
assert np.allclose(val, f(p))
def test_copy(V):
u = Function(V)
u.interpolate(lambda x: x[0] + 2 * x[1])
v = u.copy()
assert np.allclose(u.x.array, v.x.array)
u.x.array[:] = 1
assert not np.allclose(u.x.array, v.x.array)
def test_additivity(mode):
mesh = create_unit_square(MPI.COMM_WORLD, 12, 12, ghost_mode=mode)
V = FunctionSpace(mesh, ("Lagrange", 1))
f1 = Function(V)
f2 = Function(V)
f3 = Function(V)
f1.x.array[:] = 1.0
f2.x.array[:] = 2.0
f3.x.array[:] = 3.0
j1 = ufl.inner(f1, f1) * ufl.dx(mesh)
j2 = ufl.inner(f2, f2) * ufl.ds(mesh)
j3 = ufl.inner(ufl.avg(f3), ufl.avg(f3)) * ufl.dS(mesh)
# Assemble each scalar form separately
J1 = mesh.comm.allreduce(assemble_scalar(form(j1)), op=MPI.SUM)
J2 = mesh.comm.allreduce(assemble_scalar(form(j2)), op=MPI.SUM)
J3 = mesh.comm.allreduce(assemble_scalar(form(j3)), op=MPI.SUM)
# Sum forms and assemble the result
J12 = mesh.comm.allreduce(assemble_scalar(form(j1 + j2)), op=MPI.SUM)
J13 = mesh.comm.allreduce(assemble_scalar(form(j1 + j3)), op=MPI.SUM)
J23 = mesh.comm.allreduce(assemble_scalar(form(j2 + j3)), op=MPI.SUM)
J123 = mesh.comm.allreduce(assemble_scalar(form(j1 + j2 + j3)), op=MPI.SUM)
# Compare assembled values
assert (J1 + J2) == pytest.approx(J12)
assert (J1 + J3) == pytest.approx(J13)
assert (J2 + J3) == pytest.approx(J23)
assert (J1 + J2 + J3) == pytest.approx(J123)
def test_scatter_forward(element):
mesh = create_unit_square(MPI.COMM_WORLD, 5, 5)
V = FunctionSpace(mesh, element)
u = Function(V)
bs = V.dofmap.bs
u.interpolate(lambda x: [x[i] for i in range(bs)])
# Forward scatter should have no effect
w0 = u.x.array.copy()
u.x.scatter_forward()
assert np.allclose(w0, u.x.array)
# Fill local array with the mpi rank
u.x.array.fill(MPI.COMM_WORLD.rank)
w0 = u.x.array.copy()
u.x.scatter_forward()
# Now the ghosts should have the value of the rank of
# the owning process
ghost_owners = u.function_space.dofmap.index_map.ghost_owner_rank()
ghost_owners = np.repeat(ghost_owners, bs)
local_size = u.function_space.dofmap.index_map.size_local * bs
assert np.allclose(u.x.array[local_size:], ghost_owners)
def test_scatter_reverse(element):
comm = MPI.COMM_WORLD
mesh = create_unit_square(MPI.COMM_WORLD, 5, 5)
V = FunctionSpace(mesh, element)
u = Function(V)
bs = V.dofmap.bs
u.interpolate(lambda x: [x[i] for i in range(bs)])
# Reverse scatter (insert) should have no effect
w0 = u.x.array.copy()
u.x.scatter_reverse(_cpp.common.ScatterMode.insert)
assert np.allclose(w0, u.x.array)
# Fill with MPI rank, and sum all entries in the vector (including ghosts)
u.x.array.fill(comm.rank)
all_count0 = MPI.COMM_WORLD.allreduce(u.x.array.sum(), op=MPI.SUM)
# Reverse scatter (add)
u.x.scatter_reverse(_cpp.common.ScatterMode.add)
num_ghosts = V.dofmap.index_map.num_ghosts
ghost_count = MPI.COMM_WORLD.allreduce(num_ghosts * comm.rank, op=MPI.SUM)
# New count should have gone up by the number of ghosts times their rank
# on all processes
all_count1 = MPI.COMM_WORLD.allreduce(u.x.array.sum(), op=MPI.SUM)
assert all_count1 == (all_count0 + bs * ghost_count)
def test_constant_bc(mesh_factory):
"""Test that setting a dirichletbc with a constant yields the same
result as setting it with a function"""
func, args = mesh_factory
mesh = func(*args)
V = FunctionSpace(mesh, ("Lagrange", 1))
c = PETSc.ScalarType(2)
tdim = mesh.topology.dim
boundary_facets = locate_entities_boundary(
mesh, tdim - 1, lambda x: np.ones(x.shape[1], dtype=bool))
boundary_dofs = locate_dofs_topological(V, tdim - 1, boundary_facets)
u_bc = Function(V)
u_bc.x.array[:] = c
bc_f = dirichletbc(u_bc, boundary_dofs)
bc_c = dirichletbc(c, boundary_dofs, V)
u_f = Function(V)
set_bc(u_f.vector, [bc_f])
u_c = Function(V)
set_bc(u_c.vector, [bc_c])
assert np.allclose(u_f.vector.array, u_c.vector.array)
def test_vector_constant_bc(mesh_factory):
"""Test that setting a dirichletbc with a vector valued constant
yields the same result as setting it with a function"""
func, args = mesh_factory
mesh = func(*args)
tdim = mesh.topology.dim
V = VectorFunctionSpace(mesh, ("Lagrange", 1))
assert V.num_sub_spaces == mesh.geometry.dim
c = np.arange(1, mesh.geometry.dim + 1, dtype=PETSc.ScalarType)
boundary_facets = locate_entities_boundary(
mesh, tdim - 1, lambda x: np.ones(x.shape[1], dtype=bool))
# Set using sub-functions
Vs = [V.sub(i).collapse()[0] for i in range(V.num_sub_spaces)]
boundary_dofs = [
locate_dofs_topological((V.sub(i), Vs[i]), tdim - 1, boundary_facets)
for i in range(len(Vs))
]
u_bcs = [Function(Vs[i]) for i in range(len(Vs))]
bcs_f = []
for i, u in enumerate(u_bcs):
u_bcs[i].x.array[:] = c[i]
bcs_f.append(dirichletbc(u_bcs[i], boundary_dofs[i], V.sub(i)))
u_f = Function(V)
set_bc(u_f.vector, bcs_f)
# Set using constant
boundary_dofs = locate_dofs_topological(V, tdim - 1, boundary_facets)
bc_c = dirichletbc(c, boundary_dofs, V)
u_c = Function(V)
u_c.x.array[:] = 0.0
set_bc(u_c.vector, [bc_c])
assert np.allclose(u_f.x.array, u_c.x.array)
def test_save_1d_scalar(tempdir):
mesh = create_unit_interval(MPI.COMM_WORLD, 32)
u = Function(FunctionSpace(mesh, ("Lagrange", 2)))
u.interpolate(lambda x: x[0])
filename = os.path.join(tempdir, "u.pvd")
with VTKFile(MPI.COMM_WORLD, filename, "w") as vtk:
vtk.write_function(u, 0.)
def test_sub_constant_bc(mesh_factory):
"""Test that setting a dirichletbc with on a component of a vector
valued function yields the same result as setting it with a
function"""
func, args = mesh_factory
mesh = func(*args)
tdim = mesh.topology.dim
V = VectorFunctionSpace(mesh, ("Lagrange", 1))
c = Constant(mesh, PETSc.ScalarType(3.14))
boundary_facets = locate_entities_boundary(
mesh, tdim - 1, lambda x: np.ones(x.shape[1], dtype=bool))
for i in range(V.num_sub_spaces):
Vi = V.sub(i).collapse()[0]
u_bci = Function(Vi)
u_bci.x.array[:] = PETSc.ScalarType(c.value)
boundary_dofsi = locate_dofs_topological((V.sub(i), Vi), tdim - 1,
boundary_facets)
bc_fi = dirichletbc(u_bci, boundary_dofsi, V.sub(i))
boundary_dofs = locate_dofs_topological(V.sub(i), tdim - 1,
boundary_facets)
bc_c = dirichletbc(c, boundary_dofs, V.sub(i))
u_f = Function(V)
set_bc(u_f.vector, [bc_fi])
u_c = Function(V)
set_bc(u_c.vector, [bc_c])
assert np.allclose(u_f.vector.array, u_c.vector.array)
def monolithic_solve():
"""Monolithic (interleaved) solver"""
P2_el = ufl.VectorElement("Lagrange", mesh.ufl_cell(), 2)
P1_el = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
TH = P2_el * P1_el
W = FunctionSpace(mesh, TH)
(u, p) = ufl.TrialFunctions(W)
(v, q) = ufl.TestFunctions(W)
a00 = ufl.inner(ufl.grad(u), ufl.grad(v)) * dx
a01 = ufl.inner(p, ufl.div(v)) * dx
a10 = ufl.inner(ufl.div(u), q) * dx
a = a00 + a01 + a10
p00 = ufl.inner(ufl.grad(u), ufl.grad(v)) * dx
p11 = ufl.inner(p, q) * dx
p_form = p00 + p11
f = Function(W.sub(0).collapse()[0])
p_zero = Function(W.sub(1).collapse()[0])
L0 = inner(f, v) * dx
L1 = inner(p_zero, q) * dx
L = L0 + L1
a, p_form, L = form(a), form(p_form), form(L)
bdofsW0_P2_0 = locate_dofs_topological(W.sub(0), facetdim, bndry_facets0)
bdofsW0_P2_1 = locate_dofs_topological(W.sub(0), facetdim, bndry_facets1)
bc0 = dirichletbc(bc_value, bdofsW0_P2_0, W.sub(0))
bc1 = dirichletbc(bc_value, bdofsW0_P2_1, W.sub(0))
A = assemble_matrix(a, bcs=[bc0, bc1])
A.assemble()
P = assemble_matrix(p_form, bcs=[bc0, bc1])
P.assemble()
b = assemble_vector(L)
apply_lifting(b, [a], bcs=[[bc0, bc1]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
set_bc(b, [bc0, bc1])
ksp = PETSc.KSP()
ksp.create(mesh.comm)
ksp.setOperators(A, P)
ksp.setType("minres")
pc = ksp.getPC()
pc.setType('lu')
def monitor(ksp, its, rnorm):
# print("Num it, rnorm:", its, rnorm)
pass
ksp.setTolerances(rtol=1.0e-8, max_it=50)
ksp.setMonitor(monitor)
ksp.setFromOptions()
x = A.createVecRight()
ksp.solve(b, x)
assert ksp.getConvergedReason() > 0
return b.norm(), x.norm(), A.norm(), P.norm()
def plot_scalar():
# We start by creating a unit square mesh and interpolating a function
# into a first order Lagrange space
msh = create_unit_square(MPI.COMM_WORLD,
12,
12,
cell_type=CellType.quadrilateral)
V = FunctionSpace(msh, ("Lagrange", 1))
u = Function(V, dtype=np.float64)
u.interpolate(lambda x: np.sin(np.pi * x[0]) * np.sin(2 * x[1] * np.pi))
# As we want to visualize the function u, we have to create a grid to
# attached the dof values to We do this by creating a topology and
# geometry based on the function space V
cells, types, x = plot.create_vtk_mesh(V)
grid = pyvista.UnstructuredGrid(cells, types, x)
grid.point_data["u"] = u.x.array
# We set the function "u" as the active scalar for the mesh, and warp
# the mesh in z-direction by its values
grid.set_active_scalars("u")
warped = grid.warp_by_scalar()
# We create a plotting window consisting of to plots, one of the scalar
# values, and one where the mesh is warped by these values
subplotter = pyvista.Plotter(shape=(1, 2))
subplotter.subplot(0, 0)
subplotter.add_text("Scalar countour field",
font_size=14,
color="black",
position="upper_edge")
subplotter.add_mesh(grid, show_edges=True, show_scalar_bar=True)
subplotter.view_xy()
subplotter.subplot(0, 1)
subplotter.add_text("Warped function",
position="upper_edge",
font_size=14,
color="black")
sargs = dict(height=0.8,
width=0.1,
vertical=True,
position_x=0.05,
position_y=0.05,
fmt="%1.2e",
title_font_size=40,
color="black",
label_font_size=25)
subplotter.set_position([-3, 2.6, 0.3])
subplotter.set_focus([3, -1, -0.15])
subplotter.set_viewup([0, 0, 1])
subplotter.add_mesh(warped, show_edges=True, scalar_bar_args=sargs)
if pyvista.OFF_SCREEN:
subplotter.screenshot("2D_function_warp.png",
transparent_background=transparent,
window_size=[figsize, figsize])
else:
subplotter.show()
def run_scalar_test(mesh, V, degree):
""" Manufactured Poisson problem, solving u = x[1]**p, where p is the
degree of the Lagrange function space.
"""
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)
# 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)
u_bc = Function(V)
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 = np.where(
np.array(compute_boundary_facets(mesh.topology)) == 1)[0]
bdofs = locate_dofs_topological(V, facetdim, bndry_facets)
bc = dirichletbc(u_bc, bdofs)
b = assemble_vector(L)
apply_lifting(b, [a], bcs=[[bc]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
set_bc(b, [bc])
a = form(a)
A = assemble_matrix(a, bcs=[bc])
A.assemble()
# Create LU linear solver
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
solver.setOperators(A)
uh = Function(V)
solver.solve(b, uh.vector)
uh.x.scatter_forward()
M = (u_exact - uh)**2 * dx
M = form(M)
error = mesh.comm.allreduce(assemble_scalar(M), op=MPI.SUM)
assert np.absolute(error) < 1.0e-14
def test_mixed_interpolation():
"""Test that mixed interpolation raised an exception."""
mesh = one_cell_mesh(CellType.triangle)
A = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
B = ufl.VectorElement("Lagrange", mesh.ufl_cell(), 1)
v = Function(FunctionSpace(mesh, ufl.MixedElement([A, B])))
with pytest.raises(RuntimeError):
v.interpolate(lambda x: (x[1], 2 * x[0], 3 * x[1]))
def test_mixed_fides_functions(tempdir, dim, simplex):
"""Test saving P2 and P1 functions with Fides"""
mesh = generate_mesh(dim, simplex)
v = Function(VectorFunctionSpace(mesh, ("Lagrange", 2)))
q = Function(FunctionSpace(mesh, ("Lagrange", 1)))
filename = os.path.join(tempdir, "v.bp")
with pytest.raises(RuntimeError):
FidesWriter(mesh.comm, filename, [v, q])
def test_vtx_functions_fail(tempdir, dim, simplex):
"Test for error when elements differ"
mesh = generate_mesh(dim, simplex)
v = Function(VectorFunctionSpace(mesh, ("Lagrange", 2)))
w = Function(FunctionSpace(mesh, ("Lagrange", 1)))
filename = os.path.join(tempdir, "v.bp")
with pytest.raises(RuntimeError):
VTXWriter(mesh.comm, filename, [v, w])
def test_interpolation_function(mesh):
V = FunctionSpace(mesh, ("Lagrange", 1))
u = Function(V)
u.x.array[:] = 1
Vh = FunctionSpace(mesh, ("Lagrange", 1))
uh = Function(Vh)
uh.interpolate(u)
assert np.allclose(uh.x.array, 1)
def test_vtx_different_meshes_function(tempdir, simplex):
"Test for error when functions do not share a mesh"
mesh = generate_mesh(2, simplex)
v = Function(FunctionSpace(mesh, ("Lagrange", 1)))
mesh2 = generate_mesh(2, simplex)
w = Function(FunctionSpace(mesh2, ("Lagrange", 1)))
filename = os.path.join(tempdir, "v.bp")
with pytest.raises(RuntimeError):
VTXWriter(mesh.comm, filename, [v, w])
def test_vtx_functions_fail(tempdir, dim, simplex):
"Test saving high order Lagrange functions"
from dolfinx.cpp.io import VTXWriter
mesh = generate_mesh(dim, simplex)
v = Function(VectorFunctionSpace(mesh, ("Lagrange", 2)))
w = Function(FunctionSpace(mesh, ("Lagrange", 1)))
filename = os.path.join(tempdir, "v.bp")
with pytest.raises(RuntimeError):
VTXWriter(mesh.comm, filename, [v._cpp_object, w._cpp_object])
def test_assembly_dx_domains(mode, meshtags_factory):
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, ghost_mode=mode)
V = FunctionSpace(mesh, ("Lagrange", 1))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
# Prepare a marking structures
# indices cover all cells
# values are [1, 2, 3, 3, ...]
cell_map = mesh.topology.index_map(mesh.topology.dim)
num_cells = cell_map.size_local + cell_map.num_ghosts
indices = np.arange(0, num_cells)
values = np.full(indices.shape, 3, dtype=np.intc)
values[0] = 1
values[1] = 2
marker = meshtags_factory(mesh, mesh.topology.dim, indices, values)
dx = ufl.Measure('dx', subdomain_data=marker, domain=mesh)
w = Function(V)
w.x.array[:] = 0.5
# Assemble matrix
a = form(w * ufl.inner(u, v) * (dx(1) + dx(2) + dx(3)))
A = assemble_matrix(a)
A.assemble()
a2 = form(w * ufl.inner(u, v) * dx)
A2 = assemble_matrix(a2)
A2.assemble()
assert (A - A2).norm() < 1.0e-12
bc = dirichletbc(Function(V), range(30))
# Assemble vector
L = form(ufl.inner(w, v) * (dx(1) + dx(2) + dx(3)))
b = assemble_vector(L)
apply_lifting(b, [a], [[bc]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
set_bc(b, [bc])
L2 = form(ufl.inner(w, v) * dx)
b2 = assemble_vector(L2)
apply_lifting(b2, [a], [[bc]])
b2.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
set_bc(b2, [bc])
assert (b - b2).norm() < 1.0e-12
# Assemble scalar
L = form(w * (dx(1) + dx(2) + dx(3)))
s = assemble_scalar(L)
s = mesh.comm.allreduce(s, op=MPI.SUM)
assert s == pytest.approx(0.5, 1.0e-12)
L2 = form(w * dx)
s2 = assemble_scalar(L2)
s2 = mesh.comm.allreduce(s2, op=MPI.SUM)
assert s == pytest.approx(s2, 1.0e-12)
def test_functions_from_different_meshes_fides(tempdir):
"""Check that the underlying ADIOS2Writer catches sending in
functions on different meshes"""
filename = os.path.join(tempdir, "mesh_fides.bp")
mesh0 = create_unit_square(MPI.COMM_WORLD, 5, 5)
mesh1 = create_unit_square(MPI.COMM_WORLD, 10, 2)
u0 = Function(FunctionSpace(mesh0, ("Lagrange", 1)))
u1 = Function(FunctionSpace(mesh1, ("Lagrange", 1)))
with pytest.raises(RuntimeError):
FidesWriter(mesh0.comm, filename, [u0, u1])
def test_dof_coords_3d(degree):
mesh = create_unit_cube(MPI.COMM_WORLD, 10, 10, 10)
V = FunctionSpace(mesh, ("Lagrange", degree))
u = Function(V)
u.interpolate(lambda x: x[0])
u.x.scatter_forward()
x = V.tabulate_dof_coordinates()
val = u.vector.array
for i in range(len(val)):
assert np.isclose(x[i, 0], val[i], rtol=1e-3)
def test_assemble_empty_rank_mesh():
"""Assembly on mesh where some ranks are empty"""
comm = MPI.COMM_WORLD
cell_type = CellType.triangle
domain = ufl.Mesh(
ufl.VectorElement("Lagrange", ufl.Cell(cell_type.name), 1))
def partitioner(comm, nparts, local_graph, num_ghost_nodes, ghosting):
"""Leave cells on the curent rank"""
dest = np.full(len(cells), comm.rank, dtype=np.int32)
return graph.create_adjacencylist(dest)
if comm.rank == 0:
# Put cells on rank 0
cells = np.array([[0, 1, 2], [0, 2, 3]], dtype=np.int64)
cells = graph.create_adjacencylist(cells)
x = np.array([[0., 0.], [1., 0.], [1., 1.], [0., 1.]])
else:
# No cells onm other ranks
cells = graph.create_adjacencylist(np.empty((0, 3), dtype=np.int64))
x = np.empty((0, 2), dtype=np.float64)
mesh = create_mesh(comm, cells, x, domain, GhostMode.none, partitioner)
V = FunctionSpace(mesh, ("Lagrange", 2))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
f, k, zero = Function(V), Function(V), Function(V)
f.x.array[:] = 10.0
k.x.array[:] = 1.0
zero.x.array[:] = 0.0
a = form(inner(k * u, v) * dx + inner(zero * u, v) * ds)
L = form(inner(f, v) * dx + inner(zero, v) * ds)
M = form(2 * k * dx + k * ds)
sum = comm.allreduce(assemble_scalar(M), op=MPI.SUM)
assert sum == pytest.approx(6.0)
# Assemble
A = assemble_matrix(a)
A.assemble()
b = assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
# Solve
ksp = PETSc.KSP()
ksp.create(mesh.comm)
ksp.setOperators(A)
ksp.setTolerances(rtol=1.0e-9, max_it=50)
ksp.setFromOptions()
x = b.copy()
ksp.solve(b, x)
assert np.allclose(x.array, 10.0)
def test_collapse(W, V):
Vs = W.sub(2)
with pytest.raises(RuntimeError):
Function(Vs)
assert Vs.dofmap.cell_dofs(0)[0] != V.dofmap.cell_dofs(0)[0]
# Collapse the space it should now be the same as V
Vc = Vs.collapse()[0]
assert Vc.dofmap.cell_dofs(0)[0] == V.dofmap.cell_dofs(0)[0]
f0 = Function(V)
f1 = Function(Vc)
assert f0.vector.getSize() == f1.vector.getSize()
def test_rank1_hdiv():
"""Test rank-1 Expression, i.e. Expression containing Argument (TrialFunction)
Test compiles linear interpolation operator RT_2 -> vector DG_2 and assembles it into
global matrix A. Input space RT_2 is chosen because it requires dof permutations.
"""
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10)
vdP1 = VectorFunctionSpace(mesh, ("DG", 2))
RT1 = FunctionSpace(mesh, ("RT", 2))
f = ufl.TrialFunction(RT1)
points = vdP1.element.interpolation_points
compiled_expr = Expression(f, points)
num_cells = mesh.topology.index_map(2).size_local
array_evaluated = compiled_expr.eval(np.arange(num_cells, dtype=np.int32))
@numba.njit
def scatter(A, array_evaluated, dofmap0, dofmap1):
for i in range(num_cells):
rows = dofmap0[i, :]
cols = dofmap1[i, :]
A_local = array_evaluated[i, :]
MatSetValues(A, 12, rows.ctypes, 8, cols.ctypes, A_local.ctypes, 1)
a = form(ufl.inner(f, ufl.TestFunction(vdP1)) * ufl.dx)
sparsity_pattern = create_sparsity_pattern(a)
sparsity_pattern.assemble()
A = create_matrix(MPI.COMM_WORLD, sparsity_pattern)
dofmap_col = RT1.dofmap.list.array.reshape(-1, 8).astype(
np.dtype(PETSc.IntType))
dofmap_row = vdP1.dofmap.list.array
dofmap_row_unrolled = (2 * np.repeat(dofmap_row, 2).reshape(-1, 2) +
np.arange(2)).flatten()
dofmap_row = dofmap_row_unrolled.reshape(-1, 12).astype(
np.dtype(PETSc.IntType))
scatter(A.handle, array_evaluated, dofmap_row, dofmap_col)
A.assemble()
g = Function(RT1, name="g")
def expr1(x):
return np.row_stack((np.sin(x[0]), np.cos(x[1])))
# Interpolate a numpy expression into RT1
g.interpolate(expr1)
# Interpolate RT1 into vdP1 (non-compiled interpolation)
h = Function(vdP1)
h.interpolate(g)
# Interpolate RT1 into vdP1 (compiled, mat-vec interpolation)
h2 = Function(vdP1)
h2.vector.axpy(1.0, A * g.vector)
assert np.isclose((h2.vector - h.vector).norm(), 0.0)
def test_eval_manifold():
# Simple two-triangle surface in 3d
vertices = [(0.0, 0.0, 1.0), (1.0, 1.0, 1.0), (1.0, 0.0, 0.0), (0.0, 1.0,
0.0)]
cells = [(0, 1, 2), (0, 1, 3)]
cell = ufl.Cell("triangle", geometric_dimension=3)
domain = ufl.Mesh(ufl.VectorElement("Lagrange", cell, 1))
mesh = create_mesh(MPI.COMM_WORLD, cells, vertices, domain)
Q = FunctionSpace(mesh, ("Lagrange", 1))
u = Function(Q)
u.interpolate(lambda x: x[0] + x[1])
assert np.isclose(u.eval([0.75, 0.25, 0.5], 0)[0], 1.0)
def test_interpolation_n2curl_to_bdm(tdim, order):
if tdim == 2:
mesh = create_unit_square(MPI.COMM_WORLD, 5, 5)
else:
mesh = create_unit_cube(MPI.COMM_WORLD, 2, 2, 2)
V = FunctionSpace(mesh, ("N2curl", order))
V1 = FunctionSpace(mesh, ("BDM", order))
u, v = Function(V), Function(V1)
u.interpolate(lambda x: x[:tdim]**order)
v.interpolate(u)
s = assemble_scalar(form(ufl.inner(u - v, u - v) * ufl.dx))
assert np.isclose(s, 0)
