def test_mpc_assembly(master_point, degree, celltype,
get_assemblers): # noqa: F811
_, assemble_vector = get_assemblers
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 3, 5, celltype)
V = fem.FunctionSpace(mesh, ("Lagrange", degree))
# Generate reference vector
v = ufl.TestFunction(V)
x = ufl.SpatialCoordinate(mesh)
f = ufl.sin(2 * ufl.pi * x[0]) * ufl.sin(ufl.pi * x[1])
rhs = ufl.inner(f, v) * ufl.dx
linear_form = fem.form(rhs)
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {
l2b([1, 0]): {
l2b([0, 1]): 0.43,
l2b([1, 1]): 0.11
},
l2b([0, 0]): {
l2b(master_point): 0.69
}
}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
b = assemble_vector(linear_form, mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
# Reduce system with global matrix K after assembly
L_org = fem.petsc.assemble_vector(linear_form)
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
list_timings(comm, [TimingType.wall])
def test_homogenize(element, poly_order):
mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 8, 8)
V = dolfinx.fem.FunctionSpace(mesh,
element("CG", mesh.ufl_cell(), poly_order))
def periodic_boundary(x):
return np.isclose(x[0], 0.0)
def periodic_relation(x):
out_x = np.zeros(x.shape)
out_x[0] = 1.0 - x[0]
out_x[1] = x[1]
out_x[2] = x[2]
return out_x
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_periodic_constraint_geometrical(V, periodic_boundary,
periodic_relation, [])
mpc.finalize()
# Sanity check that the MPC class has some constraints to impose
num_slaves_global = mesh.comm.allreduce(len(mpc.slaves), op=MPI.SUM)
assert num_slaves_global > 0
u = dolfinx.fem.Function(V)
u.vector.set(1.0)
assert np.isclose(u.vector.min()[1], u.vector.max()[1])
assert np.isclose(u.vector.array_r[0], 1.0)
mpc.homogenize(u.vector)
with u.vector.localForm() as u_:
for i in range(V.dofmap.index_map.size_local * V.dofmap.index_map_bs):
if i in mpc.slaves:
assert np.isclose(u_.array_r[i], 0.0)
else:
assert np.isclose(u_.array_r[i], 1.0)
def test_slave_on_same_cell(master_point, degree, celltype,
get_assemblers): # noqa: F811
assemble_matrix, _ = get_assemblers
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 1, 8, celltype)
V = fem.FunctionSpace(mesh, ("Lagrange", degree))
# Build master slave map
s_m_c = {
np.array([1, 0], dtype=np.float64).tobytes(): {
np.array([0, 1], dtype=np.float64).tobytes(): 0.43,
np.array([1, 1], dtype=np.float64).tobytes(): 0.11
},
np.array([0, 0], dtype=np.float64).tobytes(): {
np.array(master_point, dtype=np.float64).tobytes(): 0.69
}
}
with Timer("~TEST: MPC INIT"):
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
# Test against generated code and general assembler
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
bilinear_form = fem.form(a)
with Timer("~TEST: Assemble matrix"):
A_mpc = assemble_matrix(bilinear_form, mpc)
with Timer("~TEST: Compare with numpy"):
# Create globally reduced system
A_org = fem.petsc.assemble_matrix(bilinear_form)
A_org.assemble()
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A_mpc, mpc)
list_timings(mesh.comm, [TimingType.wall])
def test_mpc_assembly(master_point, degree, celltype,
get_assemblers): # noqa: F811
assemble_matrix, _ = get_assemblers
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 5, 3, celltype)
V = fem.FunctionSpace(mesh, ("Lagrange", degree))
# Test against generated code and general assembler
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
bilinear_form = fem.form(a)
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {
l2b([1, 0]): {
l2b([0, 1]): 0.43,
l2b([1, 1]): 0.11
},
l2b([0, 0]): {
l2b(master_point): 0.69
}
}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
with Timer("~TEST: Assemble matrix"):
A_mpc = assemble_matrix(bilinear_form, mpc)
with Timer("~TEST: Compare with numpy"):
# Create globally reduced system
A_org = fem.petsc.assemble_matrix(bilinear_form)
A_org.assemble()
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A_mpc, mpc)
def test_pipeline(u_from_mpc):
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 5, 5)
V = fem.FunctionSpace(mesh, ("Lagrange", 1))
# Solve Problem without MPC for reference
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
d = fem.Constant(mesh, PETSc.ScalarType(0.01))
x = ufl.SpatialCoordinate(mesh)
f = ufl.sin(2 * ufl.pi * x[0]) * ufl.sin(ufl.pi * x[1])
a = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx - d * ufl.inner(u, v) * ufl.dx
rhs = ufl.inner(f, v) * ufl.dx
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Generate reference matrices
A_org = fem.petsc.assemble_matrix(bilinear_form)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
# Create multipoint constraint
def periodic_relation(x):
out_x = np.copy(x)
out_x[0] = 1 - x[0]
return out_x
def PeriodicBoundary(x):
return np.isclose(x[0], 1)
facets = locate_entities_boundary(mesh, mesh.topology.dim - 1, PeriodicBoundary)
arg_sort = np.argsort(facets)
mt = meshtags(mesh, mesh.topology.dim - 1, facets[arg_sort], np.full(len(facets), 2, dtype=np.int32))
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_periodic_constraint_topological(V, mt, 2, periodic_relation, [], 1)
mpc.finalize()
if u_from_mpc:
uh = fem.Function(mpc.function_space)
problem = dolfinx_mpc.LinearProblem(bilinear_form, linear_form, mpc, bcs=[], u=uh,
petsc_options={"ksp_type": "preonly", "pc_type": "lu"})
problem.solve()
root = 0
dolfinx_mpc.utils.compare_mpc_lhs(A_org, problem.A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, problem.b, mpc, root=root)
# Gather LHS, RHS and solution on one process
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh.vector, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ L_np
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K @ d
assert np.allclose(uh_numpy, u_mpc)
else:
uh = fem.Function(V)
with pytest.raises(ValueError):
problem = dolfinx_mpc.LinearProblem(bilinear_form, linear_form, mpc, bcs=[], u=uh,
petsc_options={"ksp_type": "preonly", "pc_type": "lu"})
problem.solve()
def test_vector_possion(Nx, Ny, slave_space, master_space,
get_assemblers): # noqa: F811
assemble_matrix, assemble_vector = get_assemblers
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, Nx, Ny)
V = fem.VectorFunctionSpace(mesh, ("Lagrange", 1))
def boundary(x):
return np.isclose(x.T, [0, 0, 0]).all(axis=1)
# Define boundary conditions (HAS TO BE NON-MASTER NODES)
u_bc = fem.Function(V)
with u_bc.vector.localForm() as u_local:
u_local.set(0.0)
bdofsV = fem.locate_dofs_geometrical(V, boundary)
bc = fem.dirichletbc(u_bc, bdofsV)
bcs = [bc]
# Define variational problem
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
x = ufl.SpatialCoordinate(mesh)
f = ufl.as_vector((-5 * x[1], 7 * x[0]))
a = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
rhs = ufl.inner(f, v) * ufl.dx
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Setup LU solver
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
# Create multipoint constraint
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {l2b([1, 0]): {l2b([1, 1]): 0.1, l2b([0.5, 1]): 0.3}}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c, slave_space, master_space)
mpc.finalize()
with Timer("~TEST: Assemble matrix"):
A = assemble_matrix(bilinear_form, mpc, bcs=bcs)
with Timer("~TEST: Assemble vector"):
b = dolfinx_mpc.assemble_vector(linear_form, mpc)
dolfinx_mpc.apply_lifting(b, [bilinear_form], [bcs], mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(b, bcs)
solver.setOperators(A)
uh = b.copy()
uh.set(0)
solver.solve(b, uh)
uh.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
mpc.backsubstitution(uh)
# Generate reference matrices for unconstrained problem
A_org = fem.petsc.assemble_matrix(bilinear_form, bcs)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
fem.petsc.apply_lifting(L_org, [bilinear_form], [bcs])
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(L_org, bcs)
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
# Gather LHS, RHS and solution on one process
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ L_np
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K @ d
assert np.allclose(uh_numpy, u_mpc)
list_timings(comm, [TimingType.wall])
def test_nonlinear_possion(poly_order):
# Solve a standard Poisson problem with known solution which has
# rotational symmetry of pi/2 at (x, y) = (0.5, 0.5). Therefore we may
# impose MPCs on those DoFs which lie on the symmetry plane(s) and test
# our numerical approximation. We do not impose any constraints at the
# rotationally degenerate point (x, y) = (0.5, 0.5).
N_vals = np.array([4, 8, 16], dtype=np.int32)
l2_error = np.zeros_like(N_vals, dtype=np.double)
for run_no, N in enumerate(N_vals):
mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, N, N)
V = dolfinx.fem.FunctionSpace(mesh, ("Lagrange", poly_order))
def boundary(x):
return np.ones_like(x[0], dtype=np.int8)
u_bc = dolfinx.fem.Function(V)
with u_bc.vector.localForm() as u_local:
u_local.set(0.0)
facets = dolfinx.mesh.locate_entities_boundary(mesh, 1, boundary)
topological_dofs = dolfinx.fem.locate_dofs_topological(V, 1, facets)
zero = np.array(0, dtype=PETSc.ScalarType)
bc = dolfinx.fem.dirichletbc(zero, topological_dofs, V)
bcs = [bc]
# Define variational problem
u = dolfinx.fem.Function(V)
v = ufl.TestFunction(V)
x = ufl.SpatialCoordinate(mesh)
u_soln = ufl.sin(ufl.pi * x[0]) * ufl.sin(ufl.pi * x[1])
f = -ufl.div((1 + u_soln**2) * ufl.grad(u_soln))
F = ufl.inner((1 + u**2) * ufl.grad(u), ufl.grad(v)) * ufl.dx \
- ufl.inner(f, v) * ufl.dx
J = ufl.derivative(F, u)
# -- Impose the pi/2 rotational symmetry of the solution as a constraint,
# -- except at the centre DoF
def periodic_boundary(x):
eps = 1e-10
return np.isclose(x[0], 0.5) & ((x[1] < 0.5 - eps) |
(x[1] > 0.5 + eps))
def periodic_relation(x):
out_x = np.zeros(x.shape)
out_x[0] = x[1]
out_x[1] = x[0]
out_x[2] = x[2]
return out_x
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_periodic_constraint_geometrical(V, periodic_boundary,
periodic_relation, bcs)
mpc.finalize()
# Sanity check that the MPC class has some constraints to impose
num_slaves_global = mesh.comm.allreduce(len(mpc.slaves), op=MPI.SUM)
num_masters_global = mesh.comm.allreduce(len(mpc.masters.array),
op=MPI.SUM)
assert num_slaves_global > 0
assert num_masters_global == num_slaves_global
problem = NonlinearMPCProblem(F, u, mpc, bcs=bcs, J=J)
solver = NewtonSolverMPC(mesh.comm, problem, mpc)
# Ensure the solver works with nonzero initial guess
u.interpolate(lambda x: x[0]**2 * x[1]**2)
solver.solve(u)
l2_error_local = dolfinx.fem.assemble_scalar(
dolfinx.fem.form((u - u_soln)**2 * ufl.dx))
l2_error_global = mesh.comm.allreduce(l2_error_local, op=MPI.SUM)
l2_error[run_no] = l2_error_global**0.5
rates = np.log(l2_error[:-1] / l2_error[1:]) / np.log(2.0)
assert np.all(rates > poly_order + 0.9)
def test_pipeline(master_point, get_assemblers): # noqa: F811
assemble_matrix, assemble_vector = get_assemblers
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 3, 5)
V = fem.FunctionSpace(mesh, ("Lagrange", 1))
# Solve Problem without MPC for reference
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
d = fem.Constant(mesh, PETSc.ScalarType(1.5))
c = fem.Constant(mesh, PETSc.ScalarType(2))
x = ufl.SpatialCoordinate(mesh)
f = c * ufl.sin(2 * ufl.pi * x[0]) * ufl.sin(ufl.pi * x[1])
g = fem.Function(V)
g.interpolate(lambda x: np.sin(x[0]) * x[1])
h = fem.Function(V)
h.interpolate(lambda x: 2 + x[1] * x[0])
a = d * g * ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
rhs = h * ufl.inner(f, v) * ufl.dx
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Generate reference matrices
A_org = fem.petsc.assemble_matrix(bilinear_form)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
# Create multipoint constraint
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {
l2b([1, 0]): {
l2b([0, 1]): 0.43,
l2b([1, 1]): 0.11
},
l2b([0, 0]): {
l2b(master_point): 0.69
}
}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
A = assemble_matrix(bilinear_form, mpc)
b = assemble_vector(linear_form, mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
solver.setOperators(A)
# Solve
uh = b.copy()
uh.set(0)
solver.solve(b, uh)
uh.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
mpc.backsubstitution(uh)
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
# Gather LHS, RHS and solution on one process
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ L_np
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K @ d
assert np.allclose(uh_numpy, u_mpc)
list_timings(comm, [TimingType.wall])
def test_linearproblem(master_point):
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 3, 5)
V = fem.FunctionSpace(mesh, ("Lagrange", 1))
# Solve Problem without MPC for reference
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
d = fem.Constant(mesh, PETSc.ScalarType(1.5))
c = fem.Constant(mesh, PETSc.ScalarType(2))
x = ufl.SpatialCoordinate(mesh)
f = c * ufl.sin(2 * ufl.pi * x[0]) * ufl.sin(ufl.pi * x[1])
g = fem.Function(V)
g.interpolate(lambda x: np.sin(x[0]) * x[1])
h = fem.Function(V)
h.interpolate(lambda x: 2 + x[1] * x[0])
a = d * g * ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
rhs = h * ufl.inner(f, v) * ufl.dx
# Generate reference matrices
A_org = fem.petsc.assemble_matrix(fem.form(a))
A_org.assemble()
L_org = fem.petsc.assemble_vector(fem.form(rhs))
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
# Create multipoint constraint
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {
l2b([1, 0]): {
l2b([0, 1]): 0.43,
l2b([1, 1]): 0.11
},
l2b([0, 0]): {
l2b(master_point): 0.69
}
}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
problem = dolfinx_mpc.LinearProblem(a,
rhs,
mpc,
bcs=[],
petsc_options={
"ksp_type": "preonly",
"pc_type": "lu"
})
uh = problem.solve()
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, problem._A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, problem._b, mpc, root=root)
# Gather LHS, RHS and solution on one process
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh.vector, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ L_np
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K @ d
assert np.allclose(uh_numpy, u_mpc)
list_timings(comm, [TimingType.wall])
def test_surface_integrals(get_assemblers): # noqa: F811
assemble_matrix, assemble_vector = get_assemblers
N = 4
mesh = create_unit_square(MPI.COMM_WORLD, N, N)
V = fem.VectorFunctionSpace(mesh, ("Lagrange", 1))
# Fixed Dirichlet BC on the left wall
def left_wall(x):
return np.isclose(x[0], np.finfo(float).eps)
fdim = mesh.topology.dim - 1
left_facets = locate_entities_boundary(mesh, fdim, left_wall)
bc_dofs = fem.locate_dofs_topological(V, 1, left_facets)
u_bc = fem.Function(V)
with u_bc.vector.localForm() as u_local:
u_local.set(0.0)
bc = fem.dirichletbc(u_bc, bc_dofs)
bcs = [bc]
# Traction on top of domain
def top(x):
return np.isclose(x[1], 1)
top_facets = locate_entities_boundary(mesh, 1, top)
arg_sort = np.argsort(top_facets)
mt = meshtags(mesh, fdim, top_facets[arg_sort], np.full(len(top_facets), 3, dtype=np.int32))
ds = ufl.Measure("ds", domain=mesh, subdomain_data=mt, subdomain_id=3)
g = fem.Constant(mesh, PETSc.ScalarType((0, -9.81e2)))
# Elasticity parameters
E = PETSc.ScalarType(1.0e4)
nu = 0.0
mu = fem.Constant(mesh, E / (2.0 * (1.0 + nu)))
lmbda = fem.Constant(mesh, E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu)))
# Stress computation
def sigma(v):
return (2.0 * mu * ufl.sym(ufl.grad(v))
+ lmbda * ufl.tr(ufl.sym(ufl.grad(v))) * ufl.Identity(len(v)))
# Define variational problem
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(sigma(u), ufl.grad(v)) * ufl.dx
rhs = ufl.inner(fem.Constant(mesh, PETSc.ScalarType((0, 0))), v) * ufl.dx\
+ ufl.inner(g, v) * ds
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Setup LU solver
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
# Setup multipointconstraint
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {}
for i in range(1, N):
s_m_c[l2b([1, i / N])] = {l2b([1, 1]): 0.8}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c, 1, 1)
mpc.finalize()
with Timer("~TEST: Assemble matrix old"):
A = assemble_matrix(bilinear_form, mpc, bcs=bcs)
with Timer("~TEST: Assemble vector"):
b = assemble_vector(linear_form, mpc)
dolfinx_mpc.apply_lifting(b, [bilinear_form], [bcs], mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(b, bcs)
solver.setOperators(A)
uh = b.copy()
uh.set(0)
solver.solve(b, uh)
uh.ghostUpdate(addv=PETSc.InsertMode.INSERT, mode=PETSc.ScatterMode.FORWARD)
mpc.backsubstitution(uh)
# Write solution to file
# u_h = dolfinx.Function(mpc.function_space)
# u_h.vector.setArray(uh.array)
# u_h.name = "u_mpc"
# outfile = dolfinx.io.XDMFFile(MPI.COMM_WORLD, "output/uh.xdmf", "w")
# outfile.write_mesh(mesh)
# outfile.write_function(u_h)
# outfile.close()
# Solve the MPC problem using a global transformation matrix
# and numpy solvers to get reference values
# Generate reference matrices and unconstrained solution
A_org = fem.petsc.assemble_matrix(bilinear_form, bcs)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
fem.petsc.apply_lifting(L_org, [bilinear_form], [bcs])
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(L_org, bcs)
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
# Gather LHS, RHS and solution on one process
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ L_np
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K @ d
assert np.allclose(uh_numpy, u_mpc)
list_timings(comm, [TimingType.wall])
def test_surface_integral_dependency(get_assemblers): # noqa: F811
assemble_matrix, assemble_vector = get_assemblers
N = 10
mesh = create_unit_square(MPI.COMM_WORLD, N, N)
V = fem.VectorFunctionSpace(mesh, ("Lagrange", 1))
def top(x):
return np.isclose(x[1], 1)
fdim = mesh.topology.dim - 1
top_facets = locate_entities_boundary(mesh, fdim, top)
indices = np.array([], dtype=np.intc)
values = np.array([], dtype=np.intc)
markers = {3: top_facets}
for key in markers.keys():
indices = np.append(indices, markers[key])
values = np.append(values, np.full(len(markers[key]), key, dtype=np.intc))
sort = np.argsort(indices)
mt = meshtags(mesh, mesh.topology.dim - 1, np.array(indices[sort], dtype=np.intc),
np.array(values[sort], dtype=np.intc))
ds = ufl.Measure("ds", domain=mesh, subdomain_data=mt)
g = fem.Constant(mesh, PETSc.ScalarType((2, 1)))
h = fem.Constant(mesh, PETSc.ScalarType((3, 2)))
# Define variational problem
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(u, v) * ds(3) + ufl.inner(ufl.grad(u), ufl.grad(v)) * ds
rhs = ufl.inner(g, v) * ds + ufl.inner(h, v) * ds(3)
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Create multipoint constraint and assemble system
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {}
for i in range(1, N):
s_m_c[l2b([1, i / N])] = {l2b([1, 1]): 0.3}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c, 1, 1)
mpc.finalize()
with Timer("~TEST: Assemble matrix"):
A = assemble_matrix(bilinear_form, mpc)
with Timer("~TEST: Assemble vector"):
b = assemble_vector(linear_form, mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
# Solve the MPC problem using a global transformation matrix
# and numpy solvers to get reference values
# Generate reference matrices and unconstrained solution
A_org = fem.petsc.assemble_matrix(bilinear_form)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES, mode=PETSc.ScatterMode.REVERSE)
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
list_timings(comm, [TimingType.wall])
def test_cube_contact(generate_hex_boxes, nonslip,
get_assemblers): # noqa: F811
assemble_matrix, assemble_vector = get_assemblers
comm = MPI.COMM_WORLD
root = 0
# Generate mesh
mesh_data = generate_hex_boxes
mesh, mt = mesh_data
fdim = mesh.topology.dim - 1
# Create functionspaces
V = fem.VectorFunctionSpace(mesh, ("Lagrange", 1))
# Helper for orienting traction
# Bottom boundary is fixed in all directions
u_bc = fem.Function(V)
with u_bc.vector.localForm() as u_local:
u_local.set(0.0)
bottom_dofs = fem.locate_dofs_topological(V, fdim, mt.find(5))
bc_bottom = fem.dirichletbc(u_bc, bottom_dofs)
g_vec = [0, 0, -4.25e-1]
if not nonslip:
# Helper for orienting traction
r_matrix = dolfinx_mpc.utils.rotation_matrix(
[1 / np.sqrt(2), 1 / np.sqrt(2), 0], -theta)
# Top boundary has a given deformation normal to the interface
g_vec = np.dot(r_matrix, [0, 0, -4.25e-1])
# Top boundary has a given deformation normal to the interface
def top_v(x):
values = np.empty((3, x.shape[1]))
values[0] = g_vec[0]
values[1] = g_vec[1]
values[2] = g_vec[2]
return values
u_top = fem.Function(V)
u_top.interpolate(top_v)
top_dofs = fem.locate_dofs_topological(V, fdim, mt.find(3))
bc_top = fem.dirichletbc(u_top, top_dofs)
bcs = [bc_bottom, bc_top]
# Elasticity parameters
E = PETSc.ScalarType(1.0e3)
nu = 0
mu = fem.Constant(mesh, E / (2.0 * (1.0 + nu)))
lmbda = fem.Constant(mesh, E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu)))
# Stress computation
def sigma(v):
return (2.0 * mu * ufl.sym(ufl.grad(v)) +
lmbda * ufl.tr(ufl.sym(ufl.grad(v))) * ufl.Identity(len(v)))
# Define variational problem
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = ufl.inner(sigma(u), ufl.grad(v)) * ufl.dx
rhs = ufl.inner(fem.Constant(mesh, PETSc.ScalarType(
(0, 0, 0))), v) * ufl.dx
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Create LU solver
solver = PETSc.KSP().create(comm)
solver.setType("preonly")
solver.setTolerances(rtol=1.0e-14)
solver.getPC().setType("lu")
# Create MPC contact condition and assemble matrices
mpc = dolfinx_mpc.MultiPointConstraint(V)
if nonslip:
with Timer("~Contact: Create non-elastic constraint"):
mpc.create_contact_inelastic_condition(mt, 4, 9)
else:
with Timer("~Contact: Create contact constraint"):
nh = dolfinx_mpc.utils.create_normal_approximation(V, mt, 4)
mpc.create_contact_slip_condition(mt, 4, 9, nh)
mpc.finalize()
with Timer("~TEST: Assemble bilinear form"):
A = assemble_matrix(bilinear_form, mpc, bcs=bcs)
with Timer("~TEST: Assemble vector"):
b = assemble_vector(linear_form, mpc)
dolfinx_mpc.apply_lifting(b, [bilinear_form], [bcs], mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(b, bcs)
with Timer("~MPC: Solve"):
solver.setOperators(A)
uh = b.copy()
uh.set(0)
solver.solve(b, uh)
uh.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
mpc.backsubstitution(uh)
# Write solution to file
# u_h = fem.Function(mpc.function_space)
# u_h.vector.setArray(uh.array)
# u_h.x.scatter_forward()
# u_h.name = "u_{0:.2f}".format(theta)
# import dolfinx.io as io
# with io.XDMFFile(comm, "output/rotated_cube3D.xdmf", "w") as outfile:
# outfile.write_mesh(mesh)
# outfile.write_function(u_h, 0.0, f"Xdmf/Domain/Grid[@Name='{mesh.name}'][1]")
# Solve the MPC problem using a global transformation matrix
# and numpy solvers to get reference values
dolfinx_mpc.utils.log_info(
"Solving reference problem with global matrix (using numpy)")
with Timer("~TEST: Assemble bilinear form (unconstrained)"):
A_org = fem.petsc.assemble_matrix(bilinear_form, bcs)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
fem.petsc.apply_lifting(L_org, [bilinear_form], [bcs])
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(L_org, bcs)
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
# Gather LHS, RHS and solution on one process
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ L_np
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K @ d
assert np.allclose(uh_numpy, u_mpc)
list_timings(comm, [TimingType.wall])
def test_lifting(get_assemblers): # noqa: F811
"""
Test MPC lifting operation on a single cell
"""
assemble_matrix, assemble_vector = get_assemblers
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 1, 1, CellType.quadrilateral)
V = fem.FunctionSpace(mesh, ("Lagrange", 1))
# Solve Problem without MPC for reference
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
x = ufl.SpatialCoordinate(mesh)
f = x[1] * ufl.sin(2 * ufl.pi * x[0])
a = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
rhs = ufl.inner(f, v) * ufl.dx
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Create Dirichlet boundary condition
u_bc = fem.Function(V)
with u_bc.vector.localForm() as u_local:
u_local.set(2.3)
def dirichletboundary(x):
return np.isclose(x[0], 1)
mesh.topology.create_connectivity(2, 1)
geometrical_dofs = fem.locate_dofs_geometrical(V, dirichletboundary)
bc = fem.dirichletbc(u_bc, geometrical_dofs)
bcs = [bc]
# Generate reference matrices
A_org = fem.petsc.assemble_matrix(bilinear_form, bcs=bcs)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
fem.petsc.apply_lifting(L_org, [bilinear_form], [bcs])
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(L_org, bcs)
# Create multipoint constraint
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {l2b([0, 0]): {l2b([0, 1]): 1}}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
A = assemble_matrix(bilinear_form, mpc, bcs=bcs)
b = assemble_vector(linear_form, mpc)
dolfinx_mpc.apply_lifting(b, [bilinear_form], [bcs], mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
fem.petsc.set_bc(b, bcs)
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
solver.setOperators(A)
# Solve
uh = b.copy()
uh.set(0)
solver.solve(b, uh)
uh.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
mpc.backsubstitution(uh)
V_mpc = mpc.function_space
u_out = fem.Function(V_mpc)
u_out.vector.array[:] = uh.array
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
# Gather LHS, RHS and solution on one process
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh, root=root)
# constants = dolfinx_mpc.utils.gather_contants(mpc, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ (L_np) # - constants)
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vecto
uh_numpy = K @ (d) # + constants)
assert np.allclose(uh_numpy, u_mpc)
list_timings(comm, [TimingType.wall])
def test_cell_domains(get_assemblers): # noqa: F811
"""
Periodic MPC conditions over integral with different cell subdomains
"""
assemble_matrix, assemble_vector = get_assemblers
N = 5
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 15, N)
V = fem.FunctionSpace(mesh, ("Lagrange", 1))
def left_side(x):
return x[0] < 0.5
tdim = mesh.topology.dim
num_cells = mesh.topology.index_map(tdim).size_local
cell_midpoints = compute_midpoints(mesh, tdim, range(num_cells))
values = np.ones(num_cells, dtype=np.intc)
# All cells on right side marked one, all other with 1
values += left_side(cell_midpoints.T)
ct = meshtags(mesh, mesh.topology.dim, np.arange(num_cells,
dtype=np.int32), values)
# Solve Problem without MPC for reference
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
x = ufl.SpatialCoordinate(mesh)
c1 = fem.Constant(mesh, PETSc.ScalarType(2))
c2 = fem.Constant(mesh, PETSc.ScalarType(10))
dx = ufl.Measure("dx", domain=mesh, subdomain_data=ct)
a = c1 * ufl.inner(ufl.grad(u), ufl.grad(v)) * dx(1) +\
c2 * ufl.inner(ufl.grad(u), ufl.grad(v)) * dx(2)\
+ 0.01 * ufl.inner(u, v) * dx(1)
rhs = ufl.inner(x[1], v) * dx(1) + \
ufl.inner(fem.Constant(mesh, PETSc.ScalarType(1)), v) * dx(2)
bilinear_form = fem.form(a)
linear_form = fem.form(rhs)
# Generate reference matrices
A_org = fem.petsc.assemble_matrix(bilinear_form)
A_org.assemble()
L_org = fem.petsc.assemble_vector(linear_form)
L_org.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
def l2b(li):
return np.array(li, dtype=np.float64).tobytes()
s_m_c = {}
for i in range(0, N + 1):
s_m_c[l2b([1, i / N])] = {l2b([0, i / N]): 1}
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_general_constraint(s_m_c)
mpc.finalize()
# Setup MPC system
with Timer("~TEST: Assemble matrix old"):
A = assemble_matrix(bilinear_form, mpc)
with Timer("~TEST: Assemble vector"):
b = assemble_vector(linear_form, mpc)
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setType(PETSc.KSP.Type.PREONLY)
solver.getPC().setType(PETSc.PC.Type.LU)
solver.setOperators(A)
# Solve
uh = b.copy()
uh.set(0)
solver.solve(b, uh)
uh.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
mpc.backsubstitution(uh)
root = 0
comm = mesh.comm
with Timer("~TEST: Compare"):
dolfinx_mpc.utils.compare_mpc_lhs(A_org, A, mpc, root=root)
dolfinx_mpc.utils.compare_mpc_rhs(L_org, b, mpc, root=root)
# Gather LHS, RHS and solution on one process
A_csr = dolfinx_mpc.utils.gather_PETScMatrix(A_org, root=root)
K = dolfinx_mpc.utils.gather_transformation_matrix(mpc, root=root)
L_np = dolfinx_mpc.utils.gather_PETScVector(L_org, root=root)
u_mpc = dolfinx_mpc.utils.gather_PETScVector(uh, root=root)
if MPI.COMM_WORLD.rank == root:
KTAK = K.T * A_csr * K
reduced_L = K.T @ L_np
# Solve linear system
d = scipy.sparse.linalg.spsolve(KTAK, reduced_L)
# Back substitution to full solution vector
uh_numpy = K @ d
assert np.allclose(uh_numpy, u_mpc)
list_timings(comm, [TimingType.wall])
# ----------------------Defining boundary conditions----------------------
# Inlet velocity Dirichlet BC
inlet_velocity = dolfinx.fem.Function(V)
inlet_velocity.interpolate(inlet_velocity_expression)
inlet_velocity.x.scatter_forward()
dofs = dolfinx.fem.locate_dofs_topological(V, 1, mt.find(3))
bc1 = dolfinx.fem.dirichletbc(inlet_velocity, dofs)
# Collect Dirichlet boundary conditions
bcs = [bc1]
# Slip conditions for walls
n = dolfinx_mpc.utils.create_normal_approximation(V, mt, 1)
with dolfinx.common.Timer("~Stokes: Create slip constraint"):
mpc = dolfinx_mpc.MultiPointConstraint(V)
mpc.create_slip_constraint(V, (mt, 1), n, bcs=bcs)
mpc.finalize()
mpc_q = dolfinx_mpc.MultiPointConstraint(Q)
mpc_q.finalize()
def tangential_proj(u: Expr, n: Expr):
"""
See for instance:
https://link.springer.com/content/pdf/10.1023/A:1022235512626.pdf
"""
return (ufl.Identity(u.ufl_shape[0]) - ufl.outer(n, n)) * u
def test_mixed_element(cell_type, ghost_mode):
N = 4
mesh = dolfinx.mesh.create_unit_square(
MPI.COMM_WORLD, N, N, cell_type=cell_type, ghost_mode=ghost_mode)
# Inlet velocity Dirichlet BC
bc_facets = dolfinx.mesh.locate_entities_boundary(
mesh, mesh.topology.dim - 1, lambda x: np.isclose(x[0], 0.0))
other_facets = dolfinx.mesh.locate_entities_boundary(
mesh, mesh.topology.dim - 1, lambda x: np.isclose(x[0], 1.0))
arg_sort = np.argsort(other_facets)
mt = dolfinx.mesh.meshtags(mesh, mesh.topology.dim - 1,
other_facets[arg_sort], np.full_like(other_facets, 1))
# Rotate the mesh to induce more interesting slip BCs
th = np.pi / 4.0
rot = np.array([[np.cos(th), -np.sin(th)],
[np.sin(th), np.cos(th)]])
gdim = mesh.geometry.dim
mesh.geometry.x[:, :gdim] = (rot @ mesh.geometry.x[:, :gdim].T).T
# Create the function space
Ve = ufl.VectorElement("Lagrange", mesh.ufl_cell(), 2)
Qe = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
V = dolfinx.fem.FunctionSpace(mesh, Ve)
Q = dolfinx.fem.FunctionSpace(mesh, Qe)
W = dolfinx.fem.FunctionSpace(mesh, Ve * Qe)
inlet_velocity = dolfinx.fem.Function(V)
inlet_velocity.interpolate(
lambda x: np.zeros((mesh.geometry.dim, x[0].shape[0]), dtype=np.double))
inlet_velocity.x.scatter_forward()
# -- Nested assembly
dofs = dolfinx.fem.locate_dofs_topological(V, 1, bc_facets)
bc1 = dolfinx.fem.dirichletbc(inlet_velocity, dofs)
# Collect Dirichlet boundary conditions
bcs = [bc1]
mpc_v = dolfinx_mpc.MultiPointConstraint(V)
n_approx = dolfinx_mpc.utils.create_normal_approximation(V, mt, 1)
mpc_v.create_slip_constraint(V, (mt, 1), n_approx, bcs=bcs)
mpc_v.finalize()
mpc_q = dolfinx_mpc.MultiPointConstraint(Q)
mpc_q.finalize()
f = dolfinx.fem.Constant(mesh, PETSc.ScalarType((0, 0)))
(u, p) = ufl.TrialFunction(V), ufl.TrialFunction(Q)
(v, q) = ufl.TestFunction(V), ufl.TestFunction(Q)
a00 = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
a01 = - ufl.inner(p, ufl.div(v)) * ufl.dx
a10 = - ufl.inner(ufl.div(u), q) * ufl.dx
a11 = None
L0 = ufl.inner(f, v) * ufl.dx
L1 = ufl.inner(
dolfinx.fem.Constant(mesh, PETSc.ScalarType(0.0)), q) * ufl.dx
n = ufl.FacetNormal(mesh)
g_tau = ufl.as_vector((0.0, 0.0))
ds = ufl.Measure("ds", domain=mesh, subdomain_data=mt, subdomain_id=1)
a00 -= ufl.inner(ufl.outer(n, n) * ufl.dot(ufl.grad(u), n), v) * ds
a01 -= ufl.inner(ufl.outer(n, n) * ufl.dot(
- p * ufl.Identity(u.ufl_shape[0]), n), v) * ds
L0 += ufl.inner(g_tau, v) * ds
a_nest = dolfinx.fem.form(((a00, a01),
(a10, a11)))
L_nest = dolfinx.fem.form((L0, L1))
# Assemble MPC nest matrix
A_nest = dolfinx_mpc.create_matrix_nest(a_nest, [mpc_v, mpc_q])
dolfinx_mpc.assemble_matrix_nest(A_nest, a_nest, [mpc_v, mpc_q], bcs)
A_nest.assemble()
# Assemble original nest matrix
A_org_nest = dolfinx.fem.petsc.assemble_matrix_nest(a_nest, bcs)
A_org_nest.assemble()
# MPC nested rhs
b_nest = dolfinx_mpc.create_vector_nest(L_nest, [mpc_v, mpc_q])
dolfinx_mpc.assemble_vector_nest(b_nest, L_nest, [mpc_v, mpc_q])
dolfinx.fem.petsc.apply_lifting_nest(b_nest, a_nest, bcs)
for b_sub in b_nest.getNestSubVecs():
b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
bcs0 = dolfinx.fem.bcs_by_block(
dolfinx.fem.extract_function_spaces(L_nest), bcs)
dolfinx.fem.petsc.set_bc_nest(b_nest, bcs0)
# Original dolfinx rhs
b_org_nest = dolfinx.fem.petsc.assemble_vector_nest(L_nest)
dolfinx.fem.petsc.apply_lifting_nest(b_org_nest, a_nest, bcs)
for b_sub in b_org_nest.getNestSubVecs():
b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.petsc.set_bc_nest(b_org_nest, bcs0)
# -- Monolithic assembly
dofs = dolfinx.fem.locate_dofs_topological((W.sub(0), V), 1, bc_facets)
bc1 = dolfinx.fem.dirichletbc(inlet_velocity, dofs, W.sub(0))
bcs = [bc1]
V, V_to_W = W.sub(0).collapse()
mpc_vq = dolfinx_mpc.MultiPointConstraint(W)
n_approx = dolfinx_mpc.utils.create_normal_approximation(V, mt, 1)
mpc_vq.create_slip_constraint(W.sub(0), (mt, 1), n_approx, bcs=bcs)
mpc_vq.finalize()
f = dolfinx.fem.Constant(mesh, PETSc.ScalarType((0, 0)))
(u, p) = ufl.TrialFunctions(W)
(v, q) = ufl.TestFunctions(W)
a = (
ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
- ufl.inner(p, ufl.div(v)) * ufl.dx
- ufl.inner(ufl.div(u), q) * ufl.dx
)
L = ufl.inner(f, v) * ufl.dx + ufl.inner(
dolfinx.fem.Constant(mesh, PETSc.ScalarType(0.0)), q) * ufl.dx
# No prescribed shear stress
n = ufl.FacetNormal(mesh)
g_tau = ufl.as_vector((0.0, 0.0))
ds = ufl.Measure("ds", domain=mesh, subdomain_data=mt, subdomain_id=1)
# Terms due to slip condition
# Explained in for instance: https://arxiv.org/pdf/2001.10639.pdf
a -= ufl.inner(ufl.outer(n, n) * ufl.dot(ufl.grad(u), n), v) * ds
a -= ufl.inner(ufl.outer(n, n) * ufl.dot(
- p * ufl.Identity(u.ufl_shape[0]), n), v) * ds
L += ufl.inner(g_tau, v) * ds
a, L = dolfinx.fem.form(a), dolfinx.fem.form(L)
# Assemble LHS matrix and RHS vector
A = dolfinx_mpc.assemble_matrix(a, mpc_vq, bcs)
A.assemble()
A_org = dolfinx.fem.petsc.assemble_matrix(a, bcs)
A_org.assemble()
b = dolfinx_mpc.assemble_vector(L, mpc_vq)
b_org = dolfinx.fem.petsc.assemble_vector(L)
# Set Dirichlet boundary condition values in the RHS
dolfinx_mpc.apply_lifting(b, [a], [bcs], mpc_vq)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.petsc.set_bc(b, bcs)
dolfinx.fem.petsc.apply_lifting(b_org, [a], [bcs])
b_org.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.petsc.set_bc(b_org, bcs)
# -- Verification
def nest_matrix_norm(A):
assert A.getType() == "nest"
nrows, ncols = A.getNestSize()
sub_A = [A.getNestSubMatrix(row, col)
for row in range(nrows) for col in range(ncols)]
return sum(map(lambda A_: A_.norm()**2 if A_ else 0.0, sub_A))**0.5
# -- Ensure monolithic and nest matrices are the same
assert np.isclose(nest_matrix_norm(A_nest), A.norm())