def F_nest(self, snes, x, F):
assert x.getType() == "nest" and F.getType() == "nest"
# Update solution
x = x.getNestSubVecs()
for x_sub, var_sub in zip(x, self.soln_vars):
x_sub.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
with x_sub.localForm() as _x:
var_sub.x.array[:] = _x.array_r
# Assemble
bcs1 = bcs_by_block(extract_function_spaces(self.a, 1), self.bcs)
for L, F_sub, a in zip(self.L, F.getNestSubVecs(), self.a):
with F_sub.localForm() as F_sub_local:
F_sub_local.set(0.0)
assemble_vector(F_sub, L)
apply_lifting(F_sub, a, bcs=bcs1, x0=x, scale=-1.0)
F_sub.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
# Set bc value in RHS
bcs0 = bcs_by_block(extract_function_spaces(self.L), self.bcs)
for F_sub, bc, x_sub in zip(F.getNestSubVecs(), bcs0, x):
set_bc(F_sub, bc, x_sub, -1.0)
# Must assemble F here in the case of nest matrices
F.assemble()
def test_extract_forms():
"""Test extraction on unique function spaces for rows and columns of
a block system"""
mesh = create_unit_square(MPI.COMM_WORLD, 32, 31)
V0 = FunctionSpace(mesh, ("Lagrange", 1))
V1 = FunctionSpace(mesh, ("Lagrange", 2))
V2 = V0.clone()
V3 = V1.clone()
v0, u0 = TestFunction(V0), TrialFunction(V0)
v1, u1 = TestFunction(V1), TrialFunction(V1)
v2, u2 = TestFunction(V2), TrialFunction(V2)
v3, u3 = TestFunction(V3), TrialFunction(V3)
a = form([[inner(u0, v0) * dx, inner(u1, v1) * dx],
[inner(u2, v2) * dx, inner(u3, v3) * dx]])
with pytest.raises(AssertionError):
extract_function_spaces(a, 0)
with pytest.raises(AssertionError):
extract_function_spaces(a, 1)
a = form([[inner(u0, v0) * dx, inner(u2, v1) * dx],
[inner(u0, v2) * dx, inner(u2, v2) * dx]])
with pytest.raises(AssertionError):
extract_function_spaces(a, 0)
Vc = extract_function_spaces(a, 1)
assert Vc[0] is V0._cpp_object
assert Vc[1] is V2._cpp_object
a = form([[inner(u0, v0) * dx, inner(u1, v0) * dx],
[inner(u2, v1) * dx, inner(u3, v1) * dx]])
Vr = extract_function_spaces(a, 0)
assert Vr[0] is V0._cpp_object
assert Vr[1] is V1._cpp_object
with pytest.raises(AssertionError):
extract_function_spaces(a, 1)
def nested_solve():
"""Nested solver"""
A = assemble_matrix_nest(form([[a00, a01], [a10, a11]]),
bcs=[bc0, bc1],
mat_types=[["baij", "aij"], ["aij", ""]])
A.assemble()
P = assemble_matrix_nest(form([[p00, p01], [p10, p11]]),
bcs=[bc0, bc1],
mat_types=[["aij", "aij"], ["aij", ""]])
P.assemble()
b = assemble_vector_nest(form([L0, L1]))
apply_lifting_nest(b, form([[a00, a01], [a10, a11]]), [bc0, bc1])
for b_sub in b.getNestSubVecs():
b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
bcs = bcs_by_block(extract_function_spaces(form([L0, L1])), [bc0, bc1])
set_bc_nest(b, bcs)
b.assemble()
ksp = PETSc.KSP()
ksp.create(mesh.comm)
ksp.setOperators(A, P)
nested_IS = P.getNestISs()
ksp.setType("minres")
pc = ksp.getPC()
pc.setType("fieldsplit")
pc.setFieldSplitIS(["u", nested_IS[0][0]], ["p", nested_IS[1][1]])
ksp_u, ksp_p = pc.getFieldSplitSubKSP()
ksp_u.setType("preonly")
ksp_u.getPC().setType('lu')
ksp_p.setType("preonly")
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 = b.copy()
ksp.solve(b, x)
assert ksp.getConvergedReason() > 0
return b.norm(), x.norm(), nest_matrix_norm(A), nest_matrix_norm(P)
# Next, the right-hand side vector is assembled and then modified to
# account for non-homogeneous Dirichlet boundary conditions:
# +
b = fem.petsc.assemble_vector_nest(L)
# Modify ('lift') the RHS for Dirichlet boundary conditions
fem.petsc.apply_lifting_nest(b, a, bcs=bcs)
# Sum contributions from ghost entries on the owner
for b_sub in b.getNestSubVecs():
b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
# Set Dirichlet boundary condition values in the RHS
bcs0 = fem.bcs_by_block(extract_function_spaces(L), bcs)
fem.petsc.set_bc_nest(b, bcs0)
# -
# Ths pressure field for this problem is determined only up to a
# constant. We can supply the vector that spans the nullspace and any
# component of the solution in this direction will be eliminated during
# the iterative linear solution process.
# +
# Create nullspace vector
null_vec = fem.petsc.create_vector_nest(L)
# Set velocity part to zero and the pressure part to a non-zero constant
null_vecs = null_vec.getNestSubVecs()
null_vecs[0].set(0.0), null_vecs[1].set(1.0)