def xtest_mg_solver_stokes():
mesh0 = UnitCubeMesh(2, 2, 2)
mesh1 = UnitCubeMesh(4, 4, 4)
mesh2 = UnitCubeMesh(8, 8, 8)
Ve = VectorElement("CG", mesh0.ufl_cell(), 2)
Qe = FiniteElement("CG", mesh0.ufl_cell(), 1)
Ze = MixedElement([Ve, Qe])
Z0 = FunctionSpace(mesh0, Ze)
Z1 = FunctionSpace(mesh1, Ze)
Z2 = FunctionSpace(mesh2, Ze)
W = Z2
# Boundaries
def right(x, on_boundary):
return x[0] > (1.0 - DOLFIN_EPS)
def left(x, on_boundary):
return x[0] < DOLFIN_EPS
def top_bottom(x, on_boundary):
return x[1] > 1.0 - DOLFIN_EPS or x[1] < DOLFIN_EPS
# No-slip boundary condition for velocity
noslip = Constant((0.0, 0.0, 0.0))
bc0 = DirichletBC(W.sub(0), noslip, top_bottom)
# Inflow boundary condition for velocity
inflow = Expression(("-sin(x[1]*pi)", "0.0", "0.0"), degree=2)
bc1 = DirichletBC(W.sub(0), inflow, right)
# Collect boundary conditions
bcs = [bc0, bc1]
# Define variational problem
(u, p) = TrialFunctions(W)
(v, q) = TestFunctions(W)
f = Constant((0.0, 0.0, 0.0))
a = inner(grad(u), grad(v)) * dx + div(v) * p * dx + q * div(u) * dx
L = inner(f, v) * dx
# Form for use in constructing preconditioner matrix
b = inner(grad(u), grad(v)) * dx + p * q * dx
# Assemble system
A, bb = assemble_system(a, L, bcs)
# Assemble preconditioner system
P, btmp = assemble_system(b, L, bcs)
spaces = [Z0, Z1, Z2]
dm_collection = PETScDMCollection(spaces)
solver = PETScKrylovSolver()
solver.set_operators(A, P)
PETScOptions.set("ksp_type", "gcr")
PETScOptions.set("pc_type", "mg")
PETScOptions.set("pc_mg_levels", 3)
PETScOptions.set("pc_mg_galerkin")
PETScOptions.set("ksp_monitor_true_residual")
PETScOptions.set("ksp_atol", 1.0e-10)
PETScOptions.set("ksp_rtol", 1.0e-10)
solver.set_from_options()
from petsc4py import PETSc
ksp = solver.ksp()
ksp.setDM(dm_collection.dm())
ksp.setDMActive(False)
x = PETScVector()
solver.solve(x, bb)
# Check multigrid solution against LU solver
solver = LUSolver(A) # noqa
x_lu = PETScVector()
solver.solve(x_lu, bb)
assert round((x - x_lu).norm("l2"), 10) == 0
# Clear all PETSc options
opts = PETSc.Options()
for key in opts.getAll():
opts.delValue(key)
def test_krylov_reuse_pc():
"Test preconditioner re-use with PETScKrylovSolver"
# Define problem
mesh = UnitSquareMesh(MPI.comm_world, 8, 8)
V = FunctionSpace(mesh, ('Lagrange', 1))
bc = DirichletBC(V, Constant(0.0), lambda x, on_boundary: on_boundary)
u = TrialFunction(V)
v = TestFunction(V)
# Forms
a, L = inner(grad(u), grad(v)) * dx, dot(Constant(1.0), v) * dx
A, P = PETScMatrix(), PETScMatrix()
b = PETScVector()
# Assemble linear algebra objects
assemble(a, tensor=A) # noqa
assemble(a, tensor=P) # noqa
assemble(L, tensor=b) # noqa
# Apply boundary conditions
bc.apply(A)
bc.apply(P)
bc.apply(b)
# Create Krysolv solver and set operators
solver = PETScKrylovSolver("gmres", "bjacobi")
solver.set_operators(A, P)
# Solve
x = PETScVector()
num_iter_ref = solver.solve(x, b)
# Change preconditioner matrix (bad matrix) and solve (PC will be
# updated)
a_p = u * v * dx
assemble(a_p, tensor=P) # noqa
bc.apply(P)
x = PETScVector()
num_iter_mod = solver.solve(x, b)
assert num_iter_mod > num_iter_ref
# Change preconditioner matrix (good matrix) and solve (PC will be
# updated)
a_p = a
assemble(a_p, tensor=P) # noqa
bc.apply(P)
x = PETScVector()
num_iter = solver.solve(x, b)
assert num_iter == num_iter_ref
# Change preconditioner matrix (bad matrix) and solve (PC will not
# be updated)
solver.set_reuse_preconditioner(True)
a_p = u * v * dx
assemble(a_p, tensor=P) # noqa
bc.apply(P)
x = PETScVector()
num_iter = solver.solve(x, b)
assert num_iter == num_iter_ref
# Update preconditioner (bad PC, will increase iteration count)
solver.set_reuse_preconditioner(False)
x = PETScVector()
num_iter = solver.solve(x, b)
assert num_iter == num_iter_mod
