def test_assembly_solve_block(mode):
"""Solve a two-field mass-matrix like problem with block matrix approaches
and test that solution is the same.
"""
mesh = UnitSquareMesh(MPI.COMM_WORLD, 32, 31, ghost_mode=mode)
P = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
V0 = dolfinx.fem.FunctionSpace(mesh, P)
V1 = V0.clone()
def boundary(x):
return numpy.logical_or(x[0] < 1.0e-6, x[0] > 1.0 - 1.0e-6)
# Locate facets on boundary
facetdim = mesh.topology.dim - 1
bndry_facets = dolfinx.mesh.locate_entities_boundary(
mesh, facetdim, boundary)
bdofsV0 = dolfinx.fem.locate_dofs_topological(V0, facetdim, bndry_facets)
bdofsV1 = dolfinx.fem.locate_dofs_topological(V1, facetdim, bndry_facets)
u_bc0 = dolfinx.fem.Function(V0)
u_bc0.vector.set(50.0)
u_bc0.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
u_bc1 = dolfinx.fem.Function(V1)
u_bc1.vector.set(20.0)
u_bc1.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
bcs = [
dolfinx.fem.dirichletbc.DirichletBC(u_bc0, bdofsV0),
dolfinx.fem.dirichletbc.DirichletBC(u_bc1, bdofsV1)
]
# Variational problem
u, p = ufl.TrialFunction(V0), ufl.TrialFunction(V1)
v, q = ufl.TestFunction(V0), ufl.TestFunction(V1)
f = 1.0
g = -3.0
zero = dolfinx.Function(V0)
a00 = inner(u, v) * dx
a01 = zero * inner(p, v) * dx
a10 = zero * inner(u, q) * dx
a11 = inner(p, q) * dx
L0 = inner(f, v) * dx
L1 = inner(g, q) * dx
def monitor(ksp, its, rnorm):
pass
# print("Norm:", its, rnorm)
A0 = dolfinx.fem.assemble_matrix_block([[a00, a01], [a10, a11]], bcs)
b0 = dolfinx.fem.assemble_vector_block([L0, L1], [[a00, a01], [a10, a11]],
bcs)
A0.assemble()
A0norm = A0.norm()
b0norm = b0.norm()
x0 = A0.createVecLeft()
ksp = PETSc.KSP()
ksp.create(mesh.mpi_comm())
ksp.setOperators(A0)
ksp.setMonitor(monitor)
ksp.setType('cg')
ksp.setTolerances(rtol=1.0e-14)
ksp.setFromOptions()
ksp.solve(b0, x0)
x0norm = x0.norm()
# Nested (MatNest)
A1 = dolfinx.fem.assemble_matrix_nest([[a00, a01], [a10, a11]],
bcs,
diagonal=1.0)
A1.assemble()
b1 = dolfinx.fem.assemble_vector_nest([L0, L1])
dolfinx.fem.apply_lifting_nest(b1, [[a00, a01], [a10, a11]], bcs)
for b_sub in b1.getNestSubVecs():
b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
bcs0 = dolfinx.cpp.fem.bcs_rows(
dolfinx.fem.assemble._create_cpp_form([L0, L1]), bcs)
dolfinx.fem.set_bc_nest(b1, bcs0)
b1.assemble()
b1norm = b1.norm()
assert b1norm == pytest.approx(b0norm, 1.0e-12)
A1norm = nest_matrix_norm(A1)
assert A0norm == pytest.approx(A1norm, 1.0e-12)
x1 = b1.copy()
ksp = PETSc.KSP()
ksp.create(mesh.mpi_comm())
ksp.setMonitor(monitor)
ksp.setOperators(A1)
ksp.setType('cg')
ksp.setTolerances(rtol=1.0e-12)
ksp.setFromOptions()
ksp.solve(b1, x1)
x1norm = x1.norm()
assert x1norm == pytest.approx(x0norm, rel=1.0e-12)
# Monolithic version
E = P * P
W = dolfinx.fem.FunctionSpace(mesh, E)
u0, u1 = ufl.TrialFunctions(W)
v0, v1 = ufl.TestFunctions(W)
a = inner(u0, v0) * dx + inner(u1, v1) * dx
L = inner(f, v0) * ufl.dx + inner(g, v1) * dx
u0_bc = dolfinx.fem.Function(V0)
u0_bc.vector.set(50.0)
u0_bc.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
u1_bc = dolfinx.fem.Function(V1)
u1_bc.vector.set(20.0)
u1_bc.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
bdofsW0_V0 = dolfinx.fem.locate_dofs_topological((W.sub(0), V0), facetdim,
bndry_facets)
bdofsW1_V1 = dolfinx.fem.locate_dofs_topological((W.sub(1), V1), facetdim,
bndry_facets)
bcs = [
dolfinx.fem.dirichletbc.DirichletBC(u0_bc, bdofsW0_V0, W.sub(0)),
dolfinx.fem.dirichletbc.DirichletBC(u1_bc, bdofsW1_V1, W.sub(1))
]
A2 = dolfinx.fem.assemble_matrix(a, bcs)
A2.assemble()
b2 = dolfinx.fem.assemble_vector(L)
dolfinx.fem.apply_lifting(b2, [a], [bcs])
b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.set_bc(b2, bcs)
A2norm = A2.norm()
b2norm = b2.norm()
assert A2norm == pytest.approx(A0norm, 1.0e-12)
assert b2norm == pytest.approx(b0norm, 1.0e-12)
x2 = b2.copy()
ksp = PETSc.KSP()
ksp.create(mesh.mpi_comm())
ksp.setMonitor(monitor)
ksp.setOperators(A2)
ksp.setType('cg')
ksp.getPC().setType('jacobi')
ksp.setTolerances(rtol=1.0e-12)
ksp.setFromOptions()
ksp.solve(b2, x2)
x2norm = x2.norm()
assert x2norm == pytest.approx(x0norm, 1.0e-10)
def test_matrix_assembly_block(mode):
"""Test assembly of block matrices and vectors into (a) monolithic
blocked structures, PETSc Nest structures, and monolithic structures.
"""
mesh = UnitSquareMesh(MPI.COMM_WORLD, 4, 8, ghost_mode=mode)
p0, p1 = 1, 2
P0 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), p0)
P1 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), p1)
V0 = dolfinx.fem.FunctionSpace(mesh, P0)
V1 = dolfinx.fem.FunctionSpace(mesh, P1)
def boundary(x):
return numpy.logical_or(x[0] < 1.0e-6, x[0] > 1.0 - 1.0e-6)
# Locate facets on boundary
facetdim = mesh.topology.dim - 1
bndry_facets = dolfinx.mesh.locate_entities_boundary(
mesh, facetdim, boundary)
bdofsV1 = dolfinx.fem.locate_dofs_topological(V1, facetdim, bndry_facets)
u_bc = dolfinx.fem.Function(V1)
with u_bc.vector.localForm() as u_local:
u_local.set(50.0)
bc = dolfinx.fem.dirichletbc.DirichletBC(u_bc, bdofsV1)
# Define variational problem
u, p = ufl.TrialFunction(V0), ufl.TrialFunction(V1)
v, q = ufl.TestFunction(V0), ufl.TestFunction(V1)
f = 1.0
g = -3.0
zero = dolfinx.Function(V0)
a00 = inner(u, v) * dx
a01 = inner(p, v) * dx
a10 = inner(u, q) * dx
a11 = inner(p, q) * dx
L0 = zero * inner(f, v) * dx
L1 = inner(g, q) * dx
a_block = [[a00, a01], [a10, a11]]
L_block = [L0, L1]
# Monolithic blocked
A0 = dolfinx.fem.assemble_matrix_block(a_block, [bc])
A0.assemble()
b0 = dolfinx.fem.assemble_vector_block(L_block, a_block, [bc])
assert A0.getType() != "nest"
Anorm0 = A0.norm()
bnorm0 = b0.norm()
# Nested (MatNest)
A1 = dolfinx.fem.assemble_matrix_nest(a_block, [bc],
[["baij", "aij"], ["aij", ""]])
A1.assemble()
Anorm1 = nest_matrix_norm(A1)
assert Anorm0 == pytest.approx(Anorm1, 1.0e-12)
b1 = dolfinx.fem.assemble_vector_nest(L_block)
dolfinx.fem.apply_lifting_nest(b1, a_block, [bc])
for b_sub in b1.getNestSubVecs():
b_sub.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
bcs0 = dolfinx.cpp.fem.bcs_rows(
dolfinx.fem.assemble._create_cpp_form(L_block), [bc])
dolfinx.fem.set_bc_nest(b1, bcs0)
b1.assemble()
bnorm1 = math.sqrt(sum([x.norm()**2 for x in b1.getNestSubVecs()]))
assert bnorm0 == pytest.approx(bnorm1, 1.0e-12)
# Monolithic version
E = P0 * P1
W = dolfinx.fem.FunctionSpace(mesh, E)
u0, u1 = ufl.TrialFunctions(W)
v0, v1 = ufl.TestFunctions(W)
a = inner(u0, v0) * dx + inner(u1, v1) * dx + inner(u0, v1) * dx + inner(
u1, v0) * dx
L = zero * inner(f, v0) * ufl.dx + inner(g, v1) * dx
bdofsW_V1 = dolfinx.fem.locate_dofs_topological(
(W.sub(1), V1), mesh.topology.dim - 1, bndry_facets)
bc = dolfinx.fem.dirichletbc.DirichletBC(u_bc, bdofsW_V1, W.sub(1))
A2 = dolfinx.fem.assemble_matrix(a, [bc])
A2.assemble()
b2 = dolfinx.fem.assemble_vector(L)
dolfinx.fem.apply_lifting(b2, [a], [[bc]])
b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.set_bc(b2, [bc])
assert A2.getType() != "nest"
assert A2.norm() == pytest.approx(Anorm0, 1.0e-9)
assert b2.norm() == pytest.approx(bnorm0, 1.0e-9)
