def test_linear_pde():
"""Test Newton solver for a linear PDE"""
# Create mesh and function space
mesh = dolfin.generation.UnitSquareMesh(dolfin.MPI.comm_world, 12, 12)
V = functionspace.FunctionSpace(mesh, ("Lagrange", 1))
u = function.Function(V)
v = function.TestFunction(V)
F = inner(10.0, v) * dx - inner(grad(u), grad(v)) * dx
def boundary(x):
"""Define Dirichlet boundary (x = 0 or x = 1)."""
return np.logical_or(x[:, 0] < 1.0e-8, x[:, 0] > 1.0 - 1.0e-8)
u_bc = function.Function(V)
u_bc.vector.set(1.0)
u_bc.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
bc = fem.DirichletBC(V, u_bc, boundary)
# Create nonlinear problem
problem = NonlinearPDEProblem(F, u, bc)
# Create Newton solver and solve
solver = dolfin.cpp.nls.NewtonSolver(dolfin.MPI.comm_world)
n, converged = solver.solve(problem, u.vector)
assert converged
assert n == 1
# Increment boundary condition and solve again
u_bc.vector.set(2.0)
u_bc.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
n, converged = solver.solve(problem, u.vector)
assert converged
assert n == 1
def test_basic_assembly_constant():
"""Tests assembly with Constant
The following test should be sensitive to order of flattening the
matrix-valued constant.
"""
mesh = dolfin.generation.UnitSquareMesh(dolfin.MPI.comm_world, 5, 5)
V = functionspace.FunctionSpace(mesh, ("Lagrange", 1))
u, v = dolfin.TrialFunction(V), dolfin.TestFunction(V)
c = constant.Constant(mesh, [[1.0, 2.0], [5.0, 3.0]])
a = inner(c[1, 0] * u, v) * dx + inner(c[1, 0] * u, v) * ds
L = inner(c[1, 0], v) * dx + inner(c[1, 0], v) * ds
# Initial assembly
A1 = dolfin.fem.assemble_matrix(a)
A1.assemble()
b1 = dolfin.fem.assemble_vector(L)
b1.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
c.value = [[1.0, 2.0], [3.0, 4.0]]
A2 = dolfin.fem.assemble_matrix(a)
A2.assemble()
b2 = dolfin.fem.assemble_vector(L)
b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
assert (A1 * 3.0 - A2 * 5.0).norm() == pytest.approx(0.0)
assert (b1 * 3.0 - b2 * 5.0).norm() == pytest.approx(0.0)
def test_basic_interior_facet_assembly():
ghost_mode = dolfin.cpp.mesh.GhostMode.none
if (dolfin.MPI.size(dolfin.MPI.comm_world) > 1):
ghost_mode = dolfin.cpp.mesh.GhostMode.shared_facet
mesh = dolfin.RectangleMesh(
dolfin.MPI.comm_world,
[numpy.array([0.0, 0.0, 0.0]),
numpy.array([1.0, 1.0, 0.0])], [5, 5],
cell_type=dolfin.cpp.mesh.CellType.triangle,
ghost_mode=ghost_mode)
V = functionspace.FunctionSpace(mesh, ("DG", 1))
u, v = dolfin.TrialFunction(V), dolfin.TestFunction(V)
a = ufl.inner(ufl.avg(u), ufl.avg(v)) * ufl.dS
A = dolfin.fem.assemble_matrix(a)
A.assemble()
assert isinstance(A, PETSc.Mat)
L = ufl.conj(ufl.avg(v)) * ufl.dS
b = dolfin.fem.assemble_vector(L)
b.assemble()
assert isinstance(b, PETSc.Vec)
def increase_order(
V: functionspace.FunctionSpace) -> functionspace.FunctionSpace:
"""For a given function space, return the same space, but with
polynomial degree increase by 1.
"""
e = ufl.algorithms.elementtransformations.increase_order(V.ufl_element())
return functionspace.FunctionSpace(V.mesh, e)
def change_regularity(V: functionspace.FunctionSpace,
family: str) -> functionspace.FunctionSpace:
"""For a given function space, return the corresponding space with
the finite elements specified by 'family'. Possible families are
the families supported by the form compiler
"""
e = ufl.algorithms.elementtransformations.change_regularity(
V.ufl_element(), family)
return functionspace.FunctionSpace(V.mesh, e)
def test_nonlinear_pde_snes():
"""Test Newton solver for a simple nonlinear PDE"""
# Create mesh and function space
mesh = dolfin.generation.UnitSquareMesh(dolfin.MPI.comm_world, 12, 15)
V = functionspace.FunctionSpace(mesh, ("Lagrange", 1))
u = function.Function(V)
v = function.TestFunction(V)
F = inner(5.0, v) * dx - ufl.sqrt(u * u) * inner(
grad(u), grad(v)) * dx - inner(u, v) * dx
def boundary(x):
"""Define Dirichlet boundary (x = 0 or x = 1)."""
return np.logical_or(x[:, 0] < 1.0e-8, x[:, 0] > 1.0 - 1.0e-8)
u_bc = function.Function(V)
u_bc.vector.set(1.0)
u_bc.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
bc = fem.DirichletBC(V, u_bc, boundary)
# Create nonlinear problem
problem = NonlinearPDE_SNESProblem(F, u, bc)
u.vector.set(0.9)
u.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
b = dolfin.cpp.la.create_vector(V.dofmap.index_map)
J = dolfin.cpp.fem.create_matrix(problem.a_comp._cpp_object)
# Create Newton solver and solve
snes = PETSc.SNES().create()
snes.setFunction(problem.F, b)
snes.setJacobian(problem.J, J)
snes.setTolerances(rtol=1.0e-9, max_it=10)
snes.setFromOptions()
snes.getKSP().setTolerances(rtol=1.0e-9)
snes.solve(None, u.vector)
assert snes.getConvergedReason() > 0
assert snes.getIterationNumber() < 6
# Modify boundary condition and solve again
u_bc.vector.set(0.5)
u_bc.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
snes.solve(None, u.vector)
assert snes.getConvergedReason() > 0
assert snes.getIterationNumber() < 6
def test_newton_solver_iheritance_override_methods():
import functools
called_methods = {}
def check_is_called(method):
@functools.wraps(method)
def wrapper(*args, **kwargs):
called_methods[method.__name__] = True
return method(*args, **kwargs)
return wrapper
class CustomNewtonSolver(dolfin.cpp.nls.NewtonSolver):
def __init__(self, comm):
super().__init__(comm)
@check_is_called
def update_solution(self, x, dx, relaxation,
problem, it):
return super().update_solution(x, dx, relaxation, problem, it)
@check_is_called
def converged(self, r, problem, it):
return super().converged(r, problem, it)
mesh = dolfin.generation.UnitSquareMesh(dolfin.MPI.comm_world, 12, 12)
V = functionspace.FunctionSpace(mesh, ("Lagrange", 1))
u = function.Function(V)
v = function.TestFunction(V)
F = inner(10.0, v) * dx - inner(grad(u), grad(v)) * dx
def boundary(x):
"""Define Dirichlet boundary (x = 0 or x = 1)."""
return np.logical_or(x[:, 0] < 1.0e-8, x[:, 0] > 1.0 - 1.0e-8)
u_bc = function.Function(V)
bc = fem.DirichletBC(V, u_bc, boundary)
# Create nonlinear problem
problem = NonlinearPDEProblem(F, u, bc)
# Create Newton solver and solve
solver = CustomNewtonSolver(dolfin.MPI.comm_world)
n, converged = solver.solve(problem, u.vector)
assert called_methods[CustomNewtonSolver.converged.__name__]
assert called_methods[CustomNewtonSolver.update_solution.__name__]
def collapse(self):
u_collapsed = self._cpp_object.collapse()
V_collapsed = functionspace.FunctionSpace(None, self.ufl_element(),
u_collapsed.function_space)
return Function(V_collapsed, u_collapsed.vector)
def test_assembly_solve_taylor_hood(mesh):
"""Assemble Stokes problem with Taylor-Hood elements and solve."""
P2 = functionspace.VectorFunctionSpace(mesh, ("Lagrange", 2))
P1 = functionspace.FunctionSpace(mesh, ("Lagrange", 1))
def boundary0(x):
"""Define boundary x = 0"""
return x[:, 0] < 10 * numpy.finfo(float).eps
def boundary1(x):
"""Define boundary x = 1"""
return x[:, 0] > (1.0 - 10 * numpy.finfo(float).eps)
u0 = dolfin.Function(P2)
u0.vector.set(1.0)
u0.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
bc0 = dolfin.DirichletBC(P2, u0, boundary0)
bc1 = dolfin.DirichletBC(P2, u0, boundary1)
u, p = dolfin.TrialFunction(P2), dolfin.TrialFunction(P1)
v, q = dolfin.TestFunction(P2), dolfin.TestFunction(P1)
a00 = inner(ufl.grad(u), ufl.grad(v)) * dx
a01 = ufl.inner(p, ufl.div(v)) * dx
a10 = ufl.inner(ufl.div(u), q) * dx
a11 = None
p00 = a00
p01, p10 = None, None
p11 = inner(p, q) * dx
# FIXME
# We need zero function for the 'zero' part of L
p_zero = dolfin.Function(P1)
f = dolfin.Function(P2)
L0 = ufl.inner(f, v) * dx
L1 = ufl.inner(p_zero, q) * dx
# -- Blocked and nested
A0 = dolfin.fem.assemble_matrix_nest([[a00, a01], [a10, a11]], [bc0, bc1])
A0norm = nest_matrix_norm(A0)
P0 = dolfin.fem.assemble_matrix_nest([[p00, p01], [p10, p11]], [bc0, bc1])
P0norm = nest_matrix_norm(P0)
b0 = dolfin.fem.assemble_vector_nest([L0, L1], [[a00, a01], [a10, a11]],
[bc0, bc1])
b0norm = b0.norm()
ksp = PETSc.KSP()
ksp.create(mesh.mpi_comm())
ksp.setOperators(A0, P0)
nested_IS = P0.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_u.getPC().setFactorSolverType('mumps')
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()
x0 = b0.copy()
ksp.solve(b0, x0)
assert ksp.getConvergedReason() > 0
# -- Blocked and monolithic
A1 = dolfin.fem.assemble_matrix_block([[a00, a01], [a10, a11]], [bc0, bc1])
assert A1.norm() == pytest.approx(A0norm, 1.0e-12)
P1 = dolfin.fem.assemble_matrix_block([[p00, p01], [p10, p11]], [bc0, bc1])
assert P1.norm() == pytest.approx(P0norm, 1.0e-12)
b1 = dolfin.fem.assemble_vector_block([L0, L1], [[a00, a01], [a10, a11]],
[bc0, bc1])
assert b1.norm() == pytest.approx(b0norm, 1.0e-12)
ksp = PETSc.KSP()
ksp.create(mesh.mpi_comm())
ksp.setOperators(A1, P1)
ksp.setType("minres")
pc = ksp.getPC()
pc.setType('lu')
pc.setFactorSolverType('mumps')
ksp.setTolerances(rtol=1.0e-8, max_it=50)
ksp.setFromOptions()
x1 = A1.createVecRight()
ksp.solve(b1, x1)
assert ksp.getConvergedReason() > 0
assert x1.norm() == pytest.approx(x0.norm(), 1e-8)
# -- Monolithic
P2 = ufl.VectorElement("Lagrange", mesh.ufl_cell(), 2)
P1 = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
TH = P2 * P1
W = dolfin.FunctionSpace(mesh, TH)
(u, p) = dolfin.TrialFunctions(W)
(v, q) = dolfin.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 = dolfin.Function(W.sub(0).collapse())
p_zero = dolfin.Function(W.sub(1).collapse())
L0 = inner(f, v) * dx
L1 = inner(p_zero, q) * dx
L = L0 + L1
bc0 = dolfin.DirichletBC(W.sub(0), u0, boundary0)
bc1 = dolfin.DirichletBC(W.sub(0), u0, boundary1)
A2 = dolfin.fem.assemble_matrix(a, [bc0, bc1])
A2.assemble()
assert A2.norm() == pytest.approx(A0norm, 1.0e-12)
P2 = dolfin.fem.assemble_matrix(p_form, [bc0, bc1])
P2.assemble()
assert P2.norm() == pytest.approx(P0norm, 1.0e-12)
b2 = dolfin.fem.assemble_vector(L)
dolfin.fem.apply_lifting(b2, [a], [[bc0, bc1]])
b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
dolfin.fem.set_bc(b2, [bc0, bc1])
b2norm = b2.norm()
assert b2norm == pytest.approx(b0norm, 1.0e-12)
ksp = PETSc.KSP()
ksp.create(mesh.mpi_comm())
ksp.setOperators(A2, P2)
ksp.setType("minres")
pc = ksp.getPC()
pc.setType('lu')
pc.setFactorSolverType('mumps')
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()
x2 = A2.createVecRight()
ksp.solve(b2, x2)
assert ksp.getConvergedReason() > 0
assert x0.norm() == pytest.approx(x2.norm(), 1e-8)
