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 = dolfin.function.FunctionSpace(mesh, ("Lagrange", 1))
u = dolfin.function.Function(V)
v = function.TestFunction(V)
F = inner(10.0, v) * dx - inner(grad(u), grad(v)) * dx
def boundary(x, only_boundary):
"""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_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 = dolfin.function.FunctionSpace(mesh, ("Lagrange", 1))
u = dolfin.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().update_ghosts()
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
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 = dolfin.function.FunctionSpace(mesh, ("Lagrange", 1))
u = dolfin.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, only_boundary):
"""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__]
