def step(self):
r"""Perform a backtracking line search for the next value of the
solution and compute the search direction for the next step"""
E = self.problem.E
u = self.problem.u
v = self.v
t = self.t
t.assign(1.)
E_0 = self.problem.assemble(E)
slope = self.problem.assemble(self.dE_dv)
if slope > 0:
raise firedrake.ConvergenceError(
'Minimization solver has invalid search direction. This is '
'likely due to a negative thickness or friction coefficient or'
'otherwise physically invalid input data.')
E_t = firedrake.replace(E, {u: u + t * v})
armijo = self.armijo
contraction = self.contraction
while self.problem.assemble(E_t) > E_0 + armijo * float(t) * slope:
t.assign(t * contraction)
u.assign(u + t * v)
self.search_direction_solver.solve()
self.iteration += 1
def solve(self):
r"""Step the Newton iteration until convergence"""
dE_dv = self.dE_dv
S = self.problem.S
_assemble = self.problem.assemble
while abs(_assemble(dE_dv)) > self.tolerance * _assemble(S):
self.step()
if self.iteration >= self.max_iterations:
raise firedrake.ConvergenceError(
'Newton search did not converge after {} iterations!'.
format(self.max_iterations))
def solve(self, tolerance, max_iterations):
r"""Run the iteration until the objective functional does not decrease
to within tolerance"""
objective = np.inf
for iteration in range(max_iterations):
if objective - self._objective <= tolerance * self._energy:
return
objective = self._objective
self.step()
raise firedrake.ConvergenceError(
f"Gauss-Newton CG failed to converge after {max_iterations} steps!"
)