How to increase maximum number of iterations?

variational formulation
1

I meet a problem that fenics show ‘Newton solver did not converge because maximum number of iterations reached.’ Can I increase this iteration number?

Traceback (most recent call last):
  File "/mnt/c/Users/Danie/OneDrive/桌面/ID1/PhaseFieldFracture.py", line 244, in <module>
    problem_u.solve(u.vector())
  File "/usr/local/lib/python3.6/site-packages/mgis/fenics/nonlinear_problem.py", line 486, in solve
    solv_out = self.solver.solve(self, x)
RuntimeError: 

*** -------------------------------------------------------------------------
*** DOLFIN encountered an error. If you are not able to resolve this issue
*** using the information listed below, you can ask for help at
***
***     fenics-support@googlegroups.com
***
*** Remember to include the error message listed below and, if possible,
*** include a *minimal* running example to reproduce the error.
***
*** -------------------------------------------------------------------------
*** Error:   Unable to solve nonlinear system with NewtonSolver.
*** Reason:  Newton solver did not converge because maximum number of iterations reached.
*** Where:   This error was encountered inside NewtonSolver.cpp.
*** Process: 0
*** 
*** DOLFIN version: 2019.1.0
*** Git changeset:  unknown
*** -------------------------------------------------------------------------
2

See the following example:

from dolfin import *

# Set up some simple demonstration nonlinear problem:
mesh = UnitIntervalMesh(10)
V = FunctionSpace(mesh,"CG",1)
u = Function(V)
v = TestFunction(V)
x = SpatialCoordinate(mesh)
F = (u+1)**2*dot(grad(u),grad(v))*dx + u*v*dx - sin(x[0])*v*dx
problem = NonlinearVariationalProblem(F,u,J=derivative(F,u),bcs=[])

# Create solver:
solver = NonlinearVariationalSolver(problem)
stype = 'newton'
solver.parameters['nonlinear_solver']=stype
sprms = solver.parameters[stype+'_solver']

# Set maximum iterations:
sprms['maximum_iterations'] = 100

# Force solver to reach maximum iterations for demonstration:
sprms['relative_tolerance'] = 0.0
sprms['absolute_tolerance'] = 0.0

# Print out other available options:
info(solver.parameters,True)

# Run solver:
solver.solve()
2 Likes
3

Thanks kamensky. After increasing the maximum number of iterations, error is eliminated.
Additionally, besides increasing the number of elements, which else ways can reduce newton iterations?

4

Other than the linear setting where you will converge in one iteration, Newton’s method converges optimally at least at a quadratic rate. If you aren’t achieving a quadratic convergence rate you likely have a malformed Jacobian, the update of the solution vector is not exact or your solution iterate is stuck in a saddle point and not an attractor region. Basic info available here.

2 Likes
5

Hii,
This code is not working for me, Same error is showing i.e maximum number of iteration is reached.

Thank You,
Debendra

6

Hi, as @kamensky states in the example, tolerances are set to 0.0 to reach maximum number of iterations for demonstration. However the solver converges if you relax the tolerance requirements:

from dolfin import *

# Set up some simple demonstration nonlinear problem:
mesh = UnitIntervalMesh(10)
V = FunctionSpace(mesh,"CG",1)
u = Function(V)
v = TestFunction(V)
x = SpatialCoordinate(mesh)
F = (u+1)**2*dot(grad(u),grad(v))*dx + u*v*dx - sin(x[0])*v*dx
problem = NonlinearVariationalProblem(F,u,J=derivative(F,u),bcs=[])

# Create solver:
solver = NonlinearVariationalSolver(problem)
stype = 'newton'
solver.parameters['nonlinear_solver']=stype
sprms = solver.parameters[stype+'_solver']

# Set maximum iterations:
sprms['maximum_iterations'] = 100

# Force solver to reach maximum iterations for demonstration:
sprms['relative_tolerance'] = 1e-14
sprms['absolute_tolerance'] = 0.0

# Print out other available options:
info(solver.parameters,True)

# Run solver:
solver.solve()

Result:

Solving nonlinear variational problem.
Newton iteration 0: r (abs) = 1.596e-01 (tol = 0.000e+00) r (rel) = 1.000e+00 (tol = 1.000e-14)
Newton iteration 1: r (abs) = 7.413e-02 (tol = 0.000e+00) r (rel) = 4.646e-01 (tol = 1.000e-14)
Newton iteration 2: r (abs) = 1.576e-03 (tol = 0.000e+00) r (rel) = 9.876e-03 (tol = 1.000e-14)
Newton iteration 3: r (abs) = 1.785e-07 (tol = 0.000e+00) r (rel) = 1.119e-06 (tol = 1.000e-14)
Newton iteration 4: r (abs) = 1.538e-15 (tol = 0.000e+00) r (rel) = 9.639e-15 (tol = 1.000e-14)
Newton solver finished in 4 iterations and 4 linear solver iterations.
7

Out put is

(4, True)

It is working.
Thank You

1 Like