## 5. Flux-normalised correction termination test

This is the default test to determine convergence of the Newton iterations. The flux can be considered a measure of the individual internal and external forces in the FE model. For each Newton iteration, the instantaneous flux is normalised by the average flux. The average flux is computed from the converged solutions of the previous steps and from the solution of the current Newton iteration.

For all fluxes, and for the Newton correction of the solution, the inf-norm (maximum) is used.

The flux normalisation is performed per field, because each field may have a different unit and a different range of values. The finite elements present in the analysis model define what fields are active. The following fields are commonly used in elastic analysis and heat-transfer analysis:

Field name Description
DISPLACEMENT The displacement degrees-of-freedom.
ROTATION The rotational degrees-of-freedom in shell and beam elements and in rigid-coupling elements.
LAGRANGE The degrees-of-freedom associated to Lagrange multipliers.
TEMPERATURE The degrees-of-freedom in heat-transfer elements.

The following options are active for all fields:

max_newton_iterations v

Specifies the maximum number of Newton iterations per increment. Default is 50.

max_divergences v

Defines the maximum number of consecutive divergences during the correction phase of a load step. Default is 4. When this number is reached, the correction phase is terminated unsuccessfully, and the step increment is re-started with a reduced step size.

min_newton_iterations_check_divergence v

Check divergence only after v Newton iterations. Default is 4.

The following options can be specified either for all fields or per field. In the second case, the field name must be appended to the MDL command name:

case 1
ebc                         1
analysis                    nonlinear
tol_residuum                1.e-3 # for all fields
tol_residuum.rotation       1.e-5 # only for the rotation field
end
tol_residuum v

Threshold for convergence: The maximum flux divided by the average flux must be smaller than v. Default is 1e-5.

tol_solution v

Threshold for convergence: The maximum of the Newton correction, divided by the maximum of the current step increment must be smaller than v. Default is 1e-5.

tol_residuum_linear_problem v

Threshold for linear convergence: If the maximum flux divided by the average flux is smaller than v, linear convergence is assumed, without consideration of tol_solution. Default is 1e-8.

nb_iter_nonquadratic_convergence v

Number of Newton iterations that will be executed until the convergence history will be examined to determine whether quadratic convergence has been obtained. Default is 9 iterations.

tol_residuum_nonquadratic_convergence v

If convergence is not quadratic, after nb_iter_nonquadratic_convergence Newton iterations, tol_residuum is replaced by v. Default is 2e-2.

average_flux v

Use v to normalise the flux, instead of the averaged flux which is computed from the analysis.

initial_average_flux v

Use v as start value to compute the averaged flux. Default is 0.01.

zero_flux_criterion v

If the magnitude of the instantaneous flux divided by the averaged flux is smaller then v, the flux will be considered zero, and tol_solution_zero_flux will be used instead of tol_solution. Default is 1e-5.

tol_solution_zero_flux v

Replaces tol_solution for fields having zero flux. Default is 1e-5.

zero_flux_relative_criterion v

For the computation of the normalised flux, discard regions in the model where the flux is below v. Default 1e-5.