Skip to content

Controls

*Controls, method, mode
<parameter 1>, ..., <parameter n>

If an incremental solution strategy based on iterative methods is to be effective, realistic criteria should be used for the termination of the iteration. At the end of each iteration, the solution obtained should be checked to see whether it has converged within preset tolerances or whether the iteration is diverging. The convergence tolerance determines the speed and accuracy of a calculation. If the criterion is too coarse, the solution may be quite inaccurate. On the other hand, a criterion which is too tight results in unnecessary computations. Similarly, an ineffective divergence check can terminate the iteration when the solution is not actually diverging or force the iteration to search for an unattainable solution.

Details on the choice and formulation of convergence controls are provided in Section Convergence criteria of the Theory Manual

In numgeo we offer the user a two level approach to evaluate the convergence of the solution:

  • Per default, we evaluate the global (overall) convergence without distinguishing between different fields \(\alpha\) (e.g. solid displacement and pore water pressure). This measure gives an idea of the overall (mean) quality of the solution, however, especially in multi-field solutions, this measure could shadow non-converged fields or lead to non-convergence due to the different fields with significantly different magnitudes.

  • Advanced users may not only adapt the error tolerance of the global convergence control, but can also use controls based on each individual type of degree of freedom (e.g. solid displacements or pore water pressure). These dof-based controls may either be used in addition to the global control or can replace it, see Fig. 1.


Figure 1. Available convergence criteria in numgeo (left) and application to the Newton's Method (right)

Global solution control

*Controls, dof=<degree of freedom name>, global
epsilon^r, epsilon^e, epsilon^d

Either set this parameter equal modify if you want to change the convergence criteria or set it to deactivate if you want to suppress the solution control for this specific degree of freedom. This parameter is mandatory.

  • If modify is chosen, a subsequent line <parameter 1>, <parameter 2>, <parameter 3> is required, where:

    • \(\epsilon^{r}\) = convergence criterion for negligible unbalance force

    • \(\epsilon^e\) = convergence criterion for the relative unbalanced energy

    • \(\epsilon^d\) = convergence criterion for the ratio of L2-norm of the solution correction to the L2-norm of the incremental solution value

    Example:
    *Controls, global, modify
    1e-3, 1e-3, 1e-3

  • If deactivate is chosen, no subsequent line is required.

    Example:
    *Controls, global, deactivate

  • Default values

    \(\epsilon^{r}\) \(\epsilon^e\) \(\epsilon^{d}\)
    \(5 \cdot 10^{-3}\) \(5 \cdot 10^{-3}\) \(1 \cdot 10^{-2}\)

Dof-based solution control

*Controls, dof=<degree of freedom name>, mode
epsilon^d, epsilon^e, epsilon^r, epsilon^{Delta d}, epsilon^{Delta e}, r^epsilon

This optional keyword enables the user to modify the default settings for the convergence evaluation of the solution. if activated, all sub-keywords (except of [\(r^\epsilon > 1\)) are mandatory. For a detailed explanation on the convergence criteria, the reader is referred to the Theory Manual.

  • dof=<degree of freedom name>

    Set this parameter equal to the degree of freedom for which the controls should be changed. This parameter is mandatory. For the following degrees of freedom the solution controls can be modified:

    • u: Solid-displacement in \(x_1\)-, \(x_2\)- and \(x_3\)-direction

    • pw: Pore-water pressure

    • pa: Pore-air pressure

    • w: Water-displacement in \(x_1\)-, \(x_2\)- and \(x_3\)-direction

  • mode

    Either set this parameter equal modify if you want to change the convergence criteria or set it to deactivate if you want to suppress the solution control for this specific degree of freedom.

    • If modify is chosen, a subsequent line is required, where:

      • \(\epsilon^{\Delta d}\) = convergence criterion for the ratio of the largest solution correction to the largest corresponding incremental solution value

      • \(\epsilon^e\) = convergence criterion for the relative unbalanced energy

      • \(\epsilon^{r}\) = convergence criterion for negligible unbalance force (default is \(\epsilon^{r}=10^{-3}\))

      • \(\epsilon^{\Delta d}\) = criterion for negligible response, i.e. the absolute value of the solution increment is smaller than the specified tolerance

      • \(\epsilon^{\Delta e}\) = criterion for negligible response, i.e. the unbalance energy is smaller than the specified tolerance

      • \(r^\epsilon > 1\) = relaxation factor for non-quadratic convergence (default is \(r^\epsilon = 2\))

      Example:
      *Controls, u, modify
      1e-3, 2e-3, 5e-4, 1e-6, 1e-6, 1.5

    • If deactivate is chosen, no subsequent line is required.

      Example:
      *Controls, u, deactivate

    • The default values for the controls are:

      dof \(\epsilon^{d}\) \(\epsilon^e\) \(\epsilon^{r}\) \(\epsilon^{\Delta d}\) \(\epsilon^{\Delta e}\) \(r^\epsilon\)
      u \(1 \cdot 10^{-2}\) \(1 \cdot 10^{-2}\) \(1 \cdot 10^{-2}\) \(1 \cdot 10^{-5}\) \(1 \cdot 10^{-6}\) 2
      w \(1 \cdot 10^{-2}\) \(1 \cdot 10^{-2}\) \(1 \cdot 10^{-2}\) \(1 \cdot 10^{-5}\) \(1 \cdot 10^{-5}\) 2
      pw \(5 \cdot 10^{-2}\) \(5 \cdot 10^{-2}\) \(5 \cdot 10^{-2}\) \(1 \cdot 10^{-3}\) \(1 \cdot 10^{-3}\) 2
      pa \(5 \cdot 10^{-2}\) \(5 \cdot 10^{-2}\) \(5 \cdot 10^{-2}\) \(1 \cdot 10^{-3}\) \(1 \cdot 10^{-3}\) 2

Maximum solution increment

*Controls, max-<dof>, activate
tilde{Delta}_{dof}, s^{max}

This optional keyword enables the user to modify the default settings for time stepping after a successful Newton iteration. If activated, all sub-keywords are mandatory.

See Maximum solution increment for further information.

  • <dof>

    Set this parameter equal to the degree of freedom for which the controls should be changed. This parameter is mandatory. For the following degrees of freedom the solution controls can be modified:

    • dpw: Change in pore-water pressure

  • \(\tilde{\Delta}_{dof}\) = target solution increment that should not be exceeded in one increment

  • \(s^{max}\) = maximum time scaling factor

Example:
*Controls, max-dpw, activate
50, 4