[Development] Should we add a minimum number of iterations for the inexact Newton's method

[sblauth]

For large scale problems, one issue with the inexact Newton's method is that the assembly of the Jacobian matrix takes lots of time. In the very early stages (first 2-5 iterations) the inexact Newton's method has a very low tolerance, so that the linear solver converges in about 1-10 iterations (this does not take a long time).

Hence, it might be an idea to let the inexact Newton's method use a minimum number of iterations (say 10-20) regardless of the tolerance, so that the information of the Jacobian matrix can be used more efficiently instead of re-assembling it (with very minor changes) so often, which is expensive.

[sblauth]

This could be implemented, but as additional parameter (which then can be set via the configuration files for optimization problems)

[sblauth]

This is available starting with PETSc >= 3.20 - the user only has to specify "ksp_min_it" in the ksp_options for the solve. Hence, it is not necessary to provide a cashocs-based interface for this.

Closing this issue and the corresponding PR #343