Allow to reuse the preconditioner in the Newton solver

[lpsaavedra]

Description of the problem

The multigrid preconditioners were being setup at every non-linear iteration, however, we want to be able to reuse them to reduce the setup time.

Description of the solution

• The MFNavierStokesPreconditionGMG class now sets the level constraints, operators and transfers in the constructor. Then, depending on the MG being used, there is an initialize function in charge of setting up the smoother and the coarse-grid solver.
• Modifications were made in the Newton nonlinear solver to allow to reuse the preconditioner along non-linear newton iterations. A new parameter reuse preconditioner was introduced for this purpose. When this change was introduced, the assemble_matrix and setup_preconditioner functions of all the NavierStokesBase solvers had to be slightly modified. This change now allows to reuse the preconditioner in both lethe-fluid and lethe-fluid-matrix-free. Due to this change, also the auxiliary physics needs a setup_preconditioner function, however, it was explicitly written that is not used for those applications.
• The constant modes are now also being used for the local smoothing approach using the recently introduced DoFTools::extract_level_constant_modes(...).
• this-> was also included several times in the MFNavierStokesPreconditionGMG class to be able to differentiate between this class member variables and others.
• The output of the coarse-grid iterations was finally corrected, and now prints all the information.

How Has This Been Tested?

• All the existent test pass.
• Ran several tests on my machine and observed a benefit in certain cases (e.g., the TGV) when reusing the preconditioner across all Newton iterations of a transient iteration.

Documentation

• The new reuse preconditioner parameter was included in the non linear solver documentation page.

Future changes

• This is the second step towards reusing parts of multigrid to improve the performance of the matrix-free solver.

[blaisb]

Some small changes. I have one more file to review, will do it tomorrow :)

[blaisb]

I am not sure why this changed, but ok :)

[lpsaavedra]

Yes, I was also not sure about this. It changed when I added the if to reuse the operators, transfer and constraints that are set in the constructor:

  if (!gmg_preconditioner)
    gmg_preconditioner = std::make_shared<MFNavierStokesPreconditionGMG<dim>>(
      this->simulation_parameters,
      this->dof_handler,
      this->mapping,
      this->cell_quadrature,
      this->forcing_function,
      this->simulation_control,
      this->mg_computing_timer,
      this->fe);

However, the number of newton iterations, linear solver iterations and coarse-grid solver iterations remain the same. It only change the residual in the 3rd/4th decimal place which caused these changes in the value of the forces. In my opinion, the change is minimal so it should not be an issue.

[blaisb]

So in this case you are recreating the preconditioner between iterations time steps for example right?

[lpsaavedra]

Exactly... it reuses it for Newton iterations within one transient iteration...

[blaisb]

One last comment. These are all minor things. ping me when everything has been incorporated then we can merge. Great work @lpsaavedra . Can you add a changelog entry?

[blaisb]

Is the best approach here to throw or would it be to just print a warning and use the max level as the min level (e.g. no GMG)

[lpsaavedra]

I am not sure about this... I will think about it and then maybe we can do this in the next MG PR