GMRES

[WeiqunZhang]

Add a GMRES solver class template

This is still work in progress. So the interface may not be stable yet.

[eebasso]

Is some generalization of this loop eventually intended to be added to either GRESMLMG or GMRES?

Could we perhaps generalize this to replace gmres with other solver types that have thus far been used only as bottom solvers? Some examples would include the CG and BiCGStab methods. I imagine it could be any class that implements solve and apply methods and gets initialized by some MLLinOpT object.

As is, MLMG seems to force the user to always use the smoother for the non-bottom steps, which uses up the overwhelming majority of computational time. It would be nice if one could make that an option. I imagine the boundary conditions would have to handled more carefully in the case of the non-smoother methods at the finer levels.

It would also be nice if one could select GMRES as an option in MLMG as the bottom solver.

[WeiqunZhang]

Thanks for your comments. This PR is just first the step of adding GMRES support. Yes, eventually we would like to be able to use GMRES as a bottom solver in MLMG and use MLMG as a multigrid preconditioner for GMRES. The GMRES class will probably be more or less the same, but we need to make some changes to MLMG and the interface class GMRESMLMG.

As is, MLMG seems to force the user to always use the smoother for the non-bottom steps,

MLMG calls linop.smooth. So it's up to the linear operator class on what to do. Nevertheless, I think the name smooth is appropriate, because that's how multigrid works. The relaxation step is supposed to smooth out the high-frequency modes of the error. I don't know what is in your mind as not a "smoother". I suspect whatever that is, it needs to behave like a smoother in terms of eliminating high-frequency errors for it to be effective.