[petsc-dev] Support for projections in petsc solvers

[Matthew Knepley]

On Thu, Oct 1, 2015 at 4:38 AM, Alejandro Cosimo <alecosimo at gmail.com>
wrote:

> Hello everybody,
>
> I'm interested in implementing FETI-1. Regardless of the iterative solver
> used for solving the interface problem, before applying the preconditioner
> it is required to project the residual and after applying the
> preconditioner to the projected residual to re-project again. It could seem
> that PCCOMPOSITE could be used in this case, performing the operation
> P*M^{-1}*P^T at once over the residual. However, this is not useful for the
> general case in FETI-1 because the convergence of the iterative solver must
> be checked with the projected residual, that is P^T*r, or in same cases
> with M^{-1}*P^T*r, but not with P*M^{-1}*P^T*r. That is why I would need
> support for projection and reprojection phases in petsc solvers.
>

>From what you say above, I still think it would be easier to use P M^{-1}
P^T as the preconditioner, and implement your
convergence test using KSPSetConvergenceTest(),
http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPSetConvergenceTest.html#KSPSetConvergenceTest

  Thanks,

     MAtt


> Right now there is no support for that. So, my question: for implementing
> the support of the projection and reprojection phases in petsc I would
> introduce the functions ApplyProjection and ApplyReProjection to the petsc
> implementation in the same way that, for example, ApplyPC is supported.
> What do you think about this? Would you proceed like this?
>
> After implementing the support for ApplyProjection and ApplyReProjection,
> I would incorporate the behavior to one of the petsc iterative solvers. For
> that I would adopt the GMRES solver because it prevents me from
> implementing the full re-orthogonalization that is required when CG is
> adopted as iterative solver for FETI-1 (something which is not implemented
> in petsc CG). In that case, do you recommend me to define a new GMRES in
> petsc, or to modify the already exiting GMRES implementation by introducing
> the option of performing the phases of projection and reprojection?
>
> Regards,
> Alejandro
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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