[petsc-dev] Support for projections in petsc solvers

[Matthew Knepley]

On Fri, Oct 2, 2015 at 1:32 PM, Alejandro Cosimo <alecosimo at gmail.com>
wrote:

> Because that's how the method is formulated, known as (Preconditioned)
> Conjugate Projected Gradient. I think it would be good to keep the design
> as close as possible to the actual formulation of the method.
>

I am not sure I agree. Usually its better to build simple pieces that can
be combined in
powerful ways, rather than complex pieces that do a single job.

   Matt


> 2015-10-02 20:16 GMT+02:00 Barry Smith <bsmith at mcs.anl.gov>:
>
>>
>> > On Oct 2, 2015, at 2:23 AM, Alejandro Cosimo <alecosimo at gmail.com>
>> wrote:
>> >
>> > Thanks Matt and Barry for the answer. Regarding the preconditioning. I
>> have three steps which act successively on the residual, projection
>> (w=P^T*r), preconditioning (z=M^{-1}*w) and re-projection (y=P*z). But all
>> those steps can be interpreted as a single preconditioning step, mainly the
>> application of P*M^{-1}*P^T on the residual. I can implement that inside my
>> PCApply.
>> >
>> > Regarding the use of a new convergence test routine for checking on
>> P^T*r for convergence: I think it could work, although it would be good to
>> manage explicitly the projections inside the solver.
>>
>>    Why would it be "good to manage the projections inside the solver"?
>>
>>   Barry
>>
>> >
>> > Regards,
>> > Alejandro
>> >
>> > 2015-10-01 23:16 GMT+02:00 Barry Smith <bsmith at mcs.anl.gov>:
>> >
>> >     Do you mean  application of the precondition is     P*M^{-1}*P^T
>> ApplyPC  P*M^{-1}*P^T  or something else?
>> >
>> >     If so then PCCOMPOSITE is not for this purpose in any way. You just
>> need to  do all three things inside your PCApply.
>> >
>> >
>> > > On 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.
>> >
>> >    As Matt said if you are checking on something like P^T*r for
>> convergence then you do that with a new convergence test routine.
>> >
>> >    BTW: Maybe you could use the source of KSPCreate_FCG() as a starting
>> point for a CG implementation that keeps a complete history.
>> >
>> >   Barry
>> >
>> > >
>> > > 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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