[petsc-dev] Golub-Kahan bidiagonalization

[Karin&NiKo]

The N matrix is not mandatory ; in some case, it can be usefull to
accelerate the convergence.
So you confirm we should look at a fieldsplit implementation with a new
-pc_fieldsplit_type gk?

Thanks,
Nicolas

2017-12-18 14:03 GMT+01:00 Matthew Knepley <knepley at gmail.com>:

> On Mon, Dec 18, 2017 at 7:42 AM, Karin&NiKo <niko.karin at gmail.com> wrote:
>
>> Dear PETSc team,
>>
>> I would like to implement and possibly commit to PETSc the Golub-Kahan
>> bidiagonalization algorithm (GK) describe in Arioli's paper :
>> http://epubs.siam.org/doi/pdf/10.1137/120866543.
>> In this work, Mario Arioli uses GK to solve saddle point problems, of the
>> form A=[A00, A01; A10, A11]. There is an outer-loop which treats the
>> constraints and an inner-loop, with its own KSP, to solve the linear
>> systems with A00 as operator. We have evaluated this algorithm on different
>> problems and have found that it exhibits very nice convergence of the
>> outer-loop (independant of the problem size).
>>
>> In order to developp a source that could be commited to PETSc, I would
>> like to have your opinion on how to implement it. Since the algorithm
>> treats saddle point problems, it seems to me that it should be implemented
>> in the fieldsplit framework. Should we add for instance a
>> new -pc_fieldsplit_type, say gk? Have you other ideas?
>>
>
> That was my first idea. From quickly looking at the paper, it looks like
> you need an auxiliary matrix N which
> does not come from the decomposition, so you will have to attach it to
> something, like we do for LSC, or
> demand that it come in as the (1,1) block of the preconditioning matrix
> which is a little hacky as well.
>
>   Thanks,
>
>      Matt
>
>
>> I look forward to hearing your opinion on the best design for
>> implementing this algorithm in PETSc.
>>
>> Regards,
>> Nicolas
>>
>
>
>
> --
> 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
>
> https://www.cse.buffalo.edu/~knepley/ <http://www.caam.rice.edu/~mk51/>
>
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