[petsc-users] [petsc-maint #86567] Question on KSPs

[Matthew Knepley]

On Tue, Sep 13, 2011 at 3:03 AM, Michele De Stefano <
mstefano at milan.westerngeco.slb.com> wrote:

> **
> Jed and others,
>
> we would like to explore more in detail the possibility to have a
> completely matrix-free preconditioner.
> May you explain which are the "few methods" that we should implement and
> that you was talking of ?
>
> Second question: are there algorithms for creating matrix-free
> preconditioners ?
> If yes, may you suggest at least one, please ?
>

There is really no conceptual difference between Krylov methods and
"preconditioners" in that they are
both approximate linear solvers. The distinction was made mostly because
Krylov solvers only need the
action of the matrix (or its transpose) and thus are "matrix-free".
Therefore, "matrix-free preconditioner"
basically means Krylov method (where I include Chebychev, which is a KSP in
PETSc).

So what many scalable solvers do is combine KSPs in a nice way, like a
multigrid iteration.

There may be things you can do for your particular equations, like analytic
simplifications, but these
would not be in PETSc since they are not generic.

  Thanks,

     Matt


> Thank you in advance.
> Best regards,
>
> Michele
>
> Jed Brown wrote:
>
> On Mon, Sep 12, 2011 at 16:28, Michele De Stefano <
> mstefano at milan.westerngeco.slb.com> wrote:
>
>> KSPSetOperators is able to accept a shell matrix for the "Amat" and the
>> manual
>> says that the "Pmat" is usually the same as the "Amat". Does this really
>> work
>> also when "Amat" is a shell matrix ?
>>
>> I mean, in the multi-process case, the default preconditioning method is
>> block
>> Jacobi ... but does this work also when "Pmat" is a shell matrix ?
>>
>
> Only if a few methods are implemented for the shell matrix. This is usually
> not practical. It would be more common to assemble some approximation Pmat
> (e.g. in AIJ format) and use that for preconditioning. To do everything
> matrix-free, you would normally have to put some effort into writing your
> own custom preconditioner.
>
>
> --
> Michele De Stefano
> Senior Geophysicist - REMS
> Integrated EM Center of Excellence
>
> WesternGeco GeoSolutions,
> Via Clericetti 42/A,
> 20133, Milan - Italy
>
> +39 02 266279232 (direct)
> +39 02 266279279 (fax)
>
> mstefano at slb.com
>
> Schlumberger Private
>



-- 
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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