[petsc-users] multigrid preconditioning and adaptivity

[Matthew Knepley]

On Mon, Mar 7, 2016 at 10:28 AM, Lukasz Kaczmarczyk <
Lukasz.Kaczmarczyk at glasgow.ac.uk> wrote:

> Many thanks all for help. I started to implement function for DM.
>
> I understand that minimal implementation is that for the DM i need to
> have, is to have  DMCoarsen and in each level for all DMs, set operators
> DMKSPSetComputeOperators and DMCreateInterpolation. Matrix matrix free P
> from DMCreateInterpolation have to have operators for mult and
> mult_traspose. Is that is all?
>

Yes, that should be it. It would be nice to have some example that does
this if you would
be willing to contribute some version of your code.

  Thanks,

    Matt


> Kind regards,
> Lukasz
>
>
>
> On 7 Mar 2016, at 15:55, Mark Adams <mfadams at lbl.gov> wrote:
>
> You can just set the coarse grid matrix/operator instead of using
> Galerkin.  If you have a shell (matrix free) P then you will need to create
> and set this yourself.  Our Galerkin requires a matrix P.
>
> On Mon, Mar 7, 2016 at 9:32 AM, Lukasz Kaczmarczyk <
> Lukasz.Kaczmarczyk at glasgow.ac.uk> wrote:
>
>>
>> > On 7 Mar 2016, at 14:21, Lawrence Mitchell <
>> lawrence.mitchell at imperial.ac.uk> wrote:
>> >
>> > On 07/03/16 14:16, Lukasz Kaczmarczyk wrote:
>> >>
>> >>> On 7 Mar 2016, at 13:50, Matthew Knepley <knepley at gmail.com
>> >>> <mailto:knepley at gmail.com>> wrote:
>> >>>
>> >>> On Mon, Mar 7, 2016 at 6:58 AM, Lukasz Kaczmarczyk
>> >>> <Lukasz.Kaczmarczyk at glasgow.ac.uk
>> >>> <mailto:Lukasz.Kaczmarczyk at glasgow.ac.uk>> wrote:
>> >>>
>> >>>    Hello,
>> >>>
>> >>>    I run multi-grid solver, with adaptivity, works well, however It
>> >>>    is some space for improving efficiency. I using hierarchical
>> >>>    approximation basis, for which
>> >>>    construction of interpolation operators is simple, it is simple
>> >>>    injection.
>> >>>
>> >>>    After each refinement level (increase of order of approximation
>> >>>    on some element) I rebuild multigrid pre-conditioner with
>> >>>    additional level. It is a way to add dynamically new levels
>> >>>    without need of rebuilding whole MG pre-conditioner.
>> >>>
>> >>>
>> >>> That does not currently exist, however it would not be hard to add,
>> >>> since the MG structure jsut consists of
>> >>> arrays of pointers.
>> >>>
>> >>>
>> >>>    Looking at execution profile I noticed that 50%-60% of time is
>> >>>    spent on MatPtAP function during PCSetUP stage.
>> >>>
>> >>>
>> >>> Which means you are using a Galerkin projection to define the coarse
>> >>> operator. Do you have a direct way of defining
>> >>> this operator (rediscretization)?
>> >>
>> >> Matt,
>> >>
>> >>
>> >> Thanks for swift response. You are right, I using Galerkin projection.
>> >>
>> >> Yes, I have a way to get directly coarse operator, it is some sub
>> >> matrix of whole matrix. I taking advantage here form hierarchical
>> >> approximation.
>> >>
>> >> I could reimplement PCSetUp_MG to set the MG structure directly, but
>> >> this probably not good approach, since my implementation which will
>> >> work with current petsc version could be incompatible which  future
>> >> changes in native MG data structures. The alternative option is to
>> >> hack MatPtAP itself, and until petsc MG will use this, whatever
>> >> changes you will make in MG in the future my code will work.
>> >
>> > Why not provide a shell DM to the KSP that knows how to compute the
>> > operators (and how to refine/coarsen and therefore
>> > restrict/interpolate).  Then there's no need to use Galerkin coarse
>> > grid operators, and the KSP will just call back to your code to create
>> > the appropriate matrices.
>>
>> Hello Lawrence,
>>
>> Thanks, it is good advice.
>> I have already my DM shell, however I have not looked yet how make it in
>> the context of MG. Now is probably time to do that.
>>
>> DM shell
>> http://userweb.eng.gla.ac.uk/lukasz.kaczmarczyk/MoFem/html/group__dm.html
>>
>>
>> Regards,
>> Lukasz
>
>
>
>


-- 
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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