[petsc-users] multigrid preconditioning and adaptivity

[Lawrence Mitchell]

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.

Cheers,

Lawrence

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