[petsc-users] Is PCMG a generic PC object ?

[Vijay S. Mahadevan]

Jed and Dave, thanks for the explanation. Now I do understand that the
MG PC is generic if I have restriction/prolongation operators for
every level. But I do not have the fine grid operator on hand
explicitly (only a shell matrix with MatMult) and technically all my
coarser grid operators will also be matrix-free. I was originally
planning to hand these shell matrices to petsc as the coarse
operators but can petsc do this by itself with only access to the fine
grid operator ?

Basically my problem is that I cannot afford to create a matrix until
the coarsest level and I plan to use HYPRE BoomerAMG on the coarsest
level. With this hierarchy, would MatMult enabled shell matrices
provide enough leeway to get the optimal performance from MG ?

Matt, I will look into the ML framework also. Thanks.

Vijay

On Fri, Dec 3, 2010 at 11:02 AM, Matthew Knepley <knepley at gmail.com> wrote:
> I will also note that a good intro for implementing your own might be the ML
> PC
> in Petsc. It puts the ML AMG package into the PCMG framework.
>    Matt
>
> On Fri, Dec 3, 2010 at 3:44 AM, Dave May <dave.mayhem23 at gmail.com> wrote:
>>
>> Hey Vijay,
>>  PCMG is generic. If you provide the operators for each level, along
>> with the restriction and prolongation,
>> you can use PCMG. It doesn't need to know about the mesh.
>>
>> You don't actually need to provide the coarse grid operators.
>> Given the fine grid operator and R and optionally P, you can use
>> Galerkin coarsening by calling
>> PCMGSetGalerkin() or via the command line arg -pc_mg_galerkin
>> Also, if you don't specify the prolongation, petsc will use P = R^T.
>>
>>
>> Cheers,
>>  Dave
>>
>>
>> On 3 December 2010 06:02, Vijay S. Mahadevan <vijay.m at gmail.com> wrote:
>> > Hi all,
>> >
>> > I was wondering whether the MG preconditioner object is generic enough
>> > to work out of the box like say ILU or SOR.  To elaborate on this, if
>> > I can provide the number of levels, restriction and prolongation
>> > operators for each level and the system operators along with vectors
>> > allocated for solution and rhs, would it work as a preconditioner for
>> > my given problem and a prescribed rhs at the finest level of PCMG. Or
>> > does it need some knowledge of the fine and coarser meshes to perform
>> > the MG operations correctly ?
>> >
>> > All the examples I've seen using MG in petsc involve the DA and DMMG
>> > objects and since I use my own mesh and corresponding discretization
>> > code for an elliptic system, I'm curious about this usage. It would
>> > not be terribly difficult to write my own framework to do a simple
>> > V-cycle with my existing framework but since petsc already provides
>> > this functionality along with different types of MG solves (with
>> > verified code!), I really want to use it for my system. Any help
>> > and/or pointers are welcome.
>> >
>> > Thanks,
>> > vijay
>> >
>
>
>
> --
> 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
>