[petsc-users] V-cycle multigrid with matrix shells

[Sylvain Barbot]

Dear Jed,

Thank you for your previous comments. I am still trying to design a
multigrid preconditionner for the Navier's equation of elasticity. I
have defined shell matrices for the interpolation, restriction,
smoothing, residual calculation and the fine-level solver (see
attached my_green.f90 file with stub functions). I thought that all
these shell matrices would be enough to do the job, but upon running
KSPSetup(), I get the following error:

[0]PETSC ERROR: No support for this operation for this object type!
[0]PETSC ERROR: This matrix type, shell, does not support getting
diagonal block!
[0]PETSC ERROR:
------------------------------------------------------------------------
[0]PETSC ERROR: Petsc Release Version 3.1.0, Patch 4, Fri Jul 30
14:42:02 CDT 2010
[0]PETSC ERROR:
------------------------------------------------------------------------
[0]PETSC ERROR: PCSetUp_BJacobi() line 162 in src/ksp/pc/impls/bjacobi/bjacobi.c
[0]PETSC ERROR: PCSetUp() line 795 in src/ksp/pc/interface/precon.c
[0]PETSC ERROR: KSPSetUp() line 237 in src/ksp/ksp/interface/itfunc.c
[0]PETSC ERROR: PCSetUp_MG() line 574 in src/ksp/pc/impls/mg/mg.c

regarding your previous comments: "For Jacobi, you can have your
MatShell implement MatGetDiagonal and it will work. (...) If you want
to use a multiplicative relaxation like SOR, you would have to
implement it yourself.", I actually want to use SOR with my smoother
shell matrix. What am I doing wrong to make petsc still believe I want
to use Jacobi?

another related question: with a direct solver, one needs to assign a
shell matrix with a KSP object (KSPSetOperators); is it still required
when using multigrid? if I don't do so, I get the following error:

[0]PETSC ERROR: Null argument, when expecting valid pointer!
[0]PETSC ERROR: Null Object: Parameter # 1!
[0]PETSC ERROR: MatGetVecs() line 7265 in src/mat/interface/matrix.c
[0]PETSC ERROR: KSPGetVecs() line 806 in src/ksp/ksp/interface/iterativ.c
[0]PETSC ERROR: KSPSetUp_GMRES() line 94 in src/ksp/ksp/impls/gmres/gmres.c
[0]PETSC ERROR: KSPSetUp() line 199 in src/ksp/ksp/interface/itfunc.c

however, I don't understand why I would need this matrix in a
multigrid framework.

Is there any example out there of using PCMG with shell matrices?

Thanks in advance for your response.
Best wishes,
Sylvain Barbot


2010/10/7 Jed Brown <jed at 59a2.org>:
> On Thu, Oct 7, 2010 at 11:45, Sylvain Barbot <sylbar.vainbot at gmail.com>
> wrote:
>>
>> questions:
>> 1) is it at all possible to specify this mode of operation, from the
>> finest to the coarser level, and back? Any examples out there?
>
> -pc_mg_type multiplicative, or
>   PCMGSetType(pc,PC_MG_MULTIPLICATIVE);
>
>>
>> 2) is it readily possible to use matrix shells with DMMG? I imagine
>> the Jacobian matrix may simply be provided as a matrix shell. Is there
>> any examples of multi-grid methods with shell matrices online?
>
> You can do this, but you will have to define a custom smoother.  For Jacobi,
> you can have your MatShell implement MatGetDiagonal and it will work.  I
> thought you could implement MatGetDiagonalBlock for PBJacobi, but it's not
> currently written that way (though it should be and that would be an easy
> change to make).  If you want to use a multiplicative relaxation like SOR,
> you would have to implement it yourself.  If you need something like ILU for
> a smoother, then you will have to pay for a matrix.  Note that one
> possibility is to assemble a matrix on all but the finest level so you can
> use stronger smoothers there, then make do with Jacobi on the finest level.
>
>>
>> 3) to deal with non-uniform sampling: can I provide the coordinates of
>> the finest grid with DASetCoordinates, then expect DMMG to provide the
>> subsampled coordinates at the coarser levels?
>
> Currently no, you have to set them on each level.  Perhaps you could do this
> by rolling a loop over levels and applying MatRestrict using the restriction
> matrix from DMMG (this might not be the sampling that you want).
> Jed
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