[petsc-users] Indefinite PC

[Matthew Knepley]

On Fri, Nov 21, 2014 at 11:05 PM, Anush Krishnan <k.anush at gmail.com> wrote:

>
>
> On 21 November 2014 18:23, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>
>> > On Nov 21, 2014, at 5:09 PM, Anush Krishnan <k.anush at gmail.com> wrote:
>> >
>> > Hello petsc-users,
>> >
>> > I've been running some CFD simulations, and I ran into one case where
>> the system (which is a coupled system for pressure and body forces) did not
>> converge and the reason was KSP_DIVERGED_INDEFINITE_PC. The options I'm
>> using are -pc_gamg_agg_nsmooths 1 -pc_type gamg -pc_gamg_type agg with a
>> conjugate gradient solver.
>>
>>    We've heard reports of this happening before. You should increase the
>> number of smoothing steps for the multigrid or change to a "stronger"
>> smoother.
>>
>>    What do you get with -ksp_view for exact solver you are using?
>>
>
> I've attached a copy of the output with -ksp_view.
>
>
>>    Are you using PETSc's SNES? TS? Or just KSP?
>>
>
> Just KSP.
>
>
>>
>> >
>> > I saw in example ksp/pc/examples/tutorials/ex2.c that I should use the
>> flag -pc_factor_shift_positive_definite to avoid this.
>>
>>    This flag is only for factorization based preconditioners not gamg so
>> you should not use it.
>>
>> > I have a few questions regarding this:
>> >       • What does it mean that the preconditioner is indefinite?
>>
>>     It means that the preconditioner generated by GAMG has both negative
>> and positive eigenvalues. CG cannot handle this, CG  requires the
>> preconditioner have all eigenvalues of the same sign.
>>
>> > What can cause this to happen? And what does the above flag do?
>> >       • The error occurs midway through the simulation. Is there any
>> reason why this might be the case? The left-hand side matrix does not
>> change during the simulation.
>>
>>     Huh? If the matrix is not changing then the preconditioner should not
>> be changing and hence the preconditioner should not be rebuilt and hence
>> you should not see this message "midway through the simulation". Are you
>> sure that the matrix is not changing??
>>
>
> Yes, I'm sure that the matrix is not changing. Only the right hand side
> vector changes every time step.
>
> I have heard that CG sometimes converges even if the matrix is not
> positive definite - do you think that might be happening? Also, is there a
> way to check if a given matrix is positive definite using PETSc? And is it
> possible to
>

That is possible.

It is much more expensive to verify indefiniteness than to solve the
system. I recommend you
increase the smoothing as Barry suggested.

  Thanks,

    Matt


> generate an indefinite preconditioner from a matrix that is symmetric
> positive definite (I remember seeing a thread about this recently)?
>
>
>>
>>
>> >       • Do both -pc_factor_shift_positive_definite and
>> -pc_factor_shift_type POSITIVE_DEFINITE do the same thing?
>>
>>    Yes, they are from different versions of PETSc, but neither are for
>> gamg.
>>
>>   Barry
>>
>> > Thank you,
>> >
>> > Anush
>> >
>>
>>
>


-- 
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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