[petsc-users] KSP step not accelerating despite good preconditioning in SNES

[Dave May]

On Sunday, 4 October 2015, Timothée Nicolas <timothee.nicolas at gmail.com>
wrote:

> Thank you. It seems to be working like a charm with PCSHELL, I have the
> drastic reductions in KSP iterations ! (incidentally, my convergence
> problem was probably mostly due to a mistake in the Schur matrix, but
> putting things in the right place also helps !)
>
> Now I have to move the KSP step in the preconditioner to multigrid method,
> it should in principle be more efficient than the default KSP options for
> my specific problem. However there is almost no example using multigrid in
> the documentation. I found only ksp/ksp/examples/tutorials/ex42.c
>
and ksp/ksp/examples/tests/ex19.c, however in the first one it is not the
> default and trying to use the option -stokes_pc_type pcmg produced errors
> like
> [0]PETSC ERROR: Unable to find requested PC type pcmg
>

The option should be
-stokes_pc_type mg

Default will be a one level method so you need to set the number of levels
with an addition arguement. In ex42, levels are defined via coarsening.

I suggest using
-help | grep mg
 to learn what this option is called, and more generally to learn how
to configure the mg preconditioner.



> Regarding the second one, it says at the top that it is the "bad way", so
> I am not sure I should follow this example... In which sense is it a bad
> way ? Is it because there are only two levels and in principle we shoud
> have a hierarchy until the lowest grid ?
>
> In anycase if anyone has a nice multigrid example on a simple case like
> Laplacian, in the "good way", I would be interested
>
> Best
>
> Timothee
>
>
> 2015-09-28 14:21 GMT+02:00 Timothée Nicolas <timothee.nicolas at gmail.com
> <javascript:_e(%7B%7D,'cvml','timothee.nicolas at gmail.com');>>:
>
>> Thanks a lot, I expected something like that. I will look in this
>> direction.
>>
>> Best
>>
>> Timothée
>>
>> 2015-09-28 21:17 GMT+09:00 Matthew Knepley <knepley at gmail.com
>> <javascript:_e(%7B%7D,'cvml','knepley at gmail.com');>>:
>>
>>> On Mon, Sep 28, 2015 at 2:53 AM, Timothée Nicolas <
>>> timothee.nicolas at gmail.com
>>> <javascript:_e(%7B%7D,'cvml','timothee.nicolas at gmail.com');>> wrote:
>>>
>>>> Hi all,
>>>>
>>>> I have something strange in my application and I don't know what could
>>>> cause this. I am trying to do an implicit MHD problem and I thought I
>>>> finally figured out the preconditioner step, but somehow I don't get the
>>>> expected result, not even close.
>>>>
>>>> For the preconditioning, I am using an approximate Schur complement,
>>>> which requires two relatively easy KSP inversions at each preconditioner
>>>> application. I apply this algorithm directly to the result function at the
>>>> end of the routine FormFunction. I have checked that the approximation to
>>>> the inversion of the Jacobian is good, in the sense that when I multiply
>>>> the preconditioned vector by the *total* Jacobian matrix, I indeed
>>>> recover almost the initial unpreconditioned vector. Also, I know that my
>>>> Jacobian matrix is correct, because (i) I have checked manually that F(X +
>>>> dX) ~ F(X) + J * dX and (ii) when I don't use -snes_mf and use the provided
>>>> Jacobian matrix the result is pretty much equivalent to using -snes_mf.
>>>>
>>>> In my understanding, this means that what I effectively feed to SNES at
>>>> the end of my FormFunction routine is a good approximation to J^(-1) F. As
>>>> a result, I naturally expect that the number of KSP iterations necessary to
>>>> achieve one SNES iteration be drastically reduced. However, I observe
>>>> virtually no change whatsoever in the number of iterations.
>>>>
>>>> Any thoughts about what I could be missing ? Maybe I forgot to set a
>>>> SNES or KSP option somewhere ? I can send pieces of code if needs be.
>>>>
>>>
>>> It sounds like you are putting this in the wrong place. If you have the
>>> action of a good preconditioner for the Jacobian, then you
>>> should use a PCSHELL and pass it to the KSP. It does not belong in the
>>> FormFunction.
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Best
>>>>
>>>> Timothee
>>>>
>>>>
>>>>
>>>
>>>
>>> --
>>> 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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