[petsc-users] Fieldsplit schur complement with preonly solves

[Matthew Knepley]

On Tue, Mar 11, 2014 at 11:05 AM, Luc <luc.berger.vergiat at gmail.com> wrote:

>  Hum,
> would a *-pc_fieldsplit_schur_precondition self *use the full Schur as
> preconditioner for itself?
> I made some special choices in order to keep A diagonal which makes it
> cheap to inverse.
> Actually I am assuming that Schur will be blazing fast with my type of
> discretization...
>

We reorganized, so that now what you want is "selfp":


http://www.mcs.anl.gov/petsc/petsc-dev/docs/manualpages/PC/PCFieldSplitSchurPrecondition.html

  Thanks,

     Matt


> Best,
>
> Luc
>
> On 03/11/2014 11:36 AM, Matthew Knepley wrote:
>
>  On Tue, Mar 11, 2014 at 9:56 AM, Luc Berger-Vergiat <
> luc.berger.vergiat at gmail.com> wrote:
>
>> Hi all,
>> I am testing some preconditioners for a FEM problem involving different
>> types of fields (displacements, temperature, stresses and plastic strain).
>> To make sure that things are working correctly I am first solving this
>> problem with:
>>
>> -ksp_type preonly -pc_type lu, which works fine obviously.
>>
>>
>> Then I move on to do:
>>
>> -ksp_type gmres -pc_type lu, and I get very good convergence (one gmres
>> linear iteration per time step) which I expected.
>>
>>
>> So solving the problem exactly in a preconditioner to gmres leads to
>> optimal results.
>> This can be done using a Schur complement, but when I pass the following
>> options:
>>
>> -ksp_type gmres -pc_type fieldsplit -pc_fieldsplit_type schur
>> -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_0_fields 2,3
>> -pc_fieldsplit_1_fields 0,1 -fieldsplit_0_ksp_type
>> preonly -fieldsplit_0_pc_type lu -fieldsplit_1_ksp_type
>> preonly -fieldsplit_1_pc_type lu
>>
>> My results are terrible, gmres does not converge and my FEM code reduces
>> the size of the time step in order to converge.
>> This does not make much sense to me...
>>
>
>  The problem is the Schur complement block. We have
>
>    S = C A^{-1} B
>
>  PETSc does not form S explicitly, since it would require forming the
> dense
> inverse of A explicitly. Thus we only calculate the action of A. If you
> look in
> -ksp_view, you will see that the preconditioner for S is formed from A_11,
> which it sounds like is 0 in your case, so the LU of that is a crud
> preconditioner.
> Once you wrap the solve in GMRES, it will eventually converge.
>
>  You can try using the LSC stuff if you do not have a preconditioner
> matrix
> for the Schur complement.
>
>    Thanks,
>
>       Matt
>
>
>>  Curiously if I use the following options:
>>
>> -ksp_type gmres -pc_type fieldsplit -pc_fieldsplit_type schur
>> -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_0_fields 2,3
>> -pc_fieldsplit_1_fields 0,1 -fieldsplit_0_ksp_type gmres
>> -fieldsplit_0_pc_type lu -fieldsplit_1_ksp_type gmres -fieldsplit_1_pc_type
>> lu
>>
>> then the global gmres converges in two iterations.
>>
>>  So using a pair of ksp gmres/pc lu on the A00 block and the Schur
>> complements works, but using lu directly doesn't.
>>
>>  Because I think that all this is quite strange, I decided to dump some
>> matrices out. Namely, I dumped the complete FEM jacobian, I also do a
>> MatView on jac->B, jac->C and the result of KSPGetOperators on kspA. These
>> returns three out of the four blocks needed to do the Schur complement.
>> They are correct and I assume that the last block is also correct.
>> When I import jac->B, jac->C and the matrix corresponding to kspA in
>> MATLAB to compute the inverse of the Schur complement and pass it to gmres
>> as preconditioner the problem is solved in 1 iteration.
>>
>>  So MATLAB says:
>>
>> -ksp_type gmres -pc_type fieldsplit -pc_fieldsplit_type schur
>> -pc_fieldsplit_schur_factorization_type full -pc_fieldsplit_0_fields 2,3
>> -pc_fieldsplit_1_fields 0,1 -fieldsplit_0_ksp_type
>> preonly -fieldsplit_0_pc_type lu -fieldsplit_1_ksp_type
>> preonly -fieldsplit_1_pc_type lu
>>
>>  should yield only one iteration (maybe two depending on implementation).
>>
>>  Any ideas why the Petsc doesn't solve this correctly?
>>
>>   Best,
>> Luc
>>
>>
>
>
>  --
> 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
>
>
>


-- 
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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