[petsc-users] Some clarification on PCMG

[Barry Smith]

> On Feb 19, 2016, at 8:55 AM, Aulisa, Eugenio <eugenio.aulisa at ttu.edu> wrote:
> 
> Hi,
> 
> I would like a clarification how PCMG updates 
> the residual on the level-l before restricting it to the level l-1
> in the down-cycle.
> 
> In particular I would expect that what is projected down is the true-residual,
> the one updated using Amat_l, however from what I see in my test it seams
> to be the residual updated using Pmat_l.
> 
> My test is very simple:
> When setting up  the ksp object on the l-level, in one case I use
> 
> KSPSetOperators(_ksp_l, _Amat_l, _Pmat_l);
> 
> in the other case I use
> 
> KSPSetOperators(_ksp_l, _Pmat_l, _Pmat_l);
> 
> when I run my application I get exactly the same results for the preconditioned residual:
> 
> these are the very last 2 outputs:
> 
> with Amat,Pmat
> 9 KSP preconditioned resid norm 2.939296481331e-16 true resid norm 1.460300485277e-02 ||r(i)||/||b|| 9.999999999999e-01

 It uses the Amat to update the residual. Note that this has not worked essentially at all the true residual norm 1.46e-2 is huge while using the Pmat below it is 5e-15.  The fact that the "residual norm" is the same is a red herring.

  I suspect that the Amat, and the Pmat are "too far apart" hence using Amat to define the operator and Pmat to define the smoother produces a multigrid that really doesn't work.

  As a test try to make the Pmat be just a small perturbation of Amat (or if it is easier the other way around Amat a small perturbation of Pmat) then run and look at the true residual history.

  Barry

  
> 
> with Pmat, Pmat:
> 9 KSP preconditioned resid norm 2.939296481331e-16 true resid norm 5.165834461813e-15 ||r(i)||/||b|| 3.537514719672e-13
> 
> Since Amat and Pmat are 2 different matrices, and PCMG does not seams to see any difference, 
> the only explanation I gave  myself is that the residual projected down to the coarser level is the
> the one updated using Pmat.
> 
> Now, if this is the case, is there any way I can use Amat_l to update the residual?
> 
> If this is not the case, and Amat_l is already used, 
> do you have any other explanation why the results are identical?
> 
> Thanks,
> Eugenio
> 
> 
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> 
> Eugenio Aulisa
> 
> Department of Mathematics and Statistics,
> Texas Tech University
> Lubbock TX, 79409-1042
> room: 226
> http://www.math.ttu.edu/~eaulisa/
> phone: (806) 834-6684
> fax: (806) 742-1112
> 
> 
>