[petsc-users] singular matrix solve using MAT_SHIFT_POSITIVE_DEFINITE option

[Matthew Knepley]

On Wed, Apr 30, 2014 at 2:53 PM, Danny Lathouwers - TNW <
D.Lathouwers at tudelft.nl> wrote:

>  Dear users,
>
>
>
> I encountered a strange problem. I have a singular matrix P (Poisson,
> Neumann boundary conditions, N=4). The rhs b sums to 0.
>
> If I hand-fill the matrix with the right entries (non-zeroes only) things
> work with KSPCG and ICC preconditioning and using the
> MAT_SHIFT_POSITIVE_DEFINITE option. Convergence in 2 iterations to (a)
> correct solution. So far for the debugging problem.
>

That option changes the preconditioner matrix to (alpha I + P). I don't
know of a theoretical reason that this
should be a good preconditioner, but perhaps it exists. Certainly ICC is
exquisitely sensitive (you can easily
write down matrices where an epsilon change destroys convergence).

Yes, you should use null space, and here it is really easy

  -ksp_constant_null_space

Its possible that this fixes your convergence, if the ICC perturbation was
introducing components in the
null space to your solution.

   Matt


> My real problem computes P from D * M * D^T. If I do this I get the same
> matrix (on std out I do not see the difference to all digits).
>
> The system P * x = b now does NOT converge.
>
> More strange is that is if I remove the zeroes from D then things do work
> again.
>
> Either things are overly sensitive or I am misusing petsc.
>
> It does work when using e.g. the AMG preconditioner (again it is a correct
> but different solution). So system really seems OK.
>
>
>
> Should I also use the Null space commands as I have seen in some of the
> examples as well?
>
> But, I recall from many years ago when using MICCG (alpha) preconditioning
> that no such tricks were needed for CG with Poisson-Neumann. I am supposing
> the MAT_SHIFT_POSITIVE_DEFINITE option does something similar as MICCG.
>
>
>
> For clarity I have included the code (unfortunately this is the smallest I
> could get it; it’s quite straightforward though).
>
> By setting the value of option to 1 in main.f90 the code use P = D * M *
> D^T otherwise it will use the hand-filled matrix.
>
> The code prints the matrix P and solution etc.
>
>
>
> Anyone any hints on this?
>
> What other preconditioners (serial) are suitable for this problem besides
> ICC/AMG?
>
>
>
> Thanks very much.
>
> Danny Lathouwers
>
>
>



-- 
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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