[petsc-users] Problems with preconditioners, which one?

[Matthew Knepley]

On Tue, Aug 3, 2010 at 10:54 PM, Filippo Spiga <
filippo.spiga at disco.unimib.it> wrote:

>  Dear Hong,
>
>> This confirms that your Jacobian is singular, thus none of linear
>> solvers would work.
>>
>
> So do any preconditioner not help me to solve the problem?
>

There can exist no solutions when the matrix is singular, thus you have a
problem
with either:

  a) the problem definition

  b) the creation of your matrix in PETSc


> I put some stuff here: http://tinyurl.com/fil-petsc
> - "A_LS.m" is matrix (saved by PETSc)
> - "b_LS-m"
> - the file "eigenvalues_A" contains the eigenvalues of the matrix A,
> computed by MATLAB.
>
> I used "-pc_type lu" and 1 only processor. The result is the same of my
> previous email (*).
>

This shows that your matrix is singular.


> Anyway if I solve the problem using MATLAB I get the right solution. The
> formulation seems correct. To be


What does this mean? What method in MATLAB? Some methods (like CG) can
iterate on rank deficient
matrices with a compatible rhs and get a solution, but other Krylov methods
will fail. Most preconditioners
will fail.


> honest, the eigenvalues don't say me nothing. But I'm a computer scientist,
> not a mathematician. I'm not able to recognize which preconditioner I should
> use or which modifications (scaling all/part of the rows? reformulate the
> system in another way?...) do to solve the problem. From my side, it is not
> possible to try all the preconditioners and also it is not the right way...
>

Actually, I strongly disagree. Preconditioners are very problem specific,
and it is often impossible
to prove which one will work for a certain problem. There are many
well-known results along these
lines, such as the paper of Greenbaum, Strakos, and Ptak on GMRES.
Experimentation is essential.

    Matt


> Once again, thanks.
>
> (*)
> [0|23:14:58]: unknown: MatLUFactorNumeric_SeqAIJ() line 668 in
> src/mat/impls/aij/seq/aijfact.c: Zero pivot row 1 value 0 tolerance
> 2.77778e-14 * rowsum 0.0277778
>
> --
>
> Filippo SPIGA
>
> «Nobody will drive us out of Cantor's paradise.»
>     -- David Hilbert
>
>


-- 
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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