[petsc-users] newbie questions on preconditioner LU

[Ling Zou]

Thank you Jed.
As you explained, M is not explicitly computed. However, when setup the ksp

KSPSetOperators(KSP ksp,Mat Amat,Mat Pmat,MatStructure flag);

We need a Pmat (the M we are talking about here). In the solver, we
actually need M^{-1} as the preconditioning matrix, so we don't need to
compute the M matrix but need PC to get the approximated M^{-1}, right?
Even we don't explicitly compute M, but we still need provide non-zero
entries for this M, is it correct?

Ling

On Mon, Jan 28, 2013 at 12:33 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

>
> On Mon, Jan 28, 2013 at 1:27 PM, Ling Zou <lingzou80 at gmail.com> wrote:
>
>> Ahh.. that's true!
>> In case M is not A (as you pointed out earlier), does PCLU provide the
>> approximated inverse matrix of M^{-1} using LU factorization on M?
>>
>
> Not really, preconditioners are based on inexact algorithms applied to A,
> not explicit formation of an M that is easier to factor exactly. Since the
> preconditioner P ("=M^{-1}") is non-singular, there _exists_ an M such that
> P=M^{-1}, but M is not explicitly computed and it's not used in the solve.
> Only P is used, and only in special cases (like incomplete factorization)
> is there even a practical algorithm available to compute M if you wanted
> to. (For many interesting algorithms, M is dense even though A is sparse.)
>
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