[petsc-users] newbie questions on preconditioner LU

[Ling Zou]

Ok...
So, is it correct to say that, we provide a Pmat matrix, the PC will use
this Pmat to do the preconditioning operation (with an operation name
M^{-1}, but it is only operations not really a matrix).

This Pmat can be obtained, for example, from a lower order method of the
problem (as stated in the manual).

The PC in PETSc provides different options how to get this M^{-1}
operations from the Pmat provide by the user.

Ling


On Mon, Jan 28, 2013 at 12:50 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

>
> On Mon, Jan 28, 2013 at 1:46 PM, Ling Zou <lingzou80 at gmail.com> wrote:
>
>> 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}
>>
>
> The two statements above contradict. You can *either* have M=Pmat or you
> can have "M^{-1}" is the preconditioning operation used in the Krylov
> method.
>
>
>> 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?
>>
>
> You need to provide a matrix that will be used to compute a
> preconditioning operation. The preconditioning operation will *not* be the
> inverse of the matrix you provide, but it may be "close".
>
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