[petsc-users] newbie questions on preconditioner LU

[Jed Brown]

On Mon, Jan 28, 2013 at 1:36 PM, Ling Zou <lingzou80 at gmail.com> wrote:

> I guess I got the impression that M is generally the same as A from
> reading the manual.(PETSc Users Manual, Reversion 3.3, page 71, under 4.1
> Using KSP)
>
> "Typically the preconditioning matrix (i.e., the matrix from which the
> preconditioner is to be constructed), Pmat, is the same as the matrix that
> defines the linear system, Amat; however, occasionally these matrices
> differ (for instance, when a preconditioning matrix is obtained from a
> lower order method than that employed to form the linear system matrix)."
>

I think you are getting confused by mixed notation. A PC in PETSc is an
algorithm that takes a matrix (Pmat in the docs) and does some work to be
able to apply an operation (named "M^{-1}" in your first email). This does
*not* imply that M=Pmat, or that M is ever available or used, there is just
a a linear operation named "M^{-1}".
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