[petsc-users] Solving/creating SPD systems

[Matthew Knepley]

On Sat, Nov 28, 2015 at 10:35 AM, Patrick Sanan <patrick.sanan at gmail.com>
wrote:

> On Sat, Nov 28, 2015 at 06:31:31AM -0600, Matthew Knepley wrote:
> > On Sat, Nov 28, 2015 at 12:10 AM, Justin Chang <jychang48 at gmail.com>
> wrote:
> >
> > > Hi all,
> > >
> > > Say I have a saddle-point system for the mixed-poisson equation:
> > >
> > > [I  -grad] [u]  = [0]
> > > [-div  0  ] [p]     [-f]
> > >
> > > The above is symmetric but indefinite. I have heard that one could make
> > > the above symmetric and positive definite (SPD). How would I do that?
> And
> > > if that's the case, would this allow me to use CG instead of GMRES?
> > >
> >
> > I believe you just multiply the bottom row by -1. You can use CG for an
> SPD
> > system, but you can
> > use MINRES for symmetric indefinite.
> If I'm remembering correctly, flipping that sign lets you make your system
> alternately P.D. or
> symmetric, but not both. Maybe you were hearing about the Bramble-Pasciak
> preconditioner or a related approach?
>

Its possible that my Thanksgiving was too happy, however I was pretty sure
that div was the transpose of -grad.
Is this wrong?

  Thanks,

    Matt


> >    Matt
> >
> >
> > > Thanks,
> > > Justin
> > >
> >
> >
> >
> > --
> > 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
>



-- 
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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