[petsc-users] Solving/creating SPD systems

[Patrick Sanan]

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?
> 
>    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
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