[petsc-dev] Nullspace with right preconditioning

[Jed Brown]

Matthew Knepley <knepley at gmail.com> writes:

> On Wed, Apr 4, 2018 at 3:23 PM, Smith, Barry F. <bsmith at mcs.anl.gov> wrote:
>
>>
>>   It may not be broken; it may just be misunderstood or incorrect approach.
>>
>>   You'll need to explain why and where exactly you think it is broken.
>
>
> I am solving Stokes. I will push the example for you to run tonight.
> Basically, I put in a constant for the pressure
> as the nullspace. If you run with gmres/left it gives back a pressure with
> integral 0. If you run with gmres/right,
> it gives back a pressure with a big integral.

The code makes the Krylov basis orthogonal to the null space.  With
right preconditioning, the solution is x = P^{-1} y for some y in the
Krylov space.  I don't know how to easily make x orthogonal to the null
space so you probably have to project it out after the solve.

Note that discrete pressure has sum 0, but the continuous integral of
pressure is generally not 0 (unless on a uniform grid).  If you want the
latter, you'll to do the explicit projection.