[petsc-users] Algorithms to remove null spaces in a singular system

[Fande Kong]

On Wed, Oct 12, 2016 at 9:24 PM, Jed Brown <jed at jedbrown.org> wrote:

> Fande Kong <fdkong.jd at gmail.com> writes:
>
> > I think we need to make sure that the basis vectors are orthogonal to
> each
> > other and they are normalized. Right?
>
> Yes, that is clearly stated in the man page and checked for in debug
> mode.  The relevant code to remove the null space is
>
>   if (sp->n) {
>     ierr = VecMDot(vec,sp->n,sp->vecs,sp->alpha);CHKERRQ(ierr);
>     for (i=0; i<sp->n; i++) sp->alpha[i] = -sp->alpha[i];
>     ierr = VecMAXPY(vec,sp->n,sp->alpha,sp->vecs);CHKERRQ(ierr);
>   }
>


Right now, we are forcing users to provide orthogonal basis vectors. Is
there any issue if we orthogonalize  the arbibitry basis vectors provided
by users in PETSc?  And then users could pass arbitrary basis vectors
without doing any preprocessing.

Fande,
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