On 2014-01-23 15:24, Jan Blechta wrote:
On Thu, 23 Jan 2014 15:24:59 +0100
Anders Logg <[email protected]> wrote:
On Thu, Jan 23, 2014 at 02:18:30PM +0100, Jan Blechta wrote:
> On Thu, 23 Jan 2014 12:24:11 +0000
> "Garth N. Wells" <[email protected]> wrote:
>
> > If someone would like to condense this thread, it would make a
> > very nice 'question' on the Q&A page which could then be answered
> > by whoever posts the question.
>
> I'll do it.
Great. It would be even more useful with a documented demo that
explains all these issues in detail if you feel up to it.
Demo can come up when the question is resolved satisfactorily...
In fact, the two existing demos neumann-poisson, singular-poisson can
be
improved and new demo using DirichletBC(..., 'pointwise') approach can
be added.
I'd suggest squashing them all into one demo.
Garth
Jan
--
Anders
> Jan
>
> >
> > Garth
> >
> >
> > On 2014-01-22 19:23, Nico Schlömer wrote:
> > >> As far as I can tell, I'm trying to solve the extended system,
> > >> and it has no nullspace.
> > >
> > > There are two separate approaches discussed here:
> > >
> > > * extending the system such that the nullspace is trivial
> > > (Langrange)
> > > * using the Krylov solver on the original system with the
> > > nontrivial nullspace, paying a little attention to the details.
> > >
> > > --Nico
> > >
> > >
> > > On Wed, Jan 22, 2014 at 8:17 PM, Nikolaus Rath
> > > <[email protected]> wrote:
> > >> On 01/22/2014 11:08 AM, Nico Schlömer wrote:
> > >>>>>>> As Garth was mentioning, this problem is delicate for
> > >>>>>>> iterative solver, not only because
> > >>>>>>> its indefiniteness, but because the Lagrangian constraint
> > >>>>>>> you're imposing yields
> > >>>>>>> a column (the last one) of the full matrix that belongs
> > >>>>>>> to the kernel of the top-left block.
> > >>>>>>>
> > >>>>>>> Since the nullspace is at hands, I would provide it to the
> > >>>>>>> solver and then use CG+AMG,
> > >>>>>>> with Jacobi relaxation at coarser scale instead Gauss
> > >>>>>>> elimination (at least with petsc boomeramg).
> > >>>>>>
> > >>>>>>
> > >>>>>> Why is there a nullspace? Doesn't the \int u = 0 constraint
> > >>>>>> remove the
> > >>>>>> remaining degree of freedom resulting from the pure Neumann
> > >>>>>> boundary
> > >>>>>> conditions?
> > >>>>>
> > >>>>> It does not remove any DOF. It adds just one DOF - the
> > >>>>> Lagrange multiplier and an equation which makes the system
> > >>>>> regular.
> > >>>>
> > >>>> I'm probably just using different terminology, but how can
> > >>>> the system be
> > >>>> regular if it has a nullspace? If there is u such that A.u =
> > >>>> 0, I would
> > >>>> say that A is singular, not regular.
> > >>>
> > >>> The original problem is singular indeed. What Jan did is add a
> > >>> row and
> > >>> a column (Lagrange multiplier) such that the new extended
> > >>> system is regular.
> > >>
> > >>
> > >> This is what I thought - the extended system does *not* have a
> > >> nullspace. But the extended system is the system we're trying
> > >> to solve.
> > >> So I'm not sure how to understand Simone's suggestion above:
> > >>
> > >>>>>>> Since the nullspace is at hands, I would provide it to the
> > >>>>>>> solver and then use CG+AMG,
> > >>>>>>> with Jacobi relaxation at coarser scale instead Gauss
> > >>>>>>> elimination (at least with petsc boomeramg).
> > >>
> > >> As far as I can tell, I'm trying to solve the extended system,
> > >> and it has no nullspace.
> > >>
> > >>
> > >> Best,
> > >> Nikolaus
> > >>
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