On 2014-01-23 15:34, Jan Blechta wrote:
On Thu, 23 Jan 2014 15:26:40 +0000
"Garth N. Wells" <[email protected]> wrote:
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.
I don't agree. singular-poisson needs PETSc while neumann-poisson can
be improved that it can use PETSc for MINRES, AMG, but it can use
direct
solver either when PETSc is missing.
Still no reason why they can't be merged. A reason for merging is that
the one demo would show different ways of solving the same PDE. We have
too many demos - it doesn't help the user if they have to look all over
the place.
Garth
Jan
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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