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. 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 > > > >> > > > > _______________________________________________ > > > > fenics mailing list > > > > [email protected] > > > > http://fenicsproject.org/mailman/listinfo/fenics > > > _______________________________________________ > > > fenics mailing list > > > [email protected] > > > http://fenicsproject.org/mailman/listinfo/fenics > > > > _______________________________________________ > > fenics mailing list > > [email protected] > > http://fenicsproject.org/mailman/listinfo/fenics > _______________________________________________ > fenics mailing list > [email protected] > http://fenicsproject.org/mailman/listinfo/fenics _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics
