> 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
