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 fenics@fenicsproject.org http://fenicsproject.org/mailman/listinfo/fenics
