Exactly, it was implicitly stated. Then CG should work since is spd on the space orthogonal to the kernel.
Or, fix a point, and then shift the solution with its average. Without the knowledge of the nullspace you can either use minres or symmlq (or the new minres-qlp) on the neumann problem, but I don't really know how to choose the preconditioner (maybe the same problem with a fixed point?) On the augmented problem, I would use a direct solver :D By the way, I really open to suggestions since I'm facing similar issues on a nonlinear mechanical problem (and the nullspace is not available). Simone 2014/1/21 Kent-Andre Mardal <kent-...@simula.no> > > > On Tuesday, 21 January 2014, Simone Pezzuto <junki....@gmail.com> wrote: > >> 2014/1/21 Jan Blechta <blec...@karlin.mff.cuni.cz> >> >>> On Tue, 21 Jan 2014 17:18:54 +0000 >>> "Garth N. Wells" <gn...@cam.ac.uk> wrote: >>> >>> > On 2014-01-21 17:01, Nikolaus Rath wrote: >>> > > Hello, >>> > > >>> > > I noticed that the neumann-poisson demo >>> > > ( >>> http://fenicsproject.org/documentation/dolfin/1.3.0/python/demo/documented/neumann-poisson/python/documentation.html >>> ) >>> > > fails when using a different solver, e.g. when replacing >>> > > >>> > > solve(a == L, w) >>> > > >>> > > with >>> > > >>> > > solve(a == L, w, >>> > > solver_parameters = {'linear_solver': 'cg', >>> > > 'preconditioner': 'ilu'}) >>> > > >>> > >>> > This problem needs very careful treatment when using iterative >>> > solvers. Simple block-box preconditioners and solvers will very >>> > likely fail. >>> >>> AMG preconditioning based on operator >>> >>> (inner(grad(u), grad(v)) + c*d)*dx >>> >>> could perform well. This operator does not have a dense row like the >>> original one. This is a strategy similar to demo_stokes-iterative. >>> >>> >> In this case the preconditioner is singular (pure neumann), no it cannot >> be used. >> >> 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). >> >> Simone >> > > Providing the null space is perhaps the best alternative, but then you do > not need the lagrange multiplier. Instead you can remove the constant from > the lhs and rhs before sending it to cg. > > Kent > > > >> >> >>> Jan >>> >>> > >>> > Garth >>> > >>> > > The error that I'm getting with FEniCS 1.3 is: >>> > > >>> > > $ python demo_neumann-poisson.py >>> > > Solving linear variational problem. >>> > > Solving linear system of size 4226 x 4226 (PETSc Krylov solver). >>> > > Traceback (most recent call last): >>> > > File "demo_neumann-poisson.py", line 68, in <module> >>> > > 'preconditioner': 'ilu'}) >>> > > File >>> > > >>> "/home/nikratio/.local/FEniCS/lib/python2.7/site-packages/dolfin/fem/solving.py", >>> > > line 268, in solve >>> > > _solve_varproblem(*args, **kwargs) >>> > > File >>> > > >>> "/home/nikratio/.local/FEniCS/lib/python2.7/site-packages/dolfin/fem/solving.py", >>> > > line 297, in _solve_varproblem >>> > > solver.solve() >>> > > RuntimeError: >>> > > >>> > > *** >>> > > >>> ------------------------------------------------------------------------- >>> > > *** DOLFIN encountered an error. If you are not able to resolve >>> > > this issue >>> > > *** using the information listed below, you can ask for help at >>> > > *** >>> > > *** fenics@fenicsproject.org >>> > > *** >>> > > *** Remember to include the error message listed below and, if >>> > > possible, >>> > > *** include a *minimal* running example to reproduce the error. >>> > > *** >>> > > *** >>> > > >>> ------------------------------------------------------------------------- >>> > > *** Error: Unable to solve linear system using PETSc Krylov >>> > > solver. *** Reason: Solution failed to converge in 2 iterations >>> > > (PETSc reason DIVERGED_INDEFINITE_PC, residual norm ||r|| = >>> > > 1.541789e+19). *** Where: This error was encountered inside >>> > > PETScKrylovSolver.cpp. *** Process: 0 >>> > > *** >>> > > *** DOLFIN version: 1.3.0 >>> > > *** Git changeset: >>> > > *** >>> > > >>> ------------------------------------------------------------------------- >>> > > >>> > > >>> > > Bug or user error? >>> > > >>> > > >>> > > Best, >>> > > Nikolaus >>> > > >>> > > _______________________________________________ >>> > > fenics mailing list >>> > > fenics@fenicsproject.org >>> > > http://fenicsproject.org/mailman/listinfo/fenics >>> > _______________________________________________ >>> > fenics mailing list >>> > fenics@fenicsproject.org >>> > http://fenicsproject.org/mailman/listinfo/fenics >>> >>> _______________________________________________ >>> fenics mailing list >>> fenics@fenicsproject.org >>> http://fenicsproject.org/mailman/listinfo/fenics >>> >> >>
_______________________________________________ fenics mailing list fenics@fenicsproject.org http://fenicsproject.org/mailman/listinfo/fenics
