On 2014-01-21 18:32, Simone Pezzuto wrote:
Exactly, it was implicitly stated. Then CG should work since is spd on
the space orthogonal to the kernel.
We have a demo for this:
http://fenicsproject.org/documentation/dolfin/1.3.0/python/demo/documented/singular-poisson/python/documentation.html
Garth
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 <[email protected]>
On Tuesday, 21 January 2014, Simone Pezzuto <[email protected]>
wrote:
2014/1/21 Jan Blechta <[email protected]>
On Tue, 21 Jan 2014 17:18:54 +0000
"Garth N. Wells" <[email protected]> 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
[1])
> 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
***
*** [email protected]
***
*** 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
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[1]
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[2] http://fenicsproject.org/mailman/listinfo/fenics
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