[petsc-users] Convergence of iterative linear solver

[Matthew Knepley]

On Mon, Jun 1, 2015 at 11:24 PM, Eduardo <erocha.ssa at gmail.com> wrote:

> I am solving a FEM solid mechanics linear elasticity model, for now the
> only problem is the mesh that has needle-shaped and very flat elements.
> Have you any suggestion of preconditioner (and references).
>

The problem here is your discretization. WIth quasi-regular elements,
-pc_type gamg works fine. However, with flat elements, your FEM
basis becomes very ill-conditioned since the normal basis functions are
almost linearly dependent. I think the best use of time here is
to investigate better discretization strategies for this problem, since no
solver is really going to help you.

  Thanks,

    Matt


> Thanks,
> Eduardo
>
> On Tue, Jun 2, 2015 at 4:11 AM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>
>>
>> > On Jun 1, 2015, at 4:06 PM, Eduardo <erocha.ssa at gmail.com> wrote:
>> >
>> > I am solving a linear system for which the preconditioned residual
>> decreases, but the true residual increases (or have an erratic behavior).
>> According to Petsc FAQ, this is due to a preconditioner that is singular or
>> close to singular. What can I do in this case? I used GMRES with ILU
>> preconditioner.
>>                                               ^^^^^^^^^^^^^^^
>> >
>> > Incidentally, I tried to solve a smaller system with a direct solver
>> (superlu_dist) and it ran, so the system apparently is not singular.
>>
>>     ILU can produce very badly conditioned (one could say singular
>> PRECONDITIONER) from not singular sparse matrices. So it doesn't have
>> anything to do with the system itself being singular.
>>
>>    What type of problem are you solving? Different problems need
>> different preconditioners.
>>
>>   Barry
>>
>>
>>
>> >
>> > Thanks in advance,
>> > Eduardo
>>
>>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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