[petsc-users] Linear solver diverging

[bichinhoverde]

The reviewer said: "direct methods are useless for realistic problems".
​Unthinking prejudice?

Maybe I will just compare the performance of the non-compact iterative
version to the compact direct one and show that it is not that bad.

Thanks for the help.




On Wed, Apr 1, 2015 at 1:24 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Wed, Apr 1, 2015 at 11:07 AM, bichinhoverde <
> bichinhoverde at spwinternet.com.br> wrote:
>
>> The system I am trying to solve is a 2D Poisson equation, but split into
>> 5 1D equations. Something like this:
>>
>> p_xx + p_yy = f
>> p_xx - d(p_x)/dx = 0
>> p_yy - d(p_y)/dy = 0
>> p_x - d(p)/dx = 0
>> p_y - d(p)/dy = 0
>>
>> If I use standard finite differences, it works fine with gmres and
>> jacobi. But when I switch to compact finite differences, only the direct
>> solver works.
>>
>> It is on a staggered mesh, so p, p_xx and p_yy are on the cell center and
>> p_x and p_y are on the edges.
>>
>> I recently submitted a paper and the reviewer complained about the direct
>> linear solver. So I wanted to do a performance comparison.
>>
>
> I am not sure why the direct solver is a problem, other than
> ​​
> unthinking prejudice.
>
> If you want to use an iterative solver here, you will likely need to use
> PCFIELDSPLIT since you have saddle-point
> structure from the constraints (I think).
>
>   Thanks,
>
>     Matt
>
>
>> On Wed, Apr 1, 2015 at 12:58 PM, Matthew Knepley <knepley at gmail.com>
>> wrote:
>>
>>> On Wed, Apr 1, 2015 at 10:51 AM, bichinhoverde <
>>> bichinhoverde at spwinternet.com.br> wrote:
>>>
>>>> I have a linear system which I can easily solve using the Pardiso
>>>> library, which is a direct solver. But when I try Petsc, the solver does
>>>> not converge. It reduces the norm a little but then gets stuck.
>>>>
>>>> I tried several combinations of pc_type and ksp_type. It seems that
>>>> pc=jacobi is better, since my linear system does not have the diagonal
>>>> element in some rows.
>>>>
>>>> Is there some advice you can give me? Some way to analyse the matrix
>>>> and find out why it does not work?
>>>>
>>>
>>> Without knowing anything about the system, there is nothing you can say.
>>>
>>> Why do you want to change from using a direct solver?
>>>
>>> Have you looked in the literature for iterative solvers that work on
>>> this problem?
>>>
>>>   Thanks,
>>>
>>>     Matt
>>>
>>> --
>>> 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
>>>
>>
>>
>
>
> --
> 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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