[petsc-users] Strategies for coupled nonlinear problems

[Miguel Angel Salazar de Troya]

Are there other alternative methods that might be easier to implement?

Miguel

On Mon, Jul 8, 2024 at 1:43 PM Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Jul 8, 2024 at 6:14 AM Miguel Angel Salazar de Troya <
> miguel.salazar at corintis.com> wrote:
>
>> Thanks Adam and Matt,
>>
>> Matt, can I get away with just using PCFIELDSPLIT? Or do I need the
>> SNESFIELDSPLIT? Though it looks like the block Gauss-Seidel is only
>> implemented in serial (
>> https://urldefense.us/v3/__https://petsc.org/main/manual/ksp/*block-jacobi-and-overlapping-additive-schwarz-preconditioners__;Iw!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NH3TTKGi$ 
>> )
>>
>
> You can do what you want for the linear problem, but that will probably
> not help. The best thing I know of for this kind of nonlinear coupling is
> now called primal-dual Newton, a name which I am not wild about. It is
> discussed here (https://urldefense.us/v3/__https://core.ac.uk/download/pdf/211337815.pdf__;!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NFSFi9w1$ ) and
> originated in reference [33] from that thesis. My aim was to allow these
> kinds of solvers with that branch.
>
>
>> On a more theoretical note, I have the impression that the convergence
>> failures of the Newton-Raphson method for this kind of problem is
>> ultimately due to a lack of a diagonally dominant Jacobian. I have not
>> found any reference so I might be wrong.
>>
>
> I would say that the dominant direction for momentum hides the direction
> for improvement of the coefficient.
>
>   Thanks,
>
>     Matt
>
>
>> Best,
>> Miguel
>>
>> On Sat, Jul 6, 2024 at 3:33 PM Matthew Knepley <knepley at gmail.com> wrote:
>>
>>> On Fri, Jul 5, 2024 at 3:29 AM Miguel Angel Salazar de Troya <
>>> miguel.salazar at corintis.com> wrote:
>>>
>>>> Hello, I have the Navier-Stokes equation coupled with a
>>>> convection-diffusion equation for the temperature. It is a two-way coupling
>>>> because the viscosity depends on the temperature. One way to solve this is
>>>> with some kind of fixed point iteration
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>>>> Hello,
>>>>
>>>> I have the Navier-Stokes equation coupled with a convection-diffusion
>>>> equation for the temperature. It is a two-way coupling because the
>>>> viscosity depends on the temperature. One way to solve this is with some
>>>> kind of fixed point iteration scheme, where I solve each equation
>>>> separately in a loop until I see convergence. I am aware this is not
>>>> possible directly at the SNES level. Is there something that one can do
>>>> using PCFIELDSPLIT? I would like to assemble my fully coupled system and
>>>> play with the solver options to get some kind of fixed-point iteration
>>>> scheme. I would like to avoid having to build two separate SNES solvers,
>>>> one per equation. Any reference on techniques to solve this type of coupled
>>>> system is welcome.
>>>>
>>>
>>> Hi Miguel,
>>>
>>> I have a branch
>>>
>>>
>>> https://urldefense.us/v3/__https://gitlab.com/petsc/petsc/-/tree/knepley/feature-snes-fieldsplit?ref_type=heads__;!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NA5DeA9R$ 
>>>
>>> that will allow you to do exactly what you want to do. However, there
>>> are caveats. In order to have SNES do this, it needs a way to selectively
>>> reassemble subproblems. I assume you are using Firedrake, so this will
>>> not work. I would definitely be willing to work with those guys to get
>>> this going, introducing callbacks, just as we did on the FieldSplit case.
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Best,
>>>> Miguel
>>>>
>>>
>>>
>>> --
>>> 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
>>>
>>> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NBJa7cKb$ 
>>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NMU5f6M8$ >
>>>
>>
>
> --
> 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
>
> https://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NBJa7cKb$ 
> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!bSoUE_2lViJzEHKf5CEFph-9dqm5ZtOB6QjWVEk4zIyGBukbkcoEGiVzHu84pF637kvsxFyFQoUPYjIUFM5eZZ51NMU5f6M8$ >
>
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