[petsc-users] Strategies for coupled nonlinear problems

[Matthew Knepley]

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!eLmDWSrulgDcLMhEC5MITvrmcOrDVcAOy95wwGeNzgl7fvAnsX_ldsB3qVD5ArIV-jCyIHEPt3Po_GnSYekO$ 
> )
>

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!eLmDWSrulgDcLMhEC5MITvrmcOrDVcAOy95wwGeNzgl7fvAnsX_ldsB3qVD5ArIV-jCyIHEPt3Po_DT_42uJ$ ) 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!eLmDWSrulgDcLMhEC5MITvrmcOrDVcAOy95wwGeNzgl7fvAnsX_ldsB3qVD5ArIV-jCyIHEPt3Po_ESUOIOo$ 
>>
>> 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!eLmDWSrulgDcLMhEC5MITvrmcOrDVcAOy95wwGeNzgl7fvAnsX_ldsB3qVD5ArIV-jCyIHEPt3Po_DKriL_s$ 
>> <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!eLmDWSrulgDcLMhEC5MITvrmcOrDVcAOy95wwGeNzgl7fvAnsX_ldsB3qVD5ArIV-jCyIHEPt3Po_Ne_UeR1$ >
>>
>

-- 
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!eLmDWSrulgDcLMhEC5MITvrmcOrDVcAOy95wwGeNzgl7fvAnsX_ldsB3qVD5ArIV-jCyIHEPt3Po_DKriL_s$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!eLmDWSrulgDcLMhEC5MITvrmcOrDVcAOy95wwGeNzgl7fvAnsX_ldsB3qVD5ArIV-jCyIHEPt3Po_Ne_UeR1$ >
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