[petsc-users] Strategies for coupled nonlinear problems

[Matthew Knepley]

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!cqtcQdi0PKTs4S7KpYIdusFz-Sr1TBcqFksEpoLFWkYiP_DAZlbbQdGCNTEQxScvJW1Tm0fsMaqh1YxTAA-_$ 

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!cqtcQdi0PKTs4S7KpYIdusFz-Sr1TBcqFksEpoLFWkYiP_DAZlbbQdGCNTEQxScvJW1Tm0fsMaqh1RE4uZs7$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!cqtcQdi0PKTs4S7KpYIdusFz-Sr1TBcqFksEpoLFWkYiP_DAZlbbQdGCNTEQxScvJW1Tm0fsMaqh1beuGI7M$ >
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