[petsc-users] Strategies for coupled nonlinear problems

[Mark Adams]

Hi Miguel,

PCFIELDSPLIT is indeed what you want. There may be some PETSc examples that
could help guide algorithm selection, but I would just start by getting the
PCFIELDSPLIT infrastructure in place and running with the default solver,
which is simple block Gauss-Seidel iteration on the two block system
And you want to look in your field to see what other people have done with
systems like yours and then see about how to construct them in PCFIELDSPLIT.

Thanks,
Mark

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.
>
> Best,
> Miguel
>
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