SNES composite example?

General
1

I have set up a monolithic system for a DD problem:

\begin{pmatrix} A_{11} & A_{12}\\ A_{21} & A_{22} \end{pmatrix} \begin{pmatrix} U_1\\ U_2 \end{pmatrix} = \begin{pmatrix} R_1\\ R_2 \end{pmatrix}

using Nested matrices and vectors from petsc4py. I can solve it directly/monolithically by setting up one SNES. I want to solve it iteratively / staggeredly. After reading some documentation I found out about SNES composite but could not find any clear example on how to use SNES composite, and in particular, nothing in petsc4py.

  1. Would you use SNES composite to set up a staggered solver?
  2. Do you have any examples of SNES composite or other staggered solvers?
2

I think what you would like to do is to use a fieldsplit (KSP: Linear System Solvers — PETSc 3.23.4 documentation) which there is an example of in: Stokes equations using Taylor-Hood elements — DOLFINx 0.10.0.0 documentation

and in: