I am looking for an example with 2 overlapping meshes. One mesh should be subtracted to the other one in a ``hole cutting’’ operation. Then I am interested in the case where the resulting subdomains have some or no overlap and the problem is solved with transmission conditions at the interface.

See for instance: https://www.sciencedirect.com/science/article/abs/pii/S0045782518304523

and in general MultiMesh or CutFEM papers.

Thank you for your answer @dokken . I found an example you made a few years ago in Fenics:

I saw that there were dedicated functions for multimesh assembly. Two questions if you don’t mind:

- I believe in current dolfinx I can do the hole cutting using projections together with
`multiphenicsx`

, and then I will be able to do staggered solves on each mesh. Do you think this is feasible? - Do you think there would be a way to monolithically assemble forms from multiple meshes onto one linear system in current Fenicsx?

As far as I am aware, multiphenicsx works under the assumption of dofmap restrictions on a single conforming mesh (@francesco-ballarin can correct me if Im wrong). So I don’t see how that would work.

If you use PETSc.Nest, it might be possible to do, but I don’t see a super-simple way of doing it (it would probably boil down to interpolating data from one mesh to the other with quadrature spaces and then generate the matrices for the coupled system).

I can confirm that multiphenicsx works with subdomains on a single conforming meshes.

What is meant by conforming? No hanging nodes?

Say you have two subdomains \Omega_1 and \Omega_2, and call \Gamma their interface. It means that the mesh on \Omega_1 and \Omega_2 cannot be completely unrelated, because they are expected to match on \Gamma.