I had a go with the matched section Integration with function from parent and sub-mesh in the tutorial and the result looks correct with my case. Please correct me if I am wrong with the following idea:
u is defined on the parent mesh, while omega function, trail function and test function are defined on the submesh. It needs extra entity_maps info to explicitly formulate and assemble to A and b. Then solve projection on the submesh to get omega.
Several follow-up questions:
(1) I noticed entity_map argument of fem.form also exists in v0.8.0 with the same description, but I failed to call a_solid, L_solid = dolfinx.fem.form(ufl.system(F), entity_maps=entity_maps) as that in v0.9.0. Is it a v0.9.0-only related feature?
(2) With the use of entity_maps of fem.form, the Ax=b problem can only be solved explicitly rather than to use LinearProblem wrapper?
(3) My practical application is FSI + ALE, so the mesh moves in every step. If with a submesh, any idea to associate the movement of a submesh to the parent mesh?