Solve equation in only one phase of a two-phase problem

[dokken]

@chenyongxin

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.

You don’t need to project anything. You can leave u in the variational form, and it will behave as any function defined in a standard variational form.

@chenyongxin

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?

Various fixes related to submeshes, as well as a slight api change happened from 0.8 to 0.9

@chenyongxin

(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?

You can pass in compiled forms to LinearProblem.

@chenyongxin

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?

Then you should interpolate any displacement in the parent mesh onto the submesh and move the mesh afterwards