Different results of area of a deformed mesh in parallel

[chenyongxin]

I see. I thought the >1 result is because I added the contribution of the ghost cells for serveral times in parallel. The real problem in my code is the wrong mapping between mesh and function. So I replace with the following part and I can get 1 now with DOLFINx 0.6.0:

@dokken

for d in range(ndims):
    V_sub, sub_to_parent = u_square.sub(d).function_space.collapse()
    sub_to_parent = np.asarray(sub_to_parent)
    sub_to_parent = sub_to_parent // ndims
    mesh_square.geometry.x[sub_to_parent, d] += u_square.sub(
        d).collapse().x.array * dt

Some follow-up questions:
(1) VTXWriter vs XDMFFile. Why XDMFFile still gives correct visualization even though the mapping is actually not correct in parallel but VTXWriter can dectect that?
(2) The result of area 1 with mpirun -n 1 or mpirun -n 2 in my original code is evaluated coincidentally？The wrong mapping should be independent of number of processes.
(3) I see that you use sub_to_parent = sub_to_parent // ndims is because I used a (Vector) Function whose DOFs are ordered. What if I use a MixedElement and FunctionSpace instead of VectorFunctionSpace here? The dofs are most usually ordered for a mixed element.