Exterior facet integral over part and whole of facet gives surprising result

[wence-]

Consider the following

from firedrake import *
m = UnitSquareMesh(1, 1)

print assemble(Constant(1, cell=m.ufl_cell())*(ds(1) + ds)))

I expect to see 5, but I get 6. As if the ds term is also being included in the ds(1) integral.

I note in dolfin this is sort of unsupported, in that if I have produced a marked subdomain then I can't use a bare ds but must always select a subdomain to integral over. So maybe this is unsupported and expected.

[wence-]

Scrap that dolfin comment, if I want the whole exterior facet I do ds(). And in that case I get the expected 5 (for dolfin, not us).

[miklos1]

In ufl/algorithms/domain_analysis.py, in function build_integral_data:

            # Group integrals by subdomain id, after splitting e.g.
            #   f*dx((1,2)) + g*dx((2,3)) -> f*dx(1) + (f+g)*dx(2) + g*dx(3)
            # (note: before this call, 'everywhere' is a valid subdomain_id,
            # and after this call, 'otherwise' is a valid subdomain_id)
            single_subdomain_integrals = \
                rearrange_integrals_by_single_subdomains(ddt_integrals)

In rearrange_integrals_by_single_subdomains:

    # Add everywhere integrals to each single subdomain id integral list
    otherwise_integrals = []
    for ev_itg in everywhere_integrals:
        # Restrict everywhere integral to 'otherwise'
        otherwise_integrals.append(
            ev_itg.reconstruct(subdomain_id="otherwise"))

        # Restrict everywhere integral to each subdomain
        # and append to each integral list
        for subdomain_id in sorted(single_subdomain_integrals.keys()):
            single_subdomain_integrals[subdomain_id].append(
                ev_itg.reconstruct(subdomain_id=subdomain_id))

    if otherwise_integrals:
        single_subdomain_integrals["otherwise"] = otherwise_integrals

I guess the cause of this bug is that we treat "everywhere" and "otherwise" the same way, while "otherwise" means everywhere outside the explicitly specified subdomains.

[wence-]

Having looked at this again, this is notabug, since UFL is merging the integrals correctly. f*ds + f*ds(1) is interpreted as f*ds(not 1) + f*ds(1) + f*ds(1).

[miklos1]

Well, the bug is that we're treating 'otherwise' as 'everywhere'.

[wence-]

Oh, I see, yes.