Define measure on a marked subdomain in dolfinx incorrectly

mesh
1

I sort of just mimic two sections from the tutorial “defining subdomains” and “setting multiple boundary conditions”.

First, I defined two subdomains, two disks in a square in 2D. Then marked them. Then defined measures.

def cell1_subdomain(x):
    return (x[0]-c1_x)**2 + (x[1]-c1_y)**2 <= r1**2 

def cell2_subdomain(x):
    return (x[0]-c2_x)**2 + (x[1]-c2_y)**2 <= r2**2 

subdomain_locator = [(1, cell1_subdomain),
              (2, cell2_subdomain)]

facet_indices2, facet_markers2 = [], []
for (marker, locator) in subdomain_locator:
    facets = mesh.locate_entities(domain_p, gdim, locator)
    facet_indices2.append(facets)
    facet_markers2.append(np.full_like(facets, marker))
facet_indices2 = np.hstack(facet_indices2).astype(np.int32)
facet_markers2 = np.hstack(facet_markers2).astype(np.int32)
sorted_facets2 = np.argsort(facet_indices2)
facet_tag2 = mesh.meshtags(domain_spatial_exclusion, gdim, facet_indices2[sorted_facets2], facet_markers2[sorted_facets2])

dx_p = Measure("dx", domain=domain_p, subdomain_data=facet_tag2)

But when I tried to compute area by assemble_scale of form(1 * dx_p(1)) it seems much smaller than the actual area of the circle. It seems I did not mark all the cells in the circle? How to solve this?

2

Please read Read before posting: How do I get my question answered?

Without an actual (minimal!) code we can run, we can only guess. The only guess I can make is that you are not getting a result of \pi (r_1)^2 and \pi (r_2)^2, because your mesh is (likely) formed by triangular or rectangular cells that will never have a curved edge able to perfectly identify an arc of the circle.