# Continuity of potential at subdomain interface

Hi,

I want to solve for the potential outside a metallic cylinder (circle since it is 2D) kept at fixed potential (dirichlet bc). Just to learn how to use subdomains, I surround the said cylinder with a “dummy” cylinder with larger radius. Since I do not change the permittivity anywhere, the presence of this dummy cylinder should not change the physics. However, I get a result in which the potential becomes discontinuous across the dummy cylinder: Notice the change in color (yellow to blue) across the dummy interface. I suspect I am not getting the mesh right but I am really now sure how. If it helps, I am only trying to adapt the following tutorial example:

https://jorgensd.github.io/dolfinx-tutorial/chapter3/subdomains.html

The mesh is being generated as follows:

r1, r2, fov_r = 5, 10, 20
def generate_annulus_mesh(r1, r2, fov_r, output_file_name):
‘’‘Generates a mesh of annulus’’’
gmsh.initialize()
gdim = 2

``````inner_disk = gmsh.model.occ.addDisk(0, 0, 0, r1, r1)
outer_disk = gmsh.model.occ.addDisk(0, 0, 0, r2, r2)

# let us now cut the two geometries to have an annulus
# for some reason there is touple repetition. The first index of the touple represents dimension while the
# the second one is object number that we want
annulus_capacitor = gmsh.model.occ.cut([(gdim, outer_disk)],
[(gdim, inner_disk)])
gmsh.model.occ.synchronize()

# now create the area for air as well
fov_r_disk = gmsh.model.occ.addDisk(0, 0, 0, fov_r, fov_r)
# gmsh.model.occ.synchronize()
outer_disk2 = gmsh.model.occ.addDisk(0, 0, 0, r2, r2)

annulus_air = gmsh.model.occ.cut([(gdim, fov_r_disk)],
[(gdim, outer_disk2)])
gmsh.model.occ.synchronize()

complete_geom = gmsh.model.occ.fragment([annulus_air], [annulus_capacitor])

# complete_geometry = gmsh.model.occ.removeAllDuplicates()
# let us ignore the niceties and jump to generate the mesh directly

# get all the entities present in 2d
geom_surfaces = gmsh.model.getEntities(dim=gdim)

# add both surfaces to separate physical group
for j, surface in enumerate(geom_surfaces):
gmsh.model.addPhysicalGroup(surface, [surface], j)  # create the main group/node

# # # let us create the mesh
gmsh.option.setNumber("Mesh.CharacteristicLengthMin", 0.1)
gmsh.option.setNumber("Mesh.CharacteristicLengthMax", 0.5)
gmsh.model.mesh.generate(gdim)

gmsh.write('output/'+output_file_name+'.msh')
gmsh.finalize()
``````

I will sincerely appreciate help on this. If the mesh is all good, please let me know and I will share any necessary segment of the code.

Thanks a lot!

Folks, I somehow found out what was missing! I needed

``````gmsh.model.occ.synchronize()
``````

after the last fragment operation.

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