Gmsh, boundaries, Output,

[dokken]

This is because you need to use Boolean Fragments in your geo file. Currently, the box and the torus is meshed has individual meshes.
In the reply

Mesh, Submesh , Torus, Boundary

Hi @Noya, You may want to try creating your mesh using an external meshing tool, e.g. Gmsh. The advantage of this approach is that you can mark the subdomains and boundaries using Gmsh, save the markers to files, and load them into FEniCS MeshFunctions, which can be used to define integration measures and boundary conditions. Using your current code (i.e. with BoxMesh), you obtain a mesh that doesn’t respect the internal boundary of the torus, i.e. you will have elements that pass through the t…

This is done with the command:

@conpierce8

gmsh.model.occ.fragment([(3,3)], [(3,1),(3,2)])

I’ve also shown how to use it with the geo files in: Transitioning from mesh.xml to mesh.xdmf, from dolfin-convert to meshio - #62 by dokken

You can realize this mistake by looking at your output. You get the volume 8 by integrating dx(2) which is the whole box.