Why? calculation of integrals using tags from gmsh file fails in a subdomain

Question

Hello Fenics Users
So my problem is as follow :
I have a domain (let say a square) and two sub domains (spheres) inside,
I need to calculate the integrals overs theses sub-domains as well as on the boundaries.
I used to generate the mesh file .msh the software 'gmsh', an to convert it to xml files I use the commande line dolfin-convert square.msh square.xml

the numbers appearing in the image are physical tags
and here is the part where their assignment in the .geo file is done
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
Physical Surface(1) = {1};
Physical Surface(2) = {2};
Physical Surface(3) = {3};

// Mark physical entities
Physical Line(1) = {4};
Physical Line(2) = {3};
Physical Line(3) = {2};
Physical Line(4) = {1};
Physical Line(5) = {15, 13, 12, 16};
Physical Line(6) = {21, 17, 18, 20};
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
now I define the mesh and what's coming with

mesh = Mesh("%s.xml" %(meshfilename))
# define boundary conditions, measure, and outward normals to cells 
boundaries=MeshFunction("size_t",mesh,"%s_facet_region.xml" %(meshfilename))
ds = Measure("ds")[boundaries]  
outnormal = FacetNormal(mesh) # outward normals to cells 

when I do integrals calculations only these tests worked
f=interpolate(Expression('x[0]*x[0]'),V)

assemble(f*ds(1)) 
assemble(f*ds(2)) 
assemble(f*ds(3))
assemble(f*ds(4))

but these in the interior circles give zero ???

assemble(f*ds(5)) 
assemble(f*ds(6)) 
assemble(f*dx(1))
assemble(f*dx(2))
assemble(f*dx(3))

any help would be appreciated, thank you in advance

Answer 1

Hi,
did you try to use the measure dS to integrate over internal facets? (see the measure.py file as reference).

Comments

Hi,
I tried it like this and it worked

ds_int = Measure("dS")[boundaries]

this line enabled me to integrate over internal facets like this

assemble(f*dS(5))
assemble(f*dS(6))

For external facets I still can use

ds = Measure("ds")[boundaries]

until now half of the problem is solved, the rest now is about sub domains, how can I manipulate them, in other words how to :
- define local Finite Element spaces

- assemble local matrices

- define measures

- do integrations over these sub domains.

Could you please just point me into the right direction again?

---

I think I found an answer for the last questions, obviously I had to use the generated xml file containing physical_region

then we can define measure in the interior domains this way

subdomains = MeshFunction("size_t", mesh,"%s_physical_region.xml" %(meshfilename))
boundaries = MeshFunction("size_t",mesh,"%s_facet_region.xml" %(meshfilename))

ds = Measure("ds")[boundaries]  
outnormal = FacetNormal(mesh) # outward normals to cells
ds_int = Measure("dS")[boundaries]
dx_int = Measure("dx")[subdomains]