Integrate field over surface

Question

I have a domain $\Omega$ and a surface $f(x,y,z)=0$

I have a field $F:\mathbb{R}^3\to\mathbb{R}^n$ where n can be 2 or 3

the question is how to calculate the next integral in dolfin-fenics:

$\int_S Fds$

Answer 1

I don't think you can handle these integrals directly using FEniCS.

Integrals over mesh-unfitted surfaces can be handled using dolfin-pum, ffc-pum in the framework of XFEM/PUM method. These libraries are now deprecated. I think there were preliminary plans to integrate similar functionality directly into FEniCS by Garth, but I don't know what is the state of this.

Comments

for example:
I have a solution $\psi(x,y,z)$ and this have a level surface $\psi(x,y,z) = 0$. then I want to calculate the elastic energy over the interface for a force field $F$. (this is only a example).

other function is to calculate the volume of the function psi = 0 when is a gaussian surface