Antenna problems have additional output data that describe the far-field radiation pattern. The far-fields are computed using a near-field to far-field transformation (NFFF), which uses the fields on open boundary surfaces on the exterior of the simulation domain to compute the fields on the far field sphere. The far fields sphere is a large spherical surface defined for the purposes of this calculation. The radius of the far field sphere is large enough that all fields on the sphere can be considered safely in the far field, or Fraunhofer region. The far-fields are computed in terms of the normalized electric and magnetic vector potentials, which are given by
Here, r is the position vector of a point on the far field sphere, r' is a point on the simulation domain boundary, Sr' is the portion of the simulation domain that has open boundary conditions applied to it, and is the unit vector normal to the surface. Thus, for each point r on the far field sphere, you calculate A(r) and F(r) by integrating over the entire radiating surface.
The far field electric and magnetic fields can be written in terms of the vector potentials according to
where η0 is the free-space impedance.