This letter proposes the application of a hybrid numerical technique to two cases of interest in the space business: the reallocation of radiators and scatters on satellite platforms; and the analysis of antennas for mobile communications. It is based on the analytical manipulation of the generalized scattering matrix obtained from the finite-element method, when concave and convex spherical surfaces are defined as ports. The technique combines: the power of full-wave resolution, the flexibility and speed of the direct domain decomposition techniques and the application of analytical rotations and translations from the addition theorems for spherical vector waves, while keeping the same accuracy as a complete full-wave method since no model simplifications are considered.