  A systematic numerical study of non-pairwise vortex interaction forces in the
Ginzburg-Landau model for single- and multicomponent superconductivity is
presented. The interactions are obtained by highly accurate numerical free
energy minimization. In particular a three-body interaction is defined as the
difference between the total interaction and sum of pairwise interactions in a
system of three vortices and such interactions are studied for single and
two-component type-1, type-2, and type-1.5 superconductors. In the investigated
regimes, the three-body interaction is found to be short-range repulsive but
long-range attractive in the type-1 case, zero in the critical {\kappa}
(Bogomoln'y) case, attractive in the type-2 case and repulsive in the type-1.5
case. Some systems of four vortices are also studied and results indicate that
four-body forces are of substantially less significance than the three-body
interactions.
