  The problem of substructure characteristic modes is reformulated using a
scattering matrix-based formulation, generalizing subregion characteristic mode
decomposition to arbitrary computational tools. It is shown that the scattering
formulation is identical to the classical formulation based on the background
Green's function for lossless systems. The scattering formulation, however,
opens a variety of new subregion scenarios unavailable within previous
formulations, including cases with lumped or wave ports or subregions in
circuits. Thanks to its scattering nature, the formulation is solver-agnostic
with the possibility to utilize an arbitrary full-wave method.
