  A combined analytical and numerical study of the modes in two distinct
plasmonic nanowire systems is presented. The computations are based on a
Discontinuous Galerkin Time-Domain approach and a fully nonlinear and nonlocal
hydrodynamic Drude model for the metal is utilized. In the linear regime, these
computations demonstrate the strong influence of nonlocality on the field
distributions as well as on the scattering and absorption spectra. Based on
these results, second-harmonic generation efficiencies are computed over a
frequency range that covers all relevant modes of the linear spectra. In order
to interprete the physical mechanisms that lead to corresponding field
distributions, the associated linear quasi-electrostatic problem is solved
analytically via conformal transformation techniques. This provides an
intuitive classification of the linear excitations of the systems that is then
applied to the full Maxwell case. Based on this classification, group theory
facilitates the determination of the selection rules for the efficient
excitation of modes, both in the linear and the nonlinear regime. This leads to
significantly enhanced second-harmonic generation via judiciously exploiting
the system symmetries. These results regarding the mode structure and
second-harmonic generation are of direct relevance to other nano-antenna
systems.
