  This paper is concerned with efficient representations and approximations of
the solution to the scattering problem by a system of strongly coupled
plasmonic particles. Three schemes are developed: the first is the resonant
expansion which uses the resonant modes of the system of particles computed by
a conformal transformation, the second is the hybridized resonant expansion
which uses linear combinations of the resonant modes for each of the particles
in the system as a basis to represent the solution, and the last one is the
multipole expansion with respect to the origin. By considering a system formed
by two plasmonic particles of circular shape, we demonstrate the relations
between these expansion schemes and their advantages and disadvantages both
analytically and numerically. In particular, we emphasize the efficiency of the
resonant expansion scheme in approximating the near field of the system of
particles. The difference between these plasmonic particle systems and the
nonresonant dielectric particle system is also highlighted. The paper provides
a guidance on the challenges for numerical simulations of strongly coupled
plasmonic systems.
