  In this article, we present a $T$-matrix method for numerical computation of
second-harmonic generation from clusters of arbitrarily distributed spherical
particles made of centrosymmetric optical materials. The electromagnetic fields
at the fundamental and second-harmonic (SH) frequencies are expanded in series
of vector spherical wave functions, and the single sphere $T$-matrix entries
are computed by imposing field boundary conditions at the surface of the
particles. Different from previous approaches, we compute the SH fields by
taking into account both local surface and nonlocal bulk polarization sources,
which allows one to accurately describe the generation of SH in arbitrary
clusters of spherical particles. Our numerical method can be used to
efficiently analyze clusters of spherical particles made of various optical
materials, including metallic, dielectric, semiconductor, and polaritonic
materials.
