  We introduce the longitudinal and transverse static surface modes and use
them to solve the full-wave electromagnetic scattering problem from penetrable
objects. The longitudinal static modes are the eigenmodes with zero surface
curl of the electrostatic integral operator that gives the tangential component
of the electric field, as a function of the surface charge density. The
transverse static modes are the eigenmodes with zero surface divergence of the
magnetostatic integral operator that returns the tangential component of the
vector potential, as a function of the surface current distribution. The static
modes only depend on the shape of the object, thus, the same static basis can
be used regardless of the frequency of operation and of the material
constituting the object. We expand the unknown surface currents of the
Poggio-Miller-Chang-Harrington-Wu-Tsai surface integral equations in terms of
the static surface modes and solve them using the Galerkin-projection scheme.
The static modes expansion allows the regularization of the singular integral
operators and yields a drastic reduction of the number of unknowns compared to
a discretization based on sub-domain basis functions. The introduced expansion
significantly reduces the cpu-time required for the numerical solution of the
scattering problem from particle arrays.
