  We use the time-harmonic Maxwell partial differential equations (PDEs) to
model the wave propagation in 3-D space, which comprises a closed penetrable
scatterer and its unbounded free-space complement. Surface integral equations
(SIEs) that are equivalent to the time-harmonic Maxwell PDEs provide an
efficient framework to directly model the surface electromagnetic fields and
hence the RCS.The equivalent SIE system on the interface has the advantages
that: (a) it avoids truncation of the unbounded region and the solution exactly
satisfies the radiation condition; and (b) the surface-fields solution yields
the unknowns in the Maxwell PDEs through surface potential representations of
the interior and exterior fields. The Maxwell PDE system has been proven
(several decades ago) to be stable for all frequencies, that is, (i) it does
not possess eigenfrequencies (it is well-posed); and (ii) it does not suffer
from low-frequency. However, weakly-singular SIE reformulations of the PDE
satisfying these two properties, subject to a stabilization constraint, were
derived and mathematically proven only about a decade ago (see {J. Math. Anal.
Appl. 412 (2014) 277-300}). The aim of this article is two-fold: (I) To effect
a robust coupling of the stabilization constraint to the weakly singular SIE
and use mathematical analysis to establish that the resulting continuous
weakly-singular second-kind self-adjoint SIE system (without constraints)
retains all-frequency stability; and (II) To apply a fully-discrete spectral
algorithm for the all-frequency-stable weakly-singular second-kind SIE, and
prove spectral accuracy of the algorithm. We numerically demonstrate the
high-order accuracy of the algorithm using several dielectric and absorbing
benchmark scatterers with curved surfaces.
