  We propose here a novel stabilization strategy for the PMCHWT equation that
cures its frequency and conductivity related instabilities and is obtained by
leveraging quasi-Helmholtz projectors. The resulting formulation is
well-conditioned in the entire low-frequency regime, including the eddy current
one, and can be applied to arbitrarily penetrable materials, ranging from
dielectric to conductive ones. In addition, by choosing the rescaling
coefficients of the quasi-Helmholtz components appropriately, we prevent the
typical loss of accuracy occurring at low frequency in the presence of
inductive and capacitive type magnetic frill excitations, commonly used in
circuit modeling to impose a potential difference. Finally, leveraging on
quasi-Helmholtz projectors instead than on the standard Loop-Star
decomposition, our formulation is also compatible with most fast solvers and is
amenable to multiply connected geometries, without any computational overhead
for the search for the global loops of the structure. The efficacy of the
proposed preconditioning scheme when applied to both simply and multiply
connected geometries is corroborated by numerical examples.
