  In this paper, we consider a sorting scheme for potentially spurious
scattering resonant pairs in one- and two-dimensional electromagnetic problems
and in three-dimensional acoustic problems. The novel sorting scheme is based
on a Lippmann-Schwinger type of volume integral equation and can, therefore, be
applied to structures with graded materials as well as to configurations
including piece-wise constant material properties. For TM/TE polarized
electromagnetic waves and for acoustic waves, we compute first approximations
of scattering resonances with finite elements. Then, we apply the novel sorting
scheme to the computed eigenpairs and use it to mark potentially spurious
solutions in electromagnetic and acoustic scattering resonances computations at
a low computational cost. Several test cases with Drude-Lorentz dielectric
resonators as well as with graded material properties are considered.
