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In this paper, we consider a sorting scheme for potentially spuriousscattering resonant pairs in one- and two-dimensional electromagnetic problemsand in three-dimensional acoustic problems. The novel sorting scheme is basedon a Lippmann-Schwinger type of volume integral equation and can, therefore, beapplied to structures with graded materials as well as to configurationsincluding piece-wise constant material properties. For TM/TE polarizedelectromagnetic waves and for acoustic waves, we compute first approximationsof scattering resonances with finite elements. Then, we apply the novel sortingscheme to the computed eigenpairs and use it to mark potentially spurioussolutions in electromagnetic and acoustic scattering resonances computations ata low computational cost. Several test cases with Drude-Lorentz dielectricresonators as well as with graded material properties are considered.

On spurious solutions encountered in Helmholtz scattering resonance computations in R^d with applications to nano-photonics and acoustics