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.

在本文中，我们考虑了一维和二维电磁问题以及三维声学问题中潜在寄生散射共振对的分类方案。新颖的排序方案基于Lippmann-Schwinger类型的体积积分方程，因此可以应用于具有渐变材质的结构以及包括分段恒定材质特性的配置。对于TM / TE极化电磁波和声波，我们用有限元计算散射共振的第一近似值。然后，我们将新颖的排序方案应用于计算出的特征对，并以较低的计算成本将其用于标记电磁和声散射共振计算中的潜在杂散解。