During the last decade, several authors have addressed that the Perfectly Matched Layers (PML) technique can be used not only for the computation of the near-field in time-dependent and time-harmonic scattering problems, but also to compute numerically the resonances in open cavities. Despite such complex resonances are not natural eigen-frequencies of the physical system, the numerical determination of this kind of eigenvalues provides information about the model, what can be used in further applications. The present work will be focused on two main specific goals—firstly, the mathematical analysis of the frequency-dependent highly non-linear eigenvalue problem associated to the computation of resonances with the standard PML technique. Second, the implementation of a robust numerical method to approximate resonances in open cavities.
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