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L. Nannen, M. Wess:
"Spurious modes of the complex scaled Helmholtz Equation";
in: "ASC Report 15/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 32.

In this paper we study resonance problems in unbounded domains using a radial complex scaling method (frequently called perfectly matched layer method). The main focus of attention is given to artifi-cial or spurious resonances arising from discretization. We analyze the dependency of these artificial resonances with respect to the discretiza-tion parameters and the scaling function. This includes a frequency dependent complex scaling leading to a cubic eigenvalue problems. We show that such scalings reduce the artificial resonances generated by the discretization of the complex scaled exterior domain. Hence, they simplify the choice of the corresponding exterior discretization param-eters.

http://www.asc.tuwien.ac.at/preprint/2016/asc15x2016.pdf