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M. Wess, L. Nannen:
"Exact complex scalings based on Hardy space infinite elements";
Talk: Conference on Mathematics of Wave Phenomena, Karlsruhe; 2018-07-23 - 2018-07-27; in: "Conference on Mathematics of Wave Phenomena", T. Arens (ed.); (2018), 92 - 93.

Helmholtz scattering and resonance problems in open domains can be treated using the
Hardy space infinite element method. This method is based on the pole condition which
characterizes outgoing waves by the poles of their Laplace transforms. Outgoing solutions are
approximated in the Laplace domain.
We present an interpretation of Hardy space infinite elements as a truncation-free complex
scaling method in space. The discretization matrices can be computed numerically using suit-
able Gauss-Laguerre quadrature rules. This allows us to deal with non-homogeneous exterior
domains.
Similarly to the application of perfectly matched layers in [1] we employ our method to
discretize complex scaled Helmholtz resonance problems with frequency dependent scaling
functions. The frequency dependency of the scaling function optimizes the complex scaling
for all frequencies and reduces the dependency of the approximation on the specific choice of
scaling parameter.