M. Halla, T. Hohage, L. Nannen, J. Schöberl:

"Hardy space infinite elements for time harmonic wave equations with phase and group velocities of different signs";

Numerische Mathematik,131(2015), 4; 1 - 37.

Abstract We consider time harmonic wave equations in cylindrical wave-guides with

physical solutions for which the signs of group and phase velocities differ. The perfectly

matched layer methods select modes with positive phase velocity, and hence they

yield stable, but unphysical solutions for such problems.We derive an infinite element

method for a physically correct discretization of such wave-guide problems which

is based on a Laplace transform in propagation direction. In the Laplace domain the

space of transformed solutions can be separated into a sum of a space of incoming

and a space of outgoing functions where both function spaces are Hardy spaces of

a curved domain. The Hardy space is constructed such that it contains a simple and

convenient Riesz basis with small condition numbers. In this paper the new method

is only discussed for a one-dimensional fourth order model problem. Exponential

http://dx.doi.org/10.1007/s00211-015-0739-0

http://publik.tuwien.ac.at/files/PubDat_246145.pdf

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