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Advances in Computational Mathematics

, Volume 44, Issue 3, pp 611–643 | Cite as

Two scale Hardy space infinite elements for scalar waveguide problems

  • Martin Halla
  • Lothar Nannen
Open Access
Article
  • 165 Downloads

Abstract

We consider the numerical solution of the Helmholtz equation in domains with one infinite cylindrical waveguide. Such problems exhibit wavenumbers on different scales in the vicinity of cut-off frequencies. This leads to performance issues for non-modal methods like the perfectly matched layer or the Hardy space infinite element method. To improve the latter, we propose a two scale Hardy space infinite element method which can be optimized for wavenumbers on two different scales. It is a tensor product Galerkin method and fits into existing analysis. Up to arbitrary small thresholds it converges exponentially with respect to the number of longitudinal unknowns in the waveguide. Numerical experiments support the theoretical error bounds.

Keywords

Waveguide Cut-off frequency Wood’s anomaly Pole condition Hardy space infinite element method 

Mathematics Subject Classification (2010)

65H17 65N12 65N30 78M10 

Notes

Acknowledgments

Open access funding provided by Austrian Science Fund (FWF). The first author acknowledges support from the Austrian Science Fund (FWF) grant W1245-N25.

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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institut für Analysis und Scientific ComputingTechnische Universität WienWienAustria

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