Two scale Hardy space infinite elements for scalar waveguide problems
- 191 Downloads
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.
KeywordsWaveguide Cut-off frequency Wood’s anomaly Pole condition Hardy space infinite element method
Mathematics Subject Classification (2010)65H17 65N12 65N30 78M10
Open access funding provided by Austrian Science Fund (FWF). The first author acknowledges support from the Austrian Science Fund (FWF) grant W1245-N25.
- 8.Ciarlet, P.G.: Studies in Mathematics and its Applications, Vol. 4: The finite element method for elliptic problems. North-Holland Publishing Co., Amsterdam (1978)Google Scholar
- 11.Gohberg, I., Leiterer, J.: Methods from complex analysis in several variables: Holomorphic Operator Functions of One Variable and Applications, Volume 192 of Operator Theory Advances and Applications. Birkhäuser Verlag, Basel (2009)Google Scholar
- 13.Halla, M.: Regular Galerkin Approximation of Holomorphic T-Garding Operator Eigenvalue Problems. Report 04/2016, Institute for Analysis and Scientific Computing, TU Wien (2016)Google Scholar
- 23.Nannen, L.: Software module ngs-waves. http://sourceforge.net/projects/ngs-waves/. addon to the mesh generator Netgen and the high order finite element code NGSolve (2014)
- 29.Schöberl, J.: C++11 implementation of finite elements in ngsolve. Preprint 30/2014, Institute for Analysis and Scientific Computing, TU Wien (2014)Google Scholar
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.