Two scale Hardy space infinite elements for scalar waveguide problems

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.

Complex scaled infinite elements for exterior Helmholtz problems

“…In its standard form, this pole condition is equivalent to the radiation condition underlying the complex scaling, which is equivalent to the radiation condition of Sec. 2.1 for certain domains of complex frequencies including positive frequencies (see [16] or more explicitly for waveguides in [14,11]).…”

Radial complex scaling for anisotropic scalar resonance problems

“…These drawbacks of CS/PML methods gave rise to the development of novel alternative methods such as the two-pole Hardy space infinite element method [22,21,23] and the halfspace matching method [10,9].…”