Hardy space infinite elements for Helmholtz-type problems with unbounded inhomogeneities

TL;DR

This paper presents Hardy space infinite elements as an effective method for solving Helmholtz problems with unbounded inhomogeneities, demonstrating exponential error decay and comparing favorably to PML methods.

Contribution

The paper introduces two variants of Hardy space infinite elements for Helmholtz problems with unbounded inhomogeneities, expanding the toolkit for wave scattering simulations.

Findings

Error decays exponentially with Hardy space modes

Method handles waveguide-type inhomogeneities

Comparison shows advantages over PML

Abstract

This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed description of two variants of the Hardy space infinite element method which relays on the pole condition is given. The method can treat waveguide-type inhomogeneities in the domain with non-compact support. The results of the Hardy space infinite element method are compared to a perfectly matched layer method. Numerical experiments indicate that the approximation error of the Hardy space decays exponentially in the number of Hardy space modes.