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

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 relies 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.

Research Highlights
► Hardy space infinite elements work for inhomogeneous exterior resonance problems.
► Corner treatment for convex polygons can be avoided.
► Hardy space infinite elements show super-algebraic convergence.