Hardy space infinite elements for Helmholtz-type problems with unbounded inhomogeneities
Provides a novel numerical method for solving resonance and scattering problems with unbounded inhomogeneities, offering exponential convergence for computational domains that are polygons.
The paper introduces Hardy space infinite elements for Helmholtz-type problems on unbounded domains with waveguide-type inhomogeneities, achieving exponential error decay in the number of modes compared to perfectly matched layer methods.
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.