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

2010/04/07 by Lothar Nannen, Nannen, Lothar, Achim Schädle +1
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1004.1025

openalex publication_date 2010/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces a class of approximate transparent boundary conditions\nfor the solution of Helmholtz-type resonance and scattering problems on\nunbounded domains. The computational domain is assumed to be a polygon. A\ndetailed description of two variants of the Hardy space infinite element method\nwhich relays on the pole condition is given. The method can treat\nwaveguide-type inhomogeneities in the domain with non-compact support. The\nresults of the Hardy space infinite element method are compared to a perfectly\nmatched layer method. Numerical experiments indicate that the approximation\nerror of the Hardy space decays exponentially in the number of Hardy space\nmodes.\n

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