[Zurück]

L. Nannen:
"Hardy space infinite elements for time-harmonic wave equations";
Fakultät für Mathematik und Geoinformation, 2016.

The propagation of acoustic, electromagnetic or elastic waves is often described by time-harmonic wave equations in unbounded domains. Since standard finite element methods are restricted to bounded domains, they cannot be used directly for a numerical simulation of such problems. One remedy is to combine finite element methods for a bounded subdomain with Hardy space infinite element methods for the remaining unbounded domain. The latter rely on a radiation condition,
which characterizes radiating waves by the location of the singularities of their Laplace transform.
This so called pole condition is very flexible and can be used even in the presence of backward
propagating waves. For example such phenomenon appear for time-harmonic elastic waves in
waveguides, when the sign of phase and group velocity differ. Moreover, the pole condition and therewith the Hardy space infinite elements are frequency independent. This is an advantage in
particular for resonance problems, where the resonance frequency is part of the sought unknowns.
Therefore, Hardy space infinite element methods are well suited for scattering as well as resonance problems in open systems. They lead to stable discretizations and converge at least super-algebraically with respect to the number of unknowns in the direction of propagation. Various numerical examples show the applicability of the method for numerical simulations of wave propagation problems.
1

Wellengleichung ; Randbedingung ; Mathematik ; Finite-Elemente-Methode ; Hardy-Raum