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Hardy space infinite elements for time harmonic wave equations with phase and group velocities of different signs. (English) Zbl 1341.78024

This paper introduces a method for solving scattering problems with solutions consisting of modes with phase velocities of different signs. The abstract setting corresponds to time harmonic wave equations in cylindrical wave-guides. The method is strongly based on a Laplace transform in propagation direction. The study is developed in a Hardy space, which is constructed such that it contains a simple and convenient Riesz basis with small condition numbers. When solving resonance problems for which the frequency is the unknown resonance, the method introduced in the present paper leads to a linear matrix eigenvalue problem. Numerical simulations illustrate the exponential convergence of the Hardy space infinite element as well as approaches in the case of three different frequencies for which there are two propagating modes with different signs of the phase velocities.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J50 Variational methods for elliptic systems
30H10 Hardy spaces
78A50 Antennas, waveguides in optics and electromagnetic theory
78A40 Waves and radiation in optics and electromagnetic theory
78A45 Diffraction, scattering
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
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