Computing numerically the Green’s function of the half-plane Helmholtz operator with impedance boundary conditions

Authors:
Mario Durán;Ricardo Hein;Jean-Claude Nédélec
Affiliations:
Pontificia Universidad Católica de Chile, Facultad de Ingeniería, Av. Vicuña Mackenna, 4860, Macul, Santiago, Chile;Pontificia Universidad Católica de Chile, Facultad de Ingeniería, Av. Vicuña Mackenna, 4860, Macul, Santiago, Chile;CMAP, École Polytechnique, Av. Vicuña Mackenna, 91128, Palaiseau, Santiago, France
Venue:
Numerische Mathematik
Year:
2007

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Abstract

In this article we compute numerically the Green’s function of the half-plane Helmholtz operator with impedance boundary conditions. A compactly perturbed half-plane Helmholtz problem is used to motivate this calculation, by treating it through integral equation techniques. These require the knowledge of the calculated Green’s function, and lead to a boundary element discretization. The Green’s function is computed using the inverse Fourier operator of its spectral transform, applying an inverse FFT for the regular part, and removing the singularities analytically. Finally, some numerical results for the Green’s function and for a benchmark resonance problem are shown.