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

Abstract

The Green’s function of the half-plane Helmholtz equation with impedance boundary conditions is computed numerically. A compactly perturbed half-plane Helmholtz problem is presented to motivate this calculation, which is treated through integral equation techniques, leading to a boundary element discretization. The Green’s function is computed using an inverse Fourier transform, applying an inverse FFT for the regular part, and removing the singularities
analytically.