05201239

j

05201239 Dur\'an, Mario Hein, Ricardo N\'ed\'elec, Jean-Claude Computing numerically the Green's function of the half-plane Helmholtz operator with impedance boundary conditions. Numer. Math. 107, No. 2, 295-314 (2007). 2007 Springer-Verlag, Berlin EN Helmholtz equation Green's function boundary element numerical results fast Fourier transform

doi:10.1007/s00211-007-0087-9

Summary: We compute numerically 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. Green's function is computed using the inverse Fourier operator of its spectral transform, applying an inverse fast Fourier transform for the regular part, and removing the singularities analytically. Finally, some numerical results for Green's function and for a benchmark resonance problem are shown.