Analytical and numerical investigation of the performance of the BGT2 condition for low-frequency acoustic scattering problems

A mathematical and numerical analysis is performed to assess the performance of the second order Bayliss-Gunzburger-Turkel (BGT2) condition when applied to solving low-frequency acoustic scattering problems in the case of elongated scatterers. This investigation suggests that BGT2 retains an acceptable level of accuracy for relatively low wavenumber. A damping effect is incorporated to the BGT2 condition in order to extend the range of satisfactory performance. This damping procedure consists in adding only a constant imaginary part to the wavenumber. The numerical results indicate that the modified version of BGT2 extends the range of satisfactory performance by improving the level of accuracy by up to two orders of magnitude. Guidelines on the appropriate choice of the damping coefficient are provided.