Coupling modes in high-frequency multiple scattering problems: the case of two circles

One can reformulate a high-frequency scattering problem as a boundary integral equation. In the presence of multiple scattering obstacles, the wave pattern becomes very complicated, but wavenumber-independent simulation schemes have been proposed based on ray tracing. In such schemes, one can note that the phases of the corresponding densities on each of the obstacles converges to an equilibrium after a few iterations. For the case of two circular scatterers, we will compute a Taylor approximation of this limiting phase, independently of the incident wave and with a computational complexity independent of the wavenumber.